Measurements

MEASUREMENTS

For

ELECTRICAL ENGINEERING INSTRUMENTATION ENGINEERING

MEASUREMENTS

SYLLABUS Measurement concept, Classification of Measurement, Types of errors & Standard Measurement technics Analog Circuits, Measurement of Resistance, Inductance, Capacitance, Bridge Measurement, Concept of Cathode Ray Oscilloscope, CRO, Volt meter & Frequency measurement,

ANALYSIS OF GATE PAPERS

Electrical Engineering Instrumentation Engineering 1 Mark 2 Mark 1 Mark 2 Mark Exam Year Ques. Ques. Total Ques. Ques. Total 2003 3 8 19 5 4 13 2004 3 7 17 5 9 23 2005 3 5 13 3 7 17 2006 2 4 10 2 5 12 2007 1 1 3 3 4 11

2008 1 2 5 2 6 14

2009 2 2 6 3 3 9

2010 2 1 4 4 4 12 2011 3 1 5 - 3 6 2012 3 1 5 3 1 5 2013 2 1 4 - 2 4 2014 Set-1 2 2 6 1 1 3 2014 Set-2 2 2 6 2014 Set-3 2 2 6 2015 Set-1 2 1 4 2 2 6 2015 Set-2 3 7 17

2016 Set-1 0 0 0 4 3 10

2016 Set-2 1 2 5 2017 Set-1 2 2 6 2 4 10 2017 Set-2 2 1 4 2018 2 1 4 2 4 10

CONTENTS Topics Page No

1. CHARACTERISTIC, ERRORS & STANDARDS

1.1 Measurements 01 1.2 Classification of Instruments 01 1.3 Types of Errors 04 1.4 Standards 05 Gate Questions 07

2. ANALOG INSTRUMENTS

2.1 Introduction 09 2.2 Indication Instrument 09 2.3 Types of Supports 11 2.4 Damping Forces 12 2.5 Electromechanical Indicating Instruments 13 2.6 PMMC Instruments 13 2.7 DC Ammeters 14 2.8 Voltmeter Multipliers 15 2.9 Moving Iron Instruments 16 2.10 Classification of Moving Iron Instruments 17 2.11 Electrodynamometer Type 18 2.12 Measurement of Power and Energy 22 Gate Questions 29

3. MEASUREMENT OF RESISTANCE, INDUCTANCE & CAPACITANCE

3.1 Classification of Resistance 47 3.2 Different Method of Measurement 47 3.3 Types of Ohmmeter 47 3.4 Bridge Measurement 48 3.5 A.C Bridges 52 3.6 Measurement of Capacitance 55 3.7 Measurement of Frequency 56 Gate Questions 58

4. CATHOD RAY OSCILLOSCOPE

4.1 Capacitance Measurement 68 4.2 CRT 68 4.3 Expression of Electrostatic Deflection 69 4.4 Measurement Using CRO 69 4.5 Measurement of Frequency 71

4.6 Cathode Ray Oscilloscope 72 4.7 Vertical Input and Sweep Generator Signal 73 4.8 Blanking Circuit 74 Gate Questions 76 5. MISCELLANEOUS

5.1 Digital Voltmeters 85 5.2 Successive-Approximations Conversion 86 5.3 Digital Voltmeters 87 5.4 RAMP Technique 87 5.5 Dual Slope Integrating Type DVM 88 5.6 Successive Approximations 89 5.7 Resolutions and Sensitivity of Digital Meters 90 5.8 Block Diagram of SA DVM 90 Gate Questions 92

ASSIGNMENT QUESTIONS 95

1.1 MEASUREMENTS Summarizing, it may be stated that in general electronic instruments have The measurement of a given quantity is i) a higher sensitivity essentially an act or the result of ii) a faster response comparison between the quantity and a iii) a greater flexibility predefined standard. Since two quantities iv) lower weight are compared, the result is expressed in v) lower power consumption numerical values. vi) a higher degree of reliability than their mechanical or purely electrical 1.1.1 METHODS OF MEASUREMENTS. counterparts.

i) Direct Methods and 1.2 CLASSIFICATION OF INSTRUMENTS ii) Indirect Methods i) Absolute Instruments Direct Methods:- In these methods, the ii) Secondary Instruments. unknown quantity is directly compared against a standard. The result is expressed 1. Absolute Instruments. These as a numerical number and a unit Direct instruments give the magnitude of the methods are quite common for the quantity under measurement in terms measurement of physical quantities like of physical constants of the instrument. length, mass and time. The examples of this class of instruments are Tangent Galvanometer Indirect Methods:- Measurement by direct and Rayleigh’s Current Balance. methods are not always possible, feasible 2. Secondary Instruments. These and practicable. Then measurement is done instruments are so constructed that the by measuring Instruments. quantity being measured can only be measured by observing the output Instruments and Measurement indicated by the instrument. These Systems:- Measurements involve the use instruments are calibrated by of instruments as a physical means of comparison with an absolute instrument determining quantities or variables. or another secondary instrument which The earliest scientific instruments used the has already been calibrated against an same three essential elements as our absolute instrument. modern instruments do. These elements are: 1.2.1 DEFLECTION AND NULL TYPE i) a detector INSTRUMENTS. ii) an intermediate transfer device iii) an indicator, recorder or a storage Deflection Type:- The instruments of this device. type, the deflection of the instrument The history of development of instruments provides a basis for determining the encompasses three phases of instruments, quantity under measurement. The vis.: measured quantity produces some physical i) mechanical instruments effect with deflects or produces a ii) electrical instruments mechanical displacement of the moving iii) electronic instruments. system of the instrument.

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission NULL TYPE:- In a null type of instrument, a personnel handling the instrument or the zero or null indication leads to system for monitoring, control, or analysis determination of the magnitude of purposes. The information conveyed must measured quantity. The null condition is be in a form intelligible to the personnel or dependent upon some other known to the intelligent instrumentation system. conditions. Characteristics of Instruments and Measurement Systems Comparison of Deflection and Null Type (i) Static characteristics, and Instruments (ii) Dynamic characteristics.

i) Null type of instruments are more Static Characteristics. The main static accurate than deflection type characteristics discussed here are: instruments. i) Accuracy ii) Null type instruments can be highly ii) Sensitivity sensitive as compared with deflection iii) Reproducibility type instruments iv) Drift iii) Deflection type of instruments are more v) Static error suited for measurements under vi) Dead Zone dynamic conditions than null type of instruments whose intrinsic response is The qualities (i), (ii) and (iii) are desirable, slower. while qualities (iv), (v) and (vi) are undesirable. Applications of Measurement systems. Static Error: The most important i) Monitoring of processes and operations, characteristic of an instrument of ii) Control of processes and operations, and measurement system is its accuracy, the iii) Experimental Engineering analysis. accuracy of an instrument is measured in terms of its error. Elements of a Generalized Measurement Static error is defined as the difference System. between the measured value and the true 1. Primary sensing element, value of the quantity. Then: 2. Variable conversion element,  A = Am -At 3. Data presentation element. the ratio of absolute static error A to At, the true value of the quantity under Primary Sensing Element: A transducer is measurement. Therefore, the relative static defined as a device which converts a errorr, is given by: physical quantity into an electrical absoluteerror A 0 quantity. r= = = true value At At Variable Conversion Element: The At = Am (1- r) output of the primary sensing element may be electrical signal of any form. It may be Accuracy: It is the closeness with which an necessary to convert this output to some instrument reading approaches the true other suitable form while preserving the value of the quantity being measured. Thus information content of the original signal. accuracy of a measurement means conformity to truth. Data Presentation Element: The information about the quantity under Precision: It is a measure of the measurement has to be conveyed to the reproducibility of the measurements, the

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission term ‘Precise’ means clearly or sharply 1 Resolution = scale division =  2 defined. 10 A Wheatstone bridge requires a change of 7 =0.2 V  in the unknown arm of the bridge to produce a change in deflection of 3mm of Example A digital voltmeter has a read- the galvanometer. out range from 0 to 9,999 counts. magnitudeof output response Determine the resolution of the instrument Sensitivity= magnitudeof input in volt when the full scale reading is 9.999 V. 3mm Solution. The resolution of this instrument = = 0.429 mm/ is 1 or 1 count in 9,999. 7 1 Inverse sensitivity or scale factor =  Resolution = count = magnitudeof input 7 9999 = = 2.33 9.999 volt = 10-3 V = 1 mV. magnitudeof output response 3mm /mm Loading Effects: The ideal situation in a measurement system is that when an Linearity: One of the best characteristics of element used for any purpose may be for an instrument or a measurement system is signal sensing, conditioning, transmission considered to be linearity, that is, the or detection is introduced into the system, output is linearly proportional to the input. the original signal should remain undistorted. This means that the original Dead Time: Dead time is defined as the signal should not be distorted in any form time required by a measurement system to by introduction of any element in the begin to respond to a change in the measurement system. However, under measured. practical conditions in extraction of energy from the system thereby distorting the Dead Zone: It is defined as the largest original signal. This distortion may take the change of input quantity for which there is form of attenuation waveform distortion, no output of the instrument phase shift and many a time all these undesirable features put together. Resolution or Discrimination: If the input Errors in Measurements and Their is slowly increased from some arbitrary Statistical Analysis input value, it will again be found that Actual value of quantity Aa = As   A output does not change at all until a certain A Relative limiting error  r = = rAs increment is exceeded. This increment is A called resolution or discrimination of the s actual value nomin al value instrument. So resolution defines the  r = smallest measurable input change. nomin al value

Example Combination of Quantities with Limiting A moving coil voltmeter has a uniform scale Errors. with 100 divisions, the full scale reading is i) Sum of two quantities. X = x1 +x2 200 V and 1/10 of a scale division can be dx dx dx x dx x dx 1  2  1 1  2 2 estimated with a fair degree of certainty. X X X X x X x Determine the resolution of the instrument 12  in volt. X x1 x 1 x 2 x 2 =   Solution X X x12 X x 1 scale division = 200/100 = 2V ii) Difference of two quantities. X = x1 –x2

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission X dx dx 1 ndx m dx  = 1 - 2 , ..,12 X X X X x12 dX x dX dX dx1 x 2 dx2 dX dx dx = - , n12 m , X x X x 1 2 X x12 x

x1 x 1 x 2 x 2 xx =  .. = nm12 X x X x  12 xx12

iii) Sum of difference of more than two 1.3 TYPES OF ERRORS quantities. X= x1 x2 x3. then the relative 1. Gross Errors, limiting error in X is given by: 2. Systematic Error. x x x x xx 3. Random Errors. = 1... 1 2 2 33 X x1 X x2 X x3 Gross Errors. This class of errors mainly covers human mistakes in reading iv) Product of two Components, instruments and recording and calculation X = x x ., 1 2 measurement results. log X = log x +log x . e e 1 e 2 1. Great care should be taken in reading 1 1 dx 1 dx = . 1 + . 2 , and recording the data. X x1 dX x 2 dX 2. Two, three or even more reading should be taken for the quantity under = + , measurement. Systematic Errors. xx = 12 1. Instrumental Errors. xx12 2. Environmental Errors. 3. Observational Errors. v) Quotient x 1. Instrumental Errors. X = 1 , i) Due to inherent shortcomings in the x 2 instrument, log X = log x -log x . e e 1 e 2 ii) Due to misuse of the instruments, = . - . , and iii) Due to loading effects of = - , instruments Environmental Errors. = Observational Errors. Random Errors. Statistical Treatment of Data. vi) Product or quotient of more than two quantities i) Multi-sample test and xxx ii) Single-sample test. = 123 x x x 1 2 3 Arithmetic Mean. x x  x  x  ......  x  x vii)Composite factors X = 1 2 3 4 n = n n X = x1n.x2m, d1 = x1- loge X = n loge x1 + m loge x2

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission d2 = x2- X Pri. Standard Weston cell: saturated, …………. normal, Weston cell is used asthe pri standard of emf.. dn = xn - (x d )  The potential of saturated weston cell. E X = nn = 1.01864 volts. n Average Deviation.  It contains CdSO4 crystal, Hg2SO4, (Cd + Hg) (Amalgum). d1   d 2   d 3  ....   dn  d D  = Note : CdSO4 crystal is used in saturated n n Weston cell only. Standard Deviation (S.D.) d2 d 2  ....  d 2  d2  Variation in emf with temperature –40 S.D. =  = 1 2 n = n n v/°C When the number of observations is  Variation in potential with time. -1 V/Year greater than 20, S.D. is denoted by symbol  The max. current from saturated weston while if the number of observation is less cell is 100 A. than 20, the symbol used is s.  Internal resistance of sat. weston cell. d2 d 2  d 2  ....  d 2 600-800 s = 1 2 3 n n1 Sec. Standard  d2 n1  Unsaturated weston cell is used as sec. standards. Variance. The variance is the mean square  The potential of unsaturated weston cell deviation, E=l.0180 to 1.0194V. V = (Standard Deviation)2  It does not have CdSO4 crystal. = (S.D.)2 = 2  Porous plug is used to hold electrode in d2 d 2 d 2  ....  d 2 place. = 1 2 3 n n  Variation in potential is -30V to -  d2  d2 50V/year. = ,V = s2 = n n1 Laboratory standard of emf 1.4 STANDARDS  The zener diode circuit is used for laboratorystandard. i) International standards ii) Primary standards iii) Secondary standards iv) Working standards Standards of Resistance (i) International standards : Not available Magnine is used for the standard resistance. to everyone. Contents of Magnine: (ii) Pri. standards: National standards Ni  4% (iii)Sec. standards: used in industrial labs. Cu  84% (iv) Working standards: Used in general labs. Mn  12% Standards of EMF: Characteristics of Magnine 'Weston' cell is used for primary and secondary standards of emf.  High resistivity

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission  low temp. coefff.  low thermal expansion with copper. Errors in resistance standards  Skin effect.  stray inductances, and capacitances.  there can be contact resistances.

Bifilar winding

The bifilar winding is used to reduce the inductive effect of resistance.

Campbell type

is used as the primary standard. It consists of marble cylinders with screw threads carrying a coils of bare copper, Bare copper (without any insulation) wound under tension.

Sec, standards of mutual inductance

It consists of two coils wound on bobbin of marble and coils are separated by a flange. Cu is used as a conductor.

Pri. standards of self inductance

It is same as that of mutual inductance. (i.e. Campbell type).

Sec. standards of self inductance.

Silk covered copper wire wound on marble former.

Pri. standards of time Atomic clock is used as primary standard.

Pri._standards of freq.

a) CAESIUM (Ce) beam is used as pri- standard b) Hydrogen maser.

Sec. standards of freq.

a) rubidium crystal b) Quartz crystal

Q.1 Resistance R1 and R2 have respectively, nominal value of 10Ω and 5Ω and tolerances of 5% and 10%. The range of values for the

parallel combination of R1 and R2 is a) 3 . 0 7 7Ω t o 3 . 6 1 6 Ω b) 2 . 8 0 5Ω t o 3 . 3 7 1Ω c) 3.237Ω to3.678Ω d) 3 . 1 9 2Ω t o 3 . 4 3 5 Ω [GATE-2001] a) [123.50, 136.50] Q.2 A variable w is related to three other b)[125.89, 134.12] variables x, y, z as w=xy/z. The c) [117.00, 143.00] variables are measured with meters d) [120.25, 139.75] of accuracy 0. 5% reading, 1% of [GATE-15-1] full scale value and 1. 5% reading. The actual readings of the three Q.4 The voltage and current drawn by a meters are 80, 20 and 50 with 100 resistive load are measured with a being the full scale value for all 300 V voltmeter of accuracy ± 1% of three. The maximum uncertainty in full scale and a 5 A ammeter of the measurement of w will be accuracy ± 0.5% of full scale. The a) 0.5%rdg b) 5.5%rdg readings obtained are 200 V and 2.5 c) 6.7%rdg d) 7.0%rdg A. The limiting error (in %) in computing the load resistance is (up [GATE-2006] to two decimal places) ______. [GATE-2018] Q.3 When the Wheatstone bridge shown in the figure is used to find the value of resistor Rx, the galvanometer G indicates zero current when R1=50 Ω, R2 = 65 Ω and R3 = 100 Ω, If R3 is known with ± 5% tolerance on its nominal value of 100 Ω . What is the range of Rx in Ohms?

ANSWER KEY:

1 2 3 4 (a) (d) (a) 2.5

Q.1 (a) 5 Now R3 = 100 ± 100×0.05 = 100 ± 5 Range of R 1 0 1  0  1 100 = 95/105 Ω 9 . 5Ω t o1 0 . 5 Ω RR23 65×105 R===136.5x Ω Range of R501 10 65×95 R554.52  Ω to5.5Ω R==123.5 Ω 100 x 50 RR12 Range of R is123.5 Ω to136.5 Ω Rp  RR12 9.54.510.55.5Q.4 2.5 Range of Rto p 9.54.510.55.5  3 . 0 5Ω t o 3 . 6 1Ω Given : Voltmeter  V3001% and Ammeter A50.5% Q.2 (d) For V= 200, I = 2.5A Full scale reading of all three =100 300 Readings of x=80 %limiting errorV11.5%   Readings of y=20 200 5 Readings of z=50 %limiting errorA0.51  %  0.580 2.5 δx0.5%  of reading    0.4 V 100 %limiting errorR1.512.5   %   1100 I δy1%  of full reading   100 1.550 1δz1.5%  of reading   100 0 . 7 5 xy Given ω  z Taking log, we get logωlogxlogylogz Differenting wrt ω we get δω δx δy δz    ω x y z For maximum uncertainty δω 0.410.75    1007% ω 8020 100

Q.3 (a) Weinbridge is balanced, R1, Rx = R2R3 50×Rx = 65×100 Rx = 130Ω

2.1 INTRODUCTION The construction of a ballistic galvanometer is similar to a d’Arsonval A galvanometer is an instrument used for type galvanometer. detecting presence of small currents or voltages in a circuit or for measuring their 2.1.3 FLUX METER magnitudes. Galvanometers find their principal application in bridge and The flux meter is a special type of ballistic potentiometer measurements where their galvanometer in which the controlling function is to indicate zero current. torque is very small and the Therefore, a galvanometer in addition to electromagnetic damping is heavy. being sensitive should have a stable zero a The construction of a flux meter is general short periodic time and nearly critical the construction is similar to that of a damping. moving coil milli-ammeter. A coil of small cross-section is suspended from a spring 2.1.1 D’ARSONVAL GALVANOMETER support by means of a single silk thread. The coil moves in the narrow gap of a The instruments are very commonly used permanent magnet. There are no control in various methods of resistance springs. measurement and also in d.c. potentiometer work. 2.1.4 VIBRATION GALVANOMETERS A sensitive galvanometer is one which produces a large deflection for a small These galvanometers are of d’Arsonval type having a moving coil suspended current. We have current sensitivity, Si = G/500 K. between the pieces of a permanent magnet. When an alternating current is passed 2.1.2 BALLISTIC GALVANOMETER through the moving coil, an alternating deflecting torque is produced which makes A ballistic galvanometer is used for the coil vibrate with a frequency equal to measurement of quantity of electricity the frequency of the current passing. On (charge) passed through it. In magnetic account of inertia of the moving parts, the measurements, this quantity of electricity amplitude of vibrations is small. However, is due to an instantaneous emf induced in a if the natural frequency of the moving search coil connected across the ballistic system is made equal to the frequency of galvanometer. The instantaneous emf is the current, mechanical resonance is induced in the search coil when the flux obtained and the moving system vibrates linking with the search coil is changed. The with a large amplitude. quantity of electricity passing through the Vibration galvanometers are suitable for galvanometer is proportional to the emf use at power and low audio frequencies, induced and hence to the change in flux but they are mainly used at power linking with the search coil. The frequencies. galvanometer can therefore be calibrated to read the charge directly. 2.2 INDICATING INSTRUMENT It does not show a steady deflection it i) oscillates with decreasing amplitude, the amplitude of the first deflection or swing or throw being proportional to the charge passing. ii)

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission opposite to the deflecting force at the final steady position of pointer in order to make the deflection of the pointer definite for a particular magnitude of current. In the absence of a controlling system, the pointer will shoot (swing) beyond the iii)Principle of operation of indicating final steady position for any magnitude instruments: of current and thus the deflection will be indefinite.to bring the moving system back to zero when the force causing the instrument moving system to deflect is removed. In the absence of a controlling system the pointer will not come back to zero when current is removed. Controlling force is usually provided by springs.

OPERATING FORCES 3. Damping Force: When a deflecting force is applied to Three types of forces are needed for the the moving system, it deflects and it satisfactory operation of any indicating should come to rest at a position where instrument. These are: the deflecting force is balanced by the i) Deflecting force controlling force. The deflecting and ii) Controlling force and controlling forces are produced by iii) Damping force systems which have inertia and, therefore, the moving system 1. Deflecting Force: cannot immediately settle at its final The deflecting or operating force is position but overshoots or swings ahead required for moving the pointer from its of it. Consider Fig. Suppose O is the zero position. The system producing the equilibrium or final steady position. deflecting force is called "Deflecting Because of inertia the moving system system' or 'Moving System 'The moves to position 'a' Now for any deflecting force can be produced by position 'a' beyond the equilibrium utilizing any of the effects mentioned position the controlling force is more earlier. Thus the deflecting system of an than the deflecting force and hence the instrument converts the electric current moving system swings back. Due to or potential into a mechanical force called inertia it cannot settle at 'O' but swings to deflecting force. The deflecting system a position say 'b' behind the thus acts as the prime mover equilibrium position. At 'b' the responsible for deflection of the pointer. deflecting force is more than the 2. Controlling Force: controlling force and hence the moving This force is required in an indicating system again swings ahead. The instrument in order that the current pointer thus oscillates about its final produces deflection of the pointer steady (equilibrium) position with proportional to its magnitude. The decreasing amplitude till its kinetic system producing a controlling force is energy (on account of inertia) is dissipated called a "Controlling System". The in friction and therefore, it will settle functions of the controlling system are: down at its final steady position. If extra (i) to produce a force equal and forces are not provided to "damp" these

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission oscillations. the moving system will take a considerable time to settle to the final position and hence lime consumed in taking readings will be very large. Therefore damping forces are necessary so that the moving system comes to its equilibrium position rapidly and smoothly without any oscillations. 2.3 TYPES OF SUPPORTS Several types of supports are used The advantage of this suspension is depending upon the sensitivity required and that exact leveling is not required if the operating conditions to be met supports moving element is properly balanced. may be of the following types: Suspension and taut suspensions are i) Suspension customarily used in instruments of ii) Taut suspension galvanometer class which require a low iii)Pivot and jewel bearing (double) friction and high sensitivity mechanism. But actually there is no strict line of (i) Suspension: demarcation between galvanometers It consists of a fine, ribbon shaped and other indicating instruments. metal filament for the upper suspension Some sensitive wattmeters, and and coil of fine wire for the lower part. electrostatic voltmeters also use flexible The ribbon is made of a spring material suspension. like-beryllium copper or phosphor bronze. This coiling of lower part of iii)Pivot and Jewel Bearings: suspension is done in order to give The moving system is mounted on a negligible restraint on the moving spindle made of hardened steel. The two system. This type of system is employed ends of the spindle are made conical and only in those laboratory applications in then polished to form pivots. These which very great sensitivity is required. ends fit conical holes in jewels located in the fixed parts of instruments. These jewels, which are preferably made of sapphire form the bearings. Originally natural sapphire was used but now synthetic sapphire is being used. The combination of steel and sapphire gives lowest friction.

(ii) Taut Suspension: Suspension type o f instruments can only be used in vertical position. The taut suspension has a flat ribbon suspension both above and below the moving element, with suspension kept under tension by a spring arrangement.

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission 2.4 DAMPING FORCES spring used is made up of phosphor- bronzeit should have small resistance.

1. Air Friction damping(Moving Iron τc αθ inst.) τ = k θ Note : Torque/wt ratio of moving c system should behigh and should be k = spring constant τ  0.1 3. Eddy current damping(used in weight PMMC)

Eddy current damping by metal former

4. Electromagnetic damping (used in 2. Fluid Friction damping Galvanometer) (Electrostatic typet.)

Gravity Control wt.s are used to balance the motion of painter.

Note : 1. Electromagnetic damping and Eddy current damping cannot be used in moving iron and dynamometer type instruments. 2. Moving iron Inst. and dynamometer type both use air Friction damping system and No magfield due to damping system. 3. Eddy current Damping (PMMC) produces magfield therefore cannot be used in Ml & dynamometer type 2.4.1 METHODS OF EDDY CURRENT DAMPING:

Spring control There are two common forms of damping Hair spring is used to provide the control. devices: and used in instruments of control i) A metal former which carries the working panel. The torque produced is coil of the instrument. proportional to sin. where is the ii) A thin aluminium disc attached to the displacement of pointer from null moving system of the instrument. This position. disc moves in the field of a permanent magnet. τc αsinθ τ = k sinθ c 1. EM Damping used i n Galvanometer

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission  Hot wire type  In voltmeter, moving coil mounted on  1nduction type (Energy meter) metallic frame to provide Produces mag. field so cannot be used electromagnetic damping. in Mi or dynamometer type inst.  In ammeter, moving coil is wound on 2. PMMC: are provided with taut non-magnetic former because the suspension. electromagnetic damping is provided by coil of the shunt. 2.5 ELECTROMECHANICAL INDICATING  Material used for magnet in PMMC is INSTRUMENTS AlNiCO. (Al+Ni+Co) 2.5.1 ANALOG AMMETER, VOLTMETER Al Comax (Al + Co + …..) & OHMMETER

Types of instruments used for measurement of current and voltage

a) PMMC (Permanent Magnet Moving Coil)[For D.C. current measurement] b) Moving Iron Type (AC & DC) c) Electrodynamometer Type (AC & DC) d) Hot wire Type (AC &DC) e) Thermocouple type (AC & DC) f) Induction type (A.C only) g) Electrostatic type (AC &. DC)  The field strength in PMMC varies from h) Rectifier type (AC & DC) 0.1 Weber/m2 1 Weber/m2  Concentric magnetic construction is  Moving coil and moving iron used to get longer angular movement of instruments are most commonly used the pointer. for DC and AC measurements  Angular displacement can be over 300°. respectively.  Control force in PMMC is provided with  Moving iron instruments are cheapest springs made up of phospher- elements and mostly used in industry. bronge.  Electrodynamometer type has same  These are fine-wire springs which are calibration for AC & DC. Therefore also used to carry the coil current, Electrodyne. Type are used as transfer therefore PMMC can be used for the low instruments. current & voltage measurements.  The thermal instruments (Hot wire  Damping in PMMC: type) also gives same calibration for AC (Eddy Current Damping (Voltmeter) and DC.  Ammeter or current coil? The General sources of errors in Electromagnetic Damping) instruments  Torque produced in PMMC i) Friction ii) Heating of the instrument iii) Expansion in the spring iv) Lack of Balance in the moving system.

2.6 PMMC INSTRUMENTS d = NBIA deflecting torque due to magnetic field  Are used for measurement of DC only. c = kG controlling due to spring control

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission At balance I = Full-scale current of the ammeter NBIA - k = G l including the shunt. TC = Td Since the shunt resistance is in parallel KQ = NBIA with the meter movement, the voltage deflection produced in the instrument drops across the shunt and movement G must be the same and we can write θ= I VV k shunt movement θαI or IR were G = NBA I R I R and R mm (Hence the scale in PMMC is Linear) s s m m s I. I Since I I I , wecan write θα sm k IRmm Rs   Hence with the ageing effect of spring II m the reading will be more. For each required value of full-scale meter θαB current we can then solve for the value of Also θαN the shunt resistance required. θαA Example  Hence with the decreasing mag. field of A 1-mA meter movement with an internal magnets. reading will be less. resistance 0f 100  is to be convened into Note: a0-100 m/A ammeter. Calculate the value  If control force in the any type of of the shunt resistance required. instrument is absent then pointer will Solution be moving beyond Is = I- Im = 100 – 1 = 99 mA  The full scale. IR 1mA 100 R mm  1.01   If damping force is absent the pointer s I 99mA will oscillate around the mean position. s

2.7 DC AMMETERS

Shunt Resistor The basic movement of a dc ammeter is a Note: PMMC galvanometer. Since the coil winding • Resistance of ammeter should be of a basic movement is small and light, it reduced to mΩ to reduce the loading can carry only very small currents. When effect due to ammeter. large currents are to be measured, it is • Shunt should have small and constant necessary to bypass the major part of the temp. coefficient. current through a resistance, called a shunt. • The materials used for shunt in PMMC The resistance of the shunt can be is magnanin. calculated by applying conventional circuit • The material used for shunt in AC analysis . measuring instruments is constatntun where becausethe thermalemf of constantun is Rm = internal resistance of the movement unidirectional and is ineffective in (the oil) Rs = resistance of the shunt AC measurement. Im = full-scale deflection current of the • Meagnanin gives small thermal emf movement. Is = Shunt current with copper that is why it is preferred in DC (PMMC type).

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission Effect of temperature change in V R =  G ammeter reading: s ifs As temp. increases the resistance of copper R = (m – 1)R increase and this result into change of s m reading of instrument because coil is made up of copper and shunt is made up of magnanin which has different temp coeff. To reduce the effect of temp, a resistance having very small temp, coeff. made up of V magnanin is connected in series with the m = coil. And this coil is called “Swamping Vfs Resistance” Vfs Voltage Across coil at full scale 2.7.1 MULTI RANGE AMMETERS deflection m  multiplying factor Sensitivity of There are two methods to achieve Voltmeter: multirange of the ammeter. 1 i) By using a no. of shunts. Sv  unit / v I RI fs R m1 m Sh1 1 Note: If range 0 - 100 V. Sv = 100 /v. then m1m 1 I (Rs + Rm) = 100 x 100 = 10 k = RT RIm2 RSh2  m2 V m2m 1 I RRsm Ifs

Rs VS v R m Rs – Multiplier resistance

2.8.1 MULTIRANGE DC VOLTMETERS:

Multirange of dc voltmeters can be obtained by individual multipliers. ii) By using universal shunt or Ayrton i) Using individual multipliers shunt- for dc only ii)Using potential dividers. R R  m I (i) Using individual multipliers mII 

RRm1 R 2  m2

V R (m  1)R m  1 s1 1 m 1 v V R (m  1)R m  2 s2 2 m 2 v

2.8 VOLTMETER MULTIPLIERS ii) Using pot. Divider

R1 (m 1  1)R m m1 V 1 / v V = ifs (Rs + 4)

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission R2 (m 2  m 1 )R m m 2 V 2 / v permeability steel forms a moving R (m  m )R m V / v element of the system. It is so situated 3 3 2 m 1 3 that it can move in the magnetic field of a stationary coil carrying the current. The iron vane always try to adjust alone the path of minimum reluctance.

2.9.1 EXPRESSION FOR TORQUE:

Torque produced in the moving part I2 dL Note: Td  1. Current range of multirange ammeter 2d is1-50 A.  deflection of pointer 2. Vol. range far multirange voltmeter is L  inductance of coil moderate. 3. The loading effect reduces the 2.9.2 CONTROL FORCE : reading of instruments. is provided by the spring 2.8.2 SOURCES OF ERRORS IN PMMC Tc= K where k = Control spring const.  = i) Magnet ageing and temperature. deflection, rad. ii) Spring ageing and temperature At balance iii) Change in resistance of coil with  temperature deflection is proportional to square of current I2 dL and hence the scale of moving iron   instruments is nonlinear. 2k d For Linear Scale: I2 I2  dL 2   2k d 2.8.3 ADVANTAGES &DISADVANTAGES OF for scale to be linear PMMC dL cons tan t 1. Torque to wt. ratio is high d 2. Sensitivity is high. Note: 3. Losses arc low (25 - 200 w) Control force for panel type instruments is 4. Accuracy is high. provided with gravity control and control 5. Single instrument can be used for force for laboratory type instrument is different range. provided with spring. 6. They have uniform scale. Damping Air Friction damping is used. Disadvantages 1. Their cost is high Note: 2. They are used for measurement of i) The Mag. field if the coil is very small. DC. (0.006 - 0.007wb/m2) ii) Therefore eddy current damping cannot 2.9 MOVING IRON INSTRUMENTS (MI) be used in moving iron type instruments because field of eddy In the moving iron instruments vane currents may distort the field of coils. made upon soft iron and high

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission 2.10 CLASSIFICATION OF MOVING Note: IRON INSTRUMENTS 1. The direction of force on the vane is independent of direction of current l. Attraction type: Only one vane i.e. incoil. moving. 2. Moving iron instruments can be used for ACand DC both. 3. Scale is non-uniform angle of rotation of the pointer is usable for 80° only.

2.10.1 SHUNT OF M.I. INSTRUMENTS:

I R j L sh  mm Im R sh j L sh

2 2 2 | Ish | RLmm  2 2 2 | Im | Rsh L sh

Note:  Division of current between coil and shunt remain same only if time constant of the coil is equal to time constant of shunt. L L i.e. m  sh RRm sh  The shunt is not normally used in M.I. instruments. The range of ammeter can be increased by using current transformer. The moving iron is used for current as measurement up to 50 A.

2.10.2 MULTIPLIER OF MI INSTRUMENT

 The moving iron is used for current as measurement up to 50 A

22 Attraction type moving iron instrument | V | (RR)(L)s m   m m  22 | v | Rmm ( L ) 2. Repulsion type: In repulsion type there are two vanes one is moving another is stationary.

m changes with the frequency '' and this effect can be nullified by connecting acapacitor.

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission RS multiplier resistance. percent for frequencies between 25 to 125 Hz and they may be expected to be Note: accurate within 0.2% to 0.3% a 50 Hz • Inductance of attraction type is less if carefully designed. than repulsion type. • Scale: The scale of moving iron • Scale of repulsion type can be made instruments is no uniform and is almost linear. cramped at the lower end and therefore accurate readings are not 2.10.3 ERRORS IN MOVING IRON possible at this end INSTRUMENTS: • Errors: These instruments are subjected to serious errors due to i) Hysteresis: The reading of the meter hysteresis, frequency changes and can be different for the different cycles stray magnetic fields. of the current of the coil due to • Waveform errors hysteresis effect of iron vane ii) Frequency Error: Note: V 1. The moving coil instruments are used Im  (RR)(L)22   in aircraft and aerospace industries m s m because They provide self-shielding to magnetic fields. 2. Sensitivity of MI instruments is smaller than PMMC. 3. Accuracy of MI instruments is less as frequency increases  Im decreases than PMMC. 2 and Im  will decrease for same voltage. The effect can be nullified by 2.11 ELECTRODYNAMOMETER TYPE using a capacitor. (ELECTRODYNAMIC) L  The same current flows through C 0.412 farad Rs moving coil and fixed coil.  The fixed coil is divided into two equal iii) Eddy current error: halves to get uniform mag. field. Eddy currents in moving iron  The fixed coil is made up of fine wire instruments are ineffective from d.c. to for milliammeter and voltmeter and it 125 Hz. therefore M.I instrument are is made up of heavy wire for ammeter used only upto 125Hz. and wattmeter.  The moving-coil is mounted on non- Note: Moving iron instruments are mostly metallic former. used in industry and they require different Calibration of A.C. and D.C.

2.10.4 ADVANTAGES AND DISADVANTAGES OF M.I. INSTRUMENTS

• Less Friction Errors • Cheapness • Robustness • Accuracy: The initial accuracy of high Control force grade instruments is stated to be 0.75  is provided using springs.

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission Damping force  These instruments are also called  air friction damping is used. transfer instrument.  Eddy current damping cannot be used  These instruments are mostly used in because that can distort the magnetic field labs. of the coil.  Their sensitivity is smaller than  The magnetic field of the coil is very sensitivity of PMMC and also smaller small. (0.005 - 0.006) wb/m2 same as in than MI instruments. case of MI instruments Note: 2.11.2 ELECTRODYNAMOMETER TYPE The instrument is provided with shielding AMMETER with high permeability alloy against the external magnetic field.  current limit through moving coil is 100 mA. 2.11.1 EXPRESSION OF TORQUE  for higher range of currents shunt should be used. Circuit representation of  making the reading independent of Electrodynamometer Instrument frequency. For DC dM TII 12 d

but I1=I2 dM LL TI 2 of shunt = of moving coi1 d RR where M is mutual inductance between I2 dM the coils.  Kd dM For AC T I I cos 12 d

but I1 = I2 ,  = 0 dM TI 2 d 2.11.3 ELECTRODYNAMOMETER TYPE Now Torque in control spring VOLTMETER TC = K At balance V I  dM Z K = I2 d V2 dM  I2 dM KZ2 d    I2 Kd V2 hence scale of electro dynamometer type is non-linear.

 Electro dynamometer type instruments give same deflection for AC and DC  these devices can be calibrated by using DC and can be used for AC Sources of error (i) current Error: It reduces the reading measurement.

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission (ii) Frequency error: As , Z  men in In the absence of inductance Zp = Rp and case of voltmeter, reading is reduced  =0 and therefore the wattmeter will 1 read true power under these as  z2 conditions. The correction factor is a factor by which the actual wattmeter reading is 2.11.4 ADVANTAGE & DISADVANTAGE multiplied to get the true power. cos i) Accuracy of electrodynamometer type Correction factor  for is very high. cos cos(   ) ii) A.C. electro dynamometer type lagging loads. voltmeter is most accurate. The wattmeter will read low when the iii) the effect of external magnetic field on load power factor is leading Correction electro dynamometer type instrument cos factor for leading p.f.  can be reduced by using “Astatic cos cos(   ) System”. iv) Frequency range for electrodynamometer type instrument is d.c.-125 Hz but it can be 15 Hz - 1000 Hz for low grade instruments and it can be even up to 10 KHz with astatic system Compensation for Inductance of v) The electrodynamometer type Pressure by means of a capacitor instruments follows the square law connected in parallel with a portion of only for 0 varying. multiplier (series resistance) -45° to + 45°C or 45° to 135°c If we make, L = Cr2, then Zp  RP and M = Mmax cos   sin  0 I2 sin  Thus the error caused by pressure coil inductance is almost completely iv) Sensitivity of electrodynamometer eliminated. type inst. Is low. (10-30/v) This type of compensation is very Errors in Electrodynamometer Wattmeters slightly effected by change in frequency and can be used for frequencies at 1. Pressure Coil Inductance which ω2C2r2<< Idealized wattmeter the current in the 1. The frequency range over which the pressure coil is in phase with the above compensation holds good is applied voltage. If the pressure coils of 10 kHz. the wattmeter has an inductance the 2. Pressure coil Capacitance. current in it will lag the voltage by an 3. Error due to Mutual Inductance angle β where: Effects. β = tan-1 ωL/R = tan-1 ωL/(r + R) p p 4. Errors caused because of The angel between current in the Connections. current coil circuit and the current in 5. Eddy Current Errors than , the pressure coil circuit is less 6. Stray Magnetic Field Errors by which the load current lags the 7. Errors Caused by Vibration of applied voltage. Moving System ` = - β 8. Temperature Errors. The actual wattmeter reading is : Power in Poly-phase Systems Blondel’s (IPI/K) ` dM/d Theorem.

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission If a network is supplied through n conductors, the total power is measured by summing the readings of n wattmeter’s so arranged that a current element of a wattmeter is in each line and the corresponding. If the common point is located on one of the lines, then the power may be measured by n – 1 wattmeter’s. Energy is the total power delivered or consumed over a time interval, that is, Energy = power × time. t W =  vidt 0 Unit of energy is joule or wall second which is 1 watt over an interval of one second. Larger unit is used – then kilowatt hour.

2.11.5 ENERGY METERS FOR A.C. Current IP produces a flux  pt. This flux CIRCUITS divides itself into two parts R and p. The major portion R flows across the Induction type of energy meters are side gaps as reluctance or this path is small. universally used for measurement of The reluctance to the path of flux p is energy in domestic and industrial a.c. large and hence its magnitude is small. This circuit. Induction type of meters possess flux p goes across aluminium disc and lower friction and higher torque/weight hence is responsible for production of ratio. Also induction type meters are driving torque. Flux p is alternating in inexpensive and accurate and retain their nature, it induces an eddy emf Eep in the accuracy over a wide range of loads and disc which in turn produces eddy current, temperature conditions. Iep. The load current I flows through the 2.11.6 THEORY OF INDUCTION TYPE current coil and produces a flux s. This METERS flux is proportional to the load current and is in phase with it. This flux produces eddy In all induction instruments we have two current Ies in the disc. Now the eddy fluxes produced by current flowing in the current Ies interacts with flux p to windings of the instrument. These fluxes produce a torque and eddy current Iep are alternating in nature and so they interacts with s to produces another produce emfs in a metallic disc or a drum torque. These two torques are in the provided for the purpose. These emfs in opposite direction (as shown in fig.) and turn circulate eddy currents in the metallic the net torque is the difference of these. disc or the drum. The theory of induction type instruments has Flux  1, induced emf and this induced emf = phase angle of load, will prudence an eddy current i. Similarly flux 2 will produce an eddy current i2.  = phase angle between supply voltage Total torque is the sum of these two and pressure coil flux. torques.  = phase angle of eddy current paths, Theory and Operation of Single Phase Eq. net driving torque Energy Meters

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission f 8. Creep Adjustment Td  1 2 sin  cos = K1 1 2 sin Z cos 2.11.8 TESTING OF ENERGY METERS PHANTOM LOADING =phase angle between fluxes p and s = (   ) When the current rating of a meter under If f, Z and are constant, T4 = K3VI sin ( test is high a test with actual loading ) arrangements would involve a considerable Speed, N = KVI sin (900 -  ) = KVI cos waste of power. In order to avoid this = K (power) “Phantom” or “Fictitious” loading is done. Thus in order that the speed of rotation is Phantom loading consists of supplying the proportional to power, angle  should be pressure circuit from a circuit of required equal to 900. Hence the flux p, must be normal voltage, and the current circuit made to lag the supply voltage by exactly from a separate low voltage supply. It is 900. possible to circulate the rated current Total number of revolution through the current circuit with a low N dt  K VI sin(   )dt voltage supply as the impedance of this  circuit is very low. K (VI cos )dt 2.12 MEASUREMENT OF POWER AND  K (power)dt K  (energy)  ENERGY MEASUREMENT OF POWER 2.11.7 LAG ADJUSTMENT DEVICE The power is measured by The meter will register true energy only if electrodynamometer type voltmeters. the angle is made equal to 900  By ferrodynamic wattmeter  Thermocouple wattmeter The shunt magnet flux p can be brought exact quadrature with applied voltage V.  The electrodynaraometer type This adjustment is known as “lag wattmeter is most commonly used: adjustment”. Sometimes it is referred to as Connections of Wattmeter “power factor”, “quadrature” or “inductive load adjustment” Compensation • Light Load or Friction Compensation • Over – Load Compensation • Voltage Compensation Resis tanceof P.C. Resis tanceof C.C. • Temperature Compensation • Errors in Single Phase Energy Meters Adjustments in Single Phase Energy Meters 1. Preliminary Light Load Adjustment 2. Full Load Unity Factor Adjustment 3. Lag Adjustment (Low Power Factor I I cos dM Adjustment)  CC PC 4. Unit p.f. and low p.f. adjustments kd I V cos dM 5. Light Load Adjustment  CC PC 6. Full load – unity power factor and light kz d load adjustments I V cos dM  CC PC 7. The performance is rechecked at 0.5 p.f. kzPC d lagging.

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission (i) The inductance of the pressure-nil used in the measurement cause error and is compensated by connecting a parallel combination of R and C in series with 2 pressure coil i.e. LP  r c But practically PC is not purely resistive but inductive also, and  if Vpc  V PC  0

then ipc I PC   (ii) At low power factor measurements. Correction: Current ceil is provided the compensation by connecting a compensating ceil around the current coil such that its field opposes the field of current coil. In this connection C.C. near the load. Z RPP  j  L VV wL I p  p  tan1 p 2.12.1 FERRODYNAMICTYPE WATTMETER P ZR2 2 2  Rpp w L p 1. This is used where high torque is L tan1 p required. R p 2. In electrodynamometer type instruments Movingcoil pressurecoil Fixedcoil current coil

Note: Deflection of dynamometer II dM  12 kd Then phasor Two wattmeter method of measurement     of 3 power

cos pf .of load PIV1 1 13 I V cos dM PIV  CC PC 2 2 23 kZ dz I V cos dM    CC PC k R2 2 L 2 d I V cos cos dM  CC PC kR d R z  cos

Note :

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission Let V1 V ph sin t iii)At p. f.= 0.5.  = 60  3 V2 V ph sin(  t  120 ) P1 V I 2 ph ph V V sin(  t  120 ) 3 ph P2 0

phasedifferentin Iph andV ph iv)At p. f. = 1.  = 0  3 V1 V ph 0 PPVI1 2 ph ph  2 V2 V ph   120  2.12.3 POWER FACTOR METERS V3 V ph   120

 Power factor meters – like wattmeters have P 3V I cos(30  ) 1 ph ph a current circuit and a pressure circuit. The P 3V I cos(30   ) current circuit carries the current (or 2 ph ph definite fraction of this current) in the circuit whose power factor is to be 2.12.2 TOTAL POWER measured. The pressure circuit is connected across the circuit whose power P = P1 + P2 factor is to be measured and is usually split   3Vph I ph  cos(30  )  cos(30   ) up into two parallel paths – one inductive and the other non-inductive. The deflection 2cos30 cos  3V I cos  ph ph of the instrument depends upon the phase

P1 P 2  3V ph I ph sin  difference between the main current and currents in the two paths of the pressure PP tan 123 circuit, i.e. upon the phase angle or power PP12 factor of the circuit. The deflection is indicated by a pointer. 1 PP tan 3 12 The moving system of power factor meters PP12 is perfectly balanced at equilibrium by two opposing forces and therefore there is no Calculate  (p. f.) if two wattmeter’s reading need for a controlling force. Hence when a is given: power factor meter is disconnected from a Note: circuit the pointer remains at a the position i) At 0 p.f. which it occupied at the instant of 3 PVI disconnection. 1 2 ph ph There are two types of power factor 3 meters: PVI2  ph ph i) Electrodynamometer type, and 2 ii) Moving Iron type ii) At  = 30 Therefore the deflection of the instrument 3 P 3V I , PVI is a measure of phase angle of the circuit. 1 ph ph 2 2 ph ph

The instrument must be designed for, and Working of a single phase induction type calibrated at the frequency of the supply on energy meter which it is to be used. In case the meter is used for any other frequency or if the 2.12.6 CREEPING supply contains harmonics it will give rise Sometimesdisc rotates even when the to serious errors in the indication on current in the coil is zero and pressure coil account change in the value of reactance of is excited. choke coil. And this occurs due to compensation used to start the meter rotation under loaded 2.12.4 Q METER condition to overcome the friction of mechanical parts. Process is called creeping Basic Q-Meter Circuit energy meter formula The Q meter is an instrument designed to measure some of the electrical properties of coils and capacitors. The operation of this useful laboratory instrument is based on the familiar characteristics of series- resonant circuit, namely, that the voltage across the coil or the capacitor is equal to the applied voltage times the Q of the circuit. If a fixed voltage is applied to the circuit, a voltmeter across the capacitor can be calibrated to read Q directly. XC = XL EC = IXC = IXL 2.12.7ELECTROTHERMIC INSTRUMENTS E = IR X XE Q L CC   These instruments are used at higher RRE frequency than moving iron and electrodynamometer type of instruments.

2.12.5 MEASUREMENT OF ENERGY

The induction type instruments are used to measure energy. A simple functional

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission 2.12.8 CLASSIFICATION OF Tubular conductor Skin effect lessened. ELECTROTHERMIC INSTRUMENTS The thermoelective instruments give same call for A.C and D.C. therefore these Hot wire: expansion of heated wire instruments can be calibrated by D.C. Thermocouple: Emf at heated junction. current and can be used for A.C. measurement that is why these instruments are also called transfer instruments.  At low frequencies (voltmeter) act as precision instrument. Bolometer: change in resistance due to  (Hot wire instruments measure Irms heating, heating is due to the current and Vrms) through the devices.  (In thermocouple type instruments PMMC is used for detection of 2.12.9 HOT WIRE thermocouple emf. But its scale is calibrated to measure RMS value). Thermoelectric element used in hot wire ⦁ Disadvantage type instruments is made up of platinum ⦁ These instruments have very small indium. loading effect. sensitivity of electrothermic instruments is higher than electrodynamometer type 2.12.11 ELECTROSTATIC INSTRUMENT instruments. The force of attraction between static Advantages and disadvantages charges is principle. Force and Torque (i) Not affected by magnetic field, equationLinear Motion: (ii) Not affected by frequency hence can Controlling Force-spring Force between be used at higher frequency (more plates than 50 MHz) 1 dC FV 2 (iii)can be used for A.C. and D.C. 2 dx measurements, (iv)measurement in electrothermic C = capacitance between plates. V2 dC instruments is RMS, which is Deflection x  independent of waveform. 2K dx

2.12.10 THERMOCOUPLE TYPE INSTRUMENTS

These instruments are generally used upto 500 v and at frequency more than 50 MHz. At frequencies more than 50 MHz the skin effect is dominant and can cause an error. But this can be minimised by using.  Motion of pointer is linear (line). Tubular Conductor  x  V2 Scale is non-linear. This is preferable for current.  the motion of pointer is proportional to voltage and not to the current.

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission  electrostatic type instruments are used 3. Sensitivity = 1000 /V to 2000 /V in for measurement of voltages only (H. V) case of PMMC - highest sensitivity. around 20kV. Torque equation: 1 dc TV 2 2d 1 V2 dc T  2 K d V2 motionof point er circular 2.12.12.1 BASIC ARRANGEMENT OF A Scale non linear RECTIFIER INSTRUMENT USING A FULL WAVE RECTIFIER CIRCUIT

Inst. Are used for Electrodynamometer  (High power type instruments: measurement) Electrothermic type  (High frequency measurement (low Electrostatic type  power) (High voltage in KV) Note: electrostatic instruments are mostly used in lab. for measurement of voltage. 2.12.12.2 TYPES OF SEMICONDUCTORS Advantages of electrostatic instruments: USED IN RECTIFIER • low power required. TYPEINSTRUMENTS: • no. frequency error. 1. Selenium: PIV is 10V • No effect of stray magnetic field. 2. Germanium:PIV is 300V,current 100 • Can be used for HV (KV) measurement mA • Can be used for AC and DC both. 3. Silicon: PIV is 1000Vcurrent 500 mA All the power devices is made of silicon Disadvantage: because, they are stable at high voltages. • Expensive and costly H.W. Rectifier • Suitable for high voltage measurement V v  m only av  • non-uniform scale Vav • operating force is small. Iav  RRsm

2.12.12RECTIFIER TYPE INSTRUMENTS Vm   0.45Vrms  =Z 1. They employ a rectifier for the RR RR smsm rectification and PMMC for detection.  these instruments use PMMC for V display and measure r.m.s. value by For d.c. Im = rR calibrating the scale of instruments. sm 2. Rectifier type instruments are mostly For a.c. such that Vrms =V 0.45V used in communication or low Im = Iav = currents application with maximum RRsm current approximately 1 mA.

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission 4. Effective diode capacitance: Voltage drop across the diode capacitance causes the error.

Advantage: 1. can be operated at high frequency (Khz) 2. Scale is uniform. Sensitivity of a.c.= 0.45 Sdc 3. the operating current is small. in case of HWR Disadvantage: FWR: (Full wave rectifier) 1. Loading effect of Rectifier installment is more for a.c. than d.c. 2Vm vav  0.9Vrms 2. Rectifier type instruments respond to  av. value of the input waveform applied 0.9V II rms but these are calibrated to r.m.s. av m RR sm value of sinusoidal wave form. 3. Sensitivity ofdifferent If Rd is diode Resistance 0.9V instruments: II rms av m (i) PMMC: 20k /V Rs R m 2R d (ii) Rectifier type: 1000 - 2000 /V Sensitivitys 0.9s ac dc (iii) Electrothermic: 500 /V (iv) Electrodynamometer: 10-30 /V (v) M.I. (vi) Electrostatic

Meter type Suitability Major uses PMMC (d' Ansonval) D.C. Most widely used meter for d.c. current and voltage and resistance measurements in low and Calibration of PMMC for measurement medium impedance circuits. of Vrms Moving Iron D.C. or A.C. Inexpensivc type used for rough indication of currents and Vrms  (formfactor)Vav voltages. Widely used in indicator type RMSvalue formfactro  applications such as on panels. Av.value Electrodynamometer D.C. or A.C. Widely Factors affecting the performance of used for precise a.c. current and voltage rectifier type instrument: measurements at power frequencies. Used 1. Effect of type of waveform: Because as standard meter for calibration and also instrument is callibrated only for R.M.S. as transfer instrument. value of sinusoidal waveform. Electrostatic D.C. (or Measurement of high 2. Effect of rectifier resistance: the A.C. at one voltages where very little resistance connected in series result frequency) current can be supplied by into active power loss and causes the circuit under measurement. error. Rectifier D.C or A.C. are widely used for 3. Temp: Since the increase in temp, affect medium sensitivity service type voltage the conductivity of semiconductor measurements in medium impedance diodes thereby deflection in PMMC is circuits carried out.

Q.1 A 100μA ammeter has an internal L 10  3θ  (θ2 / 4)μH Where θ is resistance of 100 Ω . For extending the deflection in radians form the its range to measure 500μA the zero position. The control spring shunt resistance required is of torque in 2 5 1 0 N m/6 r a d i a n .the a) 20.0Ω b) 22.22 Ω deflection of the pointer in radian c) 25.0 Ω d) 50.0 Ω when the meter carries a current of [GATE-2001] 5A, is a) 2.4 b) 2.0 Q.2 A Manganin swap resistance is c) 1.32 d) 10 connected in series with a moving [GATE-2003] coil ammeter consisting of a milli – ammeter and a suitable shunt in Q.5 A galvanometer with a full scale order to current of 10mA has a resistance of a) minimize the effect of 1000Ω . The multiplying power (the temperature variation ratio of measured current to b) obtain large deflecting torque galvanometer current) of 100Ω c) reduce the size of the meter shunt with this galvanometer is d) minimize the effect of stray a) 110 b) 100 magnetic fields c) 11 d) 10 [GATE-2003] [GATE-2004]

Q.3 A rectifier type ac voltmeter consists Q.6 A moving coil of a meter has of a series resistance Rs an ideal full- 100turns, and a length and depth of wave rectifier bridge and a PMMC 10mm and 20mm respectively .It is instrument as shown in figure. The positioned in uniform radial flux internal resistance of the instrument density of 200mT. The coil caries a is 100Ω and a full scale deflection is current of 50 mA. The torque on the produced by a dc current of 1mA. coil is The value of Rs required to obtain a) 200μNm b) 100 μNm full scale deflection with an ac c) 2μNm d) 1μNm voltage of 100V (rms) applied to the [GATE-2004] input terminals is Q.7 A moving iron ammeter produces a full scale torque of 240μNm with a deflection of 120° a current of 10A. The rate of change of self inductance μH/radian of the instrument at full a) 63.56Ω b) 69.93Ω scale is c) 89.93Ω d) 141.3Ω a) 2.0μH/ radian b) 4.8μH/ radian [GATE-2003] c)12.0μH/ radian d)114.6μH/ radian [GATE-2004] Q.4 The inductance of a certain moving –iron ammeter is expressed as Q.8 A PMMC voltmeter is connected across a series combination of a DC

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission voltage source V1 2V and and AC Q.12 A periodic voltage waveform voltage source V (t) 3s i n (4t)V observed on an oscilloscope across a 2 load is shown. A permanent magnet The meter reads moving coil (PMMC) meter a) 2V b) 5V connected across the same load c) ( 2 3 / 2 ) V d)   1 7 / 2 V reads [GATE-2005]

Q.9 A 1000V DC supply has two 1-core cables as its positive and negative lead: their insulation resistances to earth are 4MΩ and 6MΩ respectively, as shown in the figure. a) 4V b) 5V A voltmeter with resistance 50 kΩ is c) 8V d) 10V [GATE-2012] used to measure the insulation of the cable. When connected between Q.13 An analog voltmeter uses external the positive core and earth, then multiplier setting. With a multiplier voltmeter reads setting of 20 kΩ it reads 440V and with a multiplier setting of 80 kΩ it reads 352 V. For a multiplier setting of 40 kΩ the voltmeter reads a) 371V b) 383V a) 8V b) 16V c) 394V d) 480V c) 24V d) 40V [GATE-2012] [GATE-2005] Q.14 The input impedance of the permanent magnet moving coil Q.10 A current of 862sin( ωt30°) A (PMMC) voltmeter is infinite. is passed through three meters. Assuming that the diode shown in They are a centre zero PMMC the figure below is ideal, the reading meters, a true rms meter and of the voltmeter in Volts is moving iron instrument. The respective reading (in A) will be a) 8,6,10 b) 8,6,8 c) -8,10,10 d)-8,2,2 [GATE-2006]

Q.11 An ammeter has a current range of a) 4.46 b) 3.15 0-5A, and its internal resistance is c) 2.23 d) 0 0.2Ω In order to change the rage to [GATE-2013] 0-25 A, we need to add a resistance of Q.15 The dc current flowing in a circuit is a) 0.8Ω in series with the meter measured by two ammeters, one b) 1.0 Ω in series with the meter PMMC and another electrodynamo- c) 0.04 Ω in parallel with the meter meter type, connected in series. The d) 0.05Ω in parallel with the meter PMMC meter contains 100 turns in [GATE-2010] the coil, the flux density in the air gap is 0.2 Wb/m2, and the area of the coil is 80 mm2. The

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission electrodynamometer ammeter has a Q.19 A (0-50A) moving coil ammeter has change in mutual inductance with a voltage drop of 0.1 V across its respect to deflection of 0.5 mH/deg. terminals at full scale deflection. The The spring constants of both the external shunt resistance (in meters are equal. The value of milliohms) needed to extend its current, at which the deflections of range to (0-500A) is the two meters are same, is [GATE-15-1] [GATE-14-1] Q.20 Match the following: Instrument Q.16 The saw-tooth voltage wave form Type Used for P. Permanent magnet shown in the figure is fed to a moving coil 1. DC only Q. Moving moving iron voltmeter. Its reading iron connected through current would be close to transformer 2. AC only R. Rectifier 3.AC and DC S. Electrodynamometer P —1 P —1 P —1 P —3 a) Q — 2 b) Q −3 c) Q — 2 d) Q —1 R —1 R —1 R —3 R — 2 S —3 S — 2 S — 3 S —1 [GATE-14-2] [GATE-15-2]

Q.17 Two ammeters X and Y have Q.21 A capacitive voltage divider is used resistances of 1.2Ω and 1.5 Ω to measure the bus voltage Vb, in a respectively and they give full scale high-voltage 50 Hz AC system as deflection with 150 mA and 250 mA shown in the figure. The respectively. The ranges have been measurement capacitor C1 and C2 extended by connecting shunts so as have tolerances of ±10% on their to give full scale deflection with 15 normal capacitance values. If the A. The ammeters along with shunts bus voltage V bus is 100 kV rms, the are connected in parallel and then maximum rms output voltage\Tout placed in a circuit in which the total (in kV), considering the capacitor current flowing is 15A. The current tolerance, is in amperes indicated in ammeter X is [GATE-15-2] [GATE-14-2] Q.22 Consider the ammeter-voltmeter Q.18 A periodic waveform observed method of determining the value of across a load is represented by the resistance R using the circuit  1 sinsin   t0t   6 shown in the figure. The maximum Vt    possible errors of the voltmeter and 1  sinsin    t6t  12 ammeter are known to be 1% and The measured value, using moving 2% of their readings, respectively. iron voltmeter connected across the Neglecting the effects of meter load, is resistances, the maximum 3 2 a) b) possible percentage error in the 2 3 value of R determined from the 3 2 measurements, is ___ %. c) d) 2 3 [GATE-14-3]

Q.23 A voltage V1 is measured 100 times a) -0.25 A b) -0.12A and its average and standard c) 0.37 A d) 0.5 A deviation are 100 V and 1.5 V [GATE-17] respectively. A second voltage V2, which is independent of V1, is measured 200 times and its average and standard deviation are 150 V and 2 V respectively. V3 is computed as: V3 = V1 + V2. Then the standard deviation of V3 in volt is____. [GATE-16]

Q.24 A 3 ½ digit DMM has an accuracy specification of ± 1% of full scale (accuracy class 1). A reading of 100.0 mA is obtained on its 200 mA full scale range. The worst case error in the reading in milliampere is ± ______. [GATE-16]

1 Q.25 A 200 mV full scale dual-slope  2 digit DMM has a reference voltage of 100 mV and a first integration time of 100 ms. For an input of [100 + 10 Cos 1  0 0 t ] mV, the conversion time (without taking the auto-zero phase time into consideration) in millisecond is______. [GATE-16]

Q.26 A current waveform, i(t), shown in the figure, is passed through a Permanent Magnet Moving coil (PMMC) type ammeter. The reading of the ammeter up to two decimal places is

ANSWER KEY:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 (c) (a) (c) (c) (c) (a) (b) (a) (a) (c) (d) (a) (d) (a) 15 16 17 18 19 20 21 22 23 24 25 26 3.2 57.7 10.15 1 0.22 c 12 3 2.5 2.1 200 (a)

l(F S )  Current required to produce full scale Q.1 (c) deflection R 100 R a d.c. sensitivity is , sh 500 m1 1 100 1 1 3  2 5 . 0Ω Sdc  10 Ω/V I(FS) 1mA Q.2 (a) For full wave rectifier a. c. sensitivity S0.9S900acdcΩ/V Resistance of multiplier,

RSVR2Rsdcmd

Since diodes are ideal R0d 

then, R900100100s  89.9kΩ Coil is made of copper. A swamping resistance (RSW) of Q.4 (c) manganin (which has a negligible Deflecting torque in moving –iron temperature coefficient) having a ammeter resistance 20to 30 times the coil 1dL Tl 2 resistance is connected in series d 2dθ with the coil and a shunt of Inductance manganin is connected across the is θ2 combination. Since copper forms a L103θμH small fraction of the series currents 4 would divided between the meter Rate of change of inductance with and the shunt would not change deflection appreciably with the change in dLd θ2 temperature.  103 θ dθdθ4  Q.3 (c) θ 3 μH / rad 2 Current l=5A

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission Deflecting torque 101020010   33 1 d L Tl 2 2 0 0 1 0 m62 d 2dθ l curent through the coil 1 26θ  3 T5310d   5 0 m A 5 0 1 0 22  T=NBAI 25 θ 3 6 3  310Nm 6 10020010200105010  22  4 Controlling torque  2  1 0 N m 200μ N m Tk  θ 2 5 1 0 θ 6 c Q.7 (b) At equilibrium Torque produced TT cd 1 d L Tl 2 6625 θ 2dθ 2510θ310  22 Where 5θ l 1 0 A a n d  3 2 T 2 4 0 μ N m θ 1 . 2 r a d  2 4 0 1 0 N m6

Q.5 (c) 1 dL 240 1062   10  2dθ Rate of change of self inductance dL 4.810H /6 radian dθ dL 4.8μH / radian Full scale current of galvanometer dθ

Im  10mA Resistance of meter R1000 Ω Q.8 (a) m Total voltage across PMMC Resistance of shunt VVVT12 R100sh  Ω IR 23sin4tV I  sh m RR PMMC reads average value shm Average value of V 2V Multiplying power 1 I RR Average value of V02   shm Average value of V 2 V IRmm T 100 1000 So PMMC reads =2V 11 100 Q.9 (a) Q.6 (a) T=Torque on the coil =NBAI Where N=No f turns =100 B=Flux density 3 200mT  200  10 T Resistance of voltmeter (Rv) A Area of the coil length  depth appears parallel to 4MΩ

R RABv | | 4 M Ω Multiplying power I 2 5 R50kv Ω0.05MΩ  m5   I5m R0.05||AB  4M Ω0.05MΩ IR sh R RACABBC R I  m RR 0.0566.05M Ω shm 10001000 I RRsh m I μA  IR R6.05AC m sh R Voltmeter reads m1 m 1000 66 R IR100.05108V sh AB 6.05 R 0 . 2 R  m 0 . 0 5 sh m1 51 Q.10 (c) Q.12 (a) As PMMC meter reads only DC value or average value and average value l  8  6 2 sin(ωt  30°)l   8A andl is equal to 12 Area under the curve V  6 2 sin(ωt 30°) avg Total time Average value of l1 = −8A 1 Average value of l = 0 101052(58) 2 2 So average value of l = −8A Vavg  PMMC reads only average value of 20 current. Therefore PMMC reads = −8A Q.13 (d) (Since it is centre zero type) 2 2 62 RMSvalueofl8  10A 2 RMS meter and moving iron meter both reads RMS value of the current So, both m2 and m3read 10 A

Q.11 (d) To extend the range of the ammeter, When a resistance R sh is connected across R20kS Ω,v440V the meter 1 440 V  20  440 ….(1) Rm When R 80kΩ,v 352V S2 352 V  80  352…(2) Rm 352 80  440  20 Rm Ia Full scale deflection current 88 m R 220kΩ,V 480V =5A m

V0 0 V In negative half cycle, D id OFF, < PMMC voltmeter measures average value of V0 In case of half wave rectification, 14.14100 X and Y ammeters are connected in Vo avg  4 . 4 5 6 V parallel π101 Shunt Registration of X and Y meters: Q.15 (3.2) 1.3 → Given pmmc and electro Rshx  3 dynamometer type meters are 1510 1 connected in series. 150 → Both meters are carrying same R 0shx . 0 1 2 1 2 Ω current. And both are have same 1.5 spring constants. →Both are R  shy 1510 3 reflecting same readings. i.e. we 1 should equate the reflecting 250 torques. For pmmc, T def = R 0shy . 0 2 5 4 2 Ω BAN.I. Current through X ammeter is dM Electrodynometer, Tdef=I2 . 0.02542 dθ 15 (0.012120.02542) dm BAN.I= I2 .0.2 × 80×10×100×I-6 = 10.157ampers dθ  2 -3 =I×0.5×10 ⇒ 1=3.2 Q.18 (A) M.I instrument reads RMS value Q.16 (57.73) 2 2  (1) 1 2 1 3 1 22 

Q.19 (0.22) Moving iron meter reads RMS value I2 = 500, I1= 500 I2 — = 450 450x only RMS value of saw-tooth Rsh = Rsh = 0.1/ 450 = 0.22mn waveform is -15 -V3 100 Q.20 (c) Meter reads  = 57.73 volts 3 Q.21 (12) Vout = Vbus Q.17 (10.157) Vbus c,-1_c,+c,_1c,+c2 =(11.1F±10%)±(91.1f±10%) =(11.1,±0.1)±(911+0.9) =(1011±1) =101.1F±10%c111±10% 1

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission = 0.1± 20% c, + c, 101.1 ± 10% = ± [2 mV + 0.1 mV] ∴ Vout =100x 103(0.1± 20%) = ± 2.1 mV =10 kV ± 20% So, the worst case error in the =10k + 2k (or)10k - 2k =12k or 8k reading is ± 2.1 m volts Q.22 (3) Q.25 200 V2%xxV  R xx R3% From the given data VI1%Ix For 200 mV full scale range, digit Q.23 (2.5) DMM Given V1 = 100 V Reference voltage (Vref) = 100 mV, Standard deviation of V1 First integration time (T1) = 100 ms = 1.5 V   Input voltage (Vin) V2 = 150 V 10010cos100tmV  Standard deviation of V2 Conversion time (Tconv) = ?   = 2V We know V3 = V1 + V2 Vin T1 = Vref T2 Standard deviation of V3 100 mV 100 ms = 100 mV T2 22 T2 = 100 ms  21.5     Tconv = T1 + T2 = 2.5 Volt = 100 ms + 100 ms So, the standard deviation of V3 is = 200 ms 2.5 Volts. So, the conversion time is 200 ms.

Q.24 2.1 Q.26 (a) 1 From given data, we have 3 digit Consider the PMMC as zero centered 2 meter DMM, Average value of the above signal is Accuracy specification = ± 1% of full 1 12 tdt1dt scale T 01 (Accuracy class 1) 2 1 t 2 1 11 Reading = 100 mA on its 200 mA full t10.25 Amps 2222 0  scale 1  100mV reading on the 200mV full scale is 1 0 0 .0 mV 1 count on this 200mV full scale is 000.1 mV % error in reading = 1 200mA 100 2 Therefore, error can be calculated as Error = ± (2% of reading +1 class) 2  100.0mV+1 000.1mV 100

Q.1 TheGATE minimum QUESTIONS number of wattmeter(IN) Q.4 The voltage –flux adjustment of a (s) required to measure 3-phase, 3- certain 1-phase 220V induction wire balanced or unbalanced power watt- hour meter is altered so that is the phase angle between the applied a) 1 b) 2 voltage and the flux due to it is 85° c) 3 d) 4 (instead of 90° ). The errors [GATE-2001] introduced in the reading of this meter when the current is 5A at Q.2 The line to line input voltage to the power factors of unity and 0.5 3-phase 50Hz, ac circuit shown in lagging are respectively figure is 100V rms assuming that the a) 3.8mW, 77.4mW phase sequence is RYB the b)-3.8mW,-77.4mW wattmeter would read. C)-4.2W,-85.1W d) 4.2W, 85.1W [GATE-2003]

Q.5 The circuit in figure is used to measure the power consumed by the load. The current coil and the voltage coil of the wattmeter have 0 . 0 2Ω and 1000Ω resistances respectively .The measured power a) W886W12 andW896W compared to the load power will be

b) W500W12 andW500W

c) W0W12 andW1000W

d) W250W12 andW750W [GATE-2002] a) 0.4%less b) 0.2%less Q.3 A wattmeter reads 400W when its c) 0.2%more d) 0.4%more current coil is connected in the R [GATE-2004] phase and its pressure coil is connected between this phase and Q.6 A dc A-h meter is rated for 15A, the natural of a symmetrical 3-phase 250V.The meter constant is 14.4A system supplying a balanced star sec/rev. The meter constant at rated connected 0.8p.f. Inductive load. voltage may be expressed as The phase sequence is RYB. What a) 3750rev/kWh b) 3600 rev/kWh will be the reading of this wattmeter c) 1000rev/kWh d) 960rev/kWh if its pressure coil alone is [GATE-2004] reconnected between the B and Y phases all other connections Q.7 A single –phase load is connected remaining as before? between R and Y terminals of a a)400.0 b)519.6 415V, symmetrical 3-phase, 4wire c) 300.0 d)692.8 system with phase sequence RYB. A [GATE-2003] wattmeter is connected in the

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission system as shown in figure. The Q.11 The Figure shows a three –phase power factor of the load is 0.8 delta connected load supplied from lagging .The wattmeter will read a 400V 50 Hz, 3-phase balanced source. The pressure coil (PC) and current coil (CC) of a wattmeter are connected to the load as shown, with the coil polarities suitably selected to ensure a positive a) -795W b) -597W deflection. The wattmeter reading c) +597W d) +795W will be [GATE-2004]

Q.8 Two wattmeter, which are connected measure the total power on a three- phase system supplying a balanced load, read 10.5kW and -2.5kW, respectively. The total power and the power factor respectively, are a) 800 Wattt b) 1600Watt a) 13.0kW, o.334 b) 13.0 kW,0.684 c) 0 d) 400Watt c) 8.0kW, 0.52 d) 8.0kW,0.334 [GATE-2009] [GATE-2005] Q.12 A Wattmeter is connected as shown Q.9 A sampling wattmeter (that computes in the figure. The wattmeter reads power from simultaneously sampled values of voltage and current) is used to measure the average power of a load. The peak to peak voltage of the square wave is 10V and the current is a triangular wave of 5A p- p as shown in the figure. The period a) Zero always is 20ms. The reading in W will be b) Total power consumed by Z12 a n d Z

c) Power consumed by Z1

d) Power consumed by Z2 [GATE-2010]

a)0W b)25W Q.13 Consider the following statements: c)50W d)100W i) The compensating coil of a low [GATE-2006] power factor wattmeter compensates the effect of the Q.10 The pressure coil of a dynamometer impedance of the current coil. type wattmeter is ii) The compensating coil of a low a) highly inductive power factor wattmeter b) highly resistive compensates the effect of the c) purely resistive impedance of the voltage coil d) purely inductive circuit [GATE-2009] a) (i) is true but (ii) is false b) (i) is false but (ii) is true

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission c) Both (i) and (ii) are true Q.17 An LPF wattmeter of power factor d) Both (i) and (ii) are false 0.2 is having three voltage settings [GATE-2011] 300 V, 150 V and 75 V, and two current settings 5 A and 10 A. The Q.14 For the circuit in the figure, the full scale reading is 150. If the voltage and current expressions are: wattmeter is used with 150 V voltage setting and 10 A current vtEsinsin 13ωtEsinsin3ωt setting, the multiplying factor of the itlsin ωtΦlsin3ωtΦ   1  13  3 wattmeter is

lsin55  ωt [GATE-2014-3] lsin3ωtΦlsin5ωt 3 35 Q.18 A 3-phase balanced load which has a The average power measured by the power factor of 0.707 is connected Wattmeter is to balanced supply. The power consumed by the load is 5kW. The power is measured by the two- wattmeter method. The readings of the two wattmeters are a) 3.94 kW and 1.06 kW c) 5.00 kW and 0.00 kW 1 a) E111 l c o s Φ c) 2.50 kW and 2.50 kW 2 d) 2.96 kW and 2.04 kW 1 b) E l cosΦE lcosΦE l  [GATE-2015-2] 2 1 111 331 5 1 Q.19 The coils of a wattmeter have c) E lcos ΦE lcosΦ  2 1 113 33 resistances 0.010 and 10000; their 1 inductances may be neglected. The d) E lcos ΦE lcosΦ  2 1 113 11 wattmeter is connected as shown in [GATE-2012] the figure, to measure the power consumed by a load, which draws Q.15 Power consumed by a balanced 3- 25A at power factor 0.8. The voltage phase, 3-wire load is measured by across the load terminals is 30V. The the two wattmeter method. The first percentage error on the wattmeter wattmeter reads twice that of the reading is second. Then the load impedance [GATE-2015-2] angle in radians is π π Q.20 An energy meter, having meter a) b) constant of 1200 revolutions kWh, 12 8 makes 20 revolutions in 30 seconds π π c) d) for a constant load. The load, in kW is 6 3 [GATE-2016-2] [GATE-2014-1] Q.21 The voltage (v) and current (A) Q.16 While measuring power of a three- across a load are as follows. phase balanced load by the two- v(t) =100 sinω(t), i(t) = 10sin(ωt - wattmeter method, the readings are 60°) + 2sin(3ωt) + sin(5ωt) 100W and 250 W. The power factor The average power consumed by of the load is the load, in W, is______. [GATE-2014-2] [GATE-2016-2]

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission Q.22 A symmetrical three-phase three- wire RYB system is connected to a balanced delta-connected load. The RMS values of the line current and line-to-line voltage are 10 A and 400 V respectively. The power in the system is measured using the two wattmeter method. The first wattmeter connected between R- line and Y-line reads zero. The reading of the second wattmeter (connected between B-line and Y- line) in watt is ______. [GATE-2016]

Q.23 Identify the instrument that does not exist: a) Dynamometer-type ammeter b) Dynamometer-type wattmeter c) Moving-iron voltmeter d) Moving-iron wattmeter [GATE-2016]

Q.24 A 300 V, 5 A, 0.2 pf low power factor wattmeter is used to measure the power consumed by a load. The wattmeter scale has 150 divisions and the pointer is on the 100th division. The power consumed by the load (in Watts) is ______. [GATE-2018]

ANSWER KEY: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 (b) (c) (b) (c) (c) (c) (b) (d) (a) (b) (a) (d) (b) (c) 15 16 17 18 19 20 21 22 23 24 (c) 0.8 2 (a) 0.15 * 250 -3464.10 (d) 200

Q.1 (b) l lRR 3 6 . 8 7 ° Two wattmeter methods can also [pf=0.8lag.inductiveload] take care of unbalance.

Q.2 (c)

VL 1 0 0V V 100 II p LpZ 3560° 20 60°A 3 VVVYBYBB

WV1LL Icos30°  Φ V120°V240° 20 3V 90°V 100cos30°60°  3 ll36.87°ARR 2000 Angle between Vandl cos90°0W YBR 3 θ90°(36.87°)

WV2LL Icos30°  Φ  5 3 . 1 3 ° 20 As pressure coil connected between 100cos30°60° Y and B phases. 3 Reading of wattmeter 1000W VlcosYBR θ From eq(i)

3Vlcos(R 53.13) 3  500  0.6  519.6W

Q.3 (b)

Taking VR as the reference and VRR l cosΦ 400W assuming phase to natural voltage=V

VlR  0.8 400W Phase to natural voltage =V V V 0° VlR  400 R

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission Vy V 1  2 0 ° Q.6 (c) And V V 2 4 0 ° Meter constant m =14.4A sec/rev B To express meter constant in the unit rev/ kWh Q.4 (c) Meter constant Measured value V I s i n (Φ) 11rev M' Where  Phase angle between M14.4Asec voltage and flux 1rev13600sec c o sΦ p o w e r f a c t o r M'3  10 14.4 Asec250V1hr True value  V I c o sΦ  360010 3 Error =Measured value –True value  rev/kWh Case-I 14.4250  85°,pfcos Φ1,Φ0° 1 0 0 0 r e v/ k W h V 2 2 0 V ,l 5 A Q.7 (b) Error VIsin  ΦVIcosΦ   Line of line voltage =450V 2205sin850°22011 415 Phase to natural voltage  V 4 . 2 W 3

Case-II Taking VR as the reference,  85°,pfcos Φ0.5,Φ60° 415 V 0 ° V RN 3 Error 415 V120°V 2205sin 8560°22050.5 YN 3 415 85.1W And V  240°V BN 3 Q.5 (c) VVVRYRNYN Load power (true power ) 415415 2002014000W 0°V120°V Resistance of current coil 33 R0.02 41530°V CC Load current Current through CCl20AC VRY 41530° Power consumed by current coil lL  2 z10036.87  lRcCC 4.156.87°A 200.028W2 Current through current coil

Measured power = power consumed lCC l L  4.15  6.87°A by load + power consumed by Voltage across pressure coil current coil Measured power =4000+8=4008W%error Phase angle between Vandl Measured power True power BNCC 100 True power Φ  240°   6.87°  40084000  233.13° 100 4000 Wattmeter reading  VBN l L cosΦ  0.2%(more) 415  4.15  cos233.13   597W 3

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission Q.8 (d) Wattmeter reading P10.5kWandP2.5kW   12 Vpccc l c o s Φ Total power PP10.52.5 12 4004cos120°   8kW 8 0 0 W Power factor

1 PP12 Q.12 (d) cosΦcostan3 PP12

1 10.5(2.5)  costan3 10.5(2.5) =0.334

Q.9 (a) Potential coil draws negligible current, so

Current through Z12 a n d Z is same Current through current coil

IIcc

Voltage across potential coil  Vpc

Voltage across Z2pc V V Positive power= negative power Wattmeter reads power consumed So average power=0W by Z2 as voltage across Potential coil =Voltage across Q.10 (b) It is difficult to have purely resistive Current through current coil pressure coil. The pressure coil has =current through a small value of inductance. Due to which error occurs in wattmeter Q.13 (b) readings.

Q.11 (a) Assuming phase sequence abc

Line to line voltage V400Vll 

Taking Vab as the reference VV0°4000°V The current coil caries a current of abl l  ll and produces a filed V400120°V p bc corresponding to this current. The Current through current coil compensating coil is connected in Vca 400 240°V lCC  series with the pressure coil circuit Z2 100 j0 and is made as nearly as possible 4240°V identical and coincident with the Voltage across pressure coil current coil. It is so connected that it

VVpcbc opposes the field of the current coil. 400  120°V The compensating coil carries a current l and produces a field Φ = angle betweenlCCand Vpc p  120  240°   120° corresponding to this current. This

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission field acts in opposition to the the wattmeter should be taken into current coil field. Thus the resultant account. Therefore, Multiplying field is due to current I only. Hence Factor = (Current range the error caused by the pressure coil used*Voltage range used*p.f) / current flowing in the current coil is Power at FSD Given, Power at Full neutralized scale reading = 150 dini‘b Current Range used = 100A - Voltage Range Q.14 (c) used r=150 VI ring Success Power Factor 1=0.2 ONNE MEM NENE v t   E13 sinωt E sin3ωt 10x150x 0.2 Therefore, m = _2 150 i t  l1 sin ωt  Φ1   l 3

sin3  ωtΦlsin5ωt35 Q.18 (a) Average power 2π Q.19 (0.15) 1 P v i d( ω t) P load = 30x25x08 = 600W avg 2π  0 Wattmeter measures loss in The products of different frequency pressure coil circuit terms have zero average value Load 11 2 2 V loss in P = -30 = 0.9W Rp 1000 PE lcosΦElcosΦ avg1 1133322 9 error = 0.x100 = 0.15% 600

Q.15 (C) Q.20 K =1200rev/kwh = 20revolutions I I π 1. "" 3600 jhrm. (30 1P = 2kW 91 When load impedance is 6 radians. The first wattmeter reads Q.21 (250) twice that if the second wattmeter. The instantaneous power of load is p(t) = V(∈)i(t) Q.16 (0.802) [(100sinωt)(10sin(ωt - 60)] + In two-wattmeter method, [(100sinωt) (2sin3ωt)]+[(100 The readings are 100 W & 250 W sinωt,)(5sin5ωt)] Power factor = cos ϕ T → since, P P t dt in the above 3 ωω avg     costan1 12 0 ωω 12 expression Only 1st term will result non zero 3(150)  costan1  answer 350 Remaining 2 terms wiII be 0. =0.8029 → so directly consider [P(t) = 100sinωt] [10(sinωt-60)] Q.17 (2) P t100sin  ωt 10(sinωt 60) In LPF wattmeter, Td on the moving 100 10 system is small owing to low power PVavgrms Icos rmsv1 θθ 22 factor even when the current and 1000 1 potential coils are fully excited. Also cos(60) 250watt the errors introduced due to 22 inductance of pressure coil tend to be large at low power factors. So for Q.22 -3464.10 calculating multiplying factor for a From given question, using formula low p.f. wattmeter, p.f. mentioned on

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission   WW21 tan3  WW   21 (Since W1 = reading of the first Wattmeter = 0, W2 = reading of the Second Wattmeter) W 332 W2 tan3601o

TotalPower PWWWT212

3VIcosLL  3400100.5  3464.10Watt The wattmeter connected between B-line and Y-line it read negative, so PT = – 3464.10 W

Q.23 (d) To Measure power we require to coils (C.C & P.C)  Dynamo meter will consist two coils. So it can measure power. Dynamo meter can also measure current and voltage, if we connect C.C & P.C in series. Moving Iron meter will have only one coil, so it can measure current and voltage but not power. Note: Moving Iron wattmeter doesn’t exist.

Q.24 200 Given : 300 V, 5 A, 0.2 pf low power factor wattmeter Wattmeter scale has 150 division and the pointer is on the 100th division. Power P300   5W 300 For 100th division P100   200 W 150

3.1 CLASSIFICATION OF RESISTANCE 1. direct deflection method (like ohmmeter method) de'Arsenol a) low resistance  less than 1 Galvanometer is used-for deflection. b) medium resistance  between '1'  2. Loss of charge method and 0.1M. 3. Mega Ohm Bridge method c) High resistance  Above 0.l M  4. Meggar (used in measurement of earth resistance).Ohm-meter 3.1.1 MEASUREMENT OF LOW RESISTANCE  It is a device which gives direct reading a) Ammeter-Voltmeter method for the measurement of a resistance. b) Kelvin's Rouble bridge method  This instrument has low degree of c) Potentiometer method accuracy. Note:  It is generally used for the 1. Low resistances have four terminals measurement of hetero resistance of two current terminalstwo voltage field winding of m/cs, Measurement of terminals. This is done to avoid contact resistances used in electrotronics lab. resistance effect  Cheking of diodes. 2. The range of resistance measured by Kelvin double bridge is from 0.1  to 1 3.3 TYPES OF OHMMETER . 3. Measurement of medium resistances. 1. Series type (i) Ammeter-Voltmeter method 2. shunt type (ii) Substitution method (iii)Wheatstone Bridge, 3.3.1 L SERIES TYPE (iv)Ohmmeter method. R  current limiting resistance. 3.1.2MEASUREMENT OF HIGH RESISTANCES se Rsh used to adjust the meter current for different categories: full scaledeflection. (i) insulation resistance of m/c and cable E  internal battery of meter. (ii) leakage resistance of the capacitor Rx = 0 Give full scale def. (iii)leakage resistance of vacuum tube Rx =  Give null def. (iv)surface resistance. 3.1.3 DIFFICULTIES IN MEASUREMENT OF HIGH RESISTANCES (i) leakage resistance (ii) Electrostatic effect. (iii)Capacitance of the specimen under measurement. Note: Guard Ckt. is used to eliminate the errors due to leakage current.

3.2 DIFFERENT METHODS OF MEASUREMENT

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission The value of resistance Rx for mid scale deflection. Rx = Rh = internal resistance of  meter gives half scale deflection

RRm sh RRh se (i) RRm sh Current supplied by battery at half scale deflection At Full scale deflection

E Rx  IIsc h 2Rh E IIm  fs  (i) IIIsh se fs RR1m E E IIsh fs RR (ii) R 1m h Ifs The voltage across Rsh = voltage across At any intermediate deflection: meter. E R x Im  I,RIRsh sh fs m RR RR R  mx mx IRIR 1 RR R fs m fs m mx sh IE/RI ER sh h fs I  x m R(RR)RR IRR 1 m x m x Rsh  fs m h (ii) ERI h fs Note: Shunt type ohmmeter is particularly suitedfor measurement of low resistances. Note: Megger: It is an instrument used for the for 10% drop in battery emf. Rsh is given measurement of insulation resistance & by:(E  0.9 E) earth resistances. IRR Scale : scale is compressed near pt. 'o' and R  fs m h sh 0.9E R I expands wards '  ' resistance. h fs The test voltage is generated by hand Note: driven generator. Mag. shunt is used across pole pieces. Polepieces of PMMC (magnets of PMMC) to reduce the effect of 3.4 BRIDGE MEASUREMENTS change in battery of emf. with changing the ckt elements. 3.4.1 A.C. BRIDGES

3.3.2 SHUNT TYPE i) used to measure self inductance, mutual inductance capacitance, and frequency. Rx = 0. Gives null deflection. ii) Types of sources Rx =  gives full scale deflection.  for low frequency: power line supply can be used,  for high frequency: electronic oscillator is used. iii) Types of detectors:  Head phones (250 Hz to 3/4 KHz)

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission  vibrational Galvanometer (5Hz- ZZZZ1 4 2 3 1000 Hz) (R1 jL)(R)  1 4  (R 2  jL)R  2 3  Tuned amp. (10 Hz -100 KHz) R1 R 4 j  L 1 R 4  R 2 R 3  j  L 2 R 3 Measurement of Inductance:

1. Self Inductance Bridges (i) Maxwell's inductance (ii) Maxwell's inductance capacitance bridge, (iii)Hay's Bridge (iv)Anderson's Bridge (v) Owen's Bridge 2. Measurement of Capacitance (i) De-Sauty Bridge (ii) Schearing Bridge 3. Measurement of frequency (i) Wein's Bridge 4. Measurement of mutual Inductance

3.4.2 GENERAL THEORY:

Comparing Real and Im. Parts

RRRR1 4 2 3

RR23 R1 (i) R 4

and L1 R 4   L 2 R 3 At balance LR L  23 (ii) Z .Z Z .Z 1 1 4 2 3 R 4

Let Z1 Z 1  1 Note ZZ2 2  2 by taking R2 + L1 as variable independent ZZ  3 3 3 balance is obtained for R1 and L1

ZZ4 4  4 3.4.4 MAXWELL'S INDUCTANCE Then Z1Z4 = Z2Z3 CAPACITANCE BRIDGE  1   4   2   3 At balance 3.4.3 MEASUREMENT OF SELF Z1Z4 = Z2Z3 INDUCTANCE R 4 [(R1+jL1)]  =R2R3 Maxwell’s inductance bridge 1 j C44 R

At balance R1 R4 + JL1R4 = R2 R3 +  C4 R2 R3 R4

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission wide range of inductance at power and audio frequencies. iv) it gives independent balances for R1 and L1.

3.4.5 HAY’S BRIDGE

Z1 = R1 + jL1 Z2 = R2 Z3 = R3 1 ZR44 jC 4 L 1 Qfactor 1 RCR1 4 4

Comparing real and im. Parts. R1R4 = R2R3

RR23 R1  R 4

and L1 R 4   C 4 R 2 R 3 R 4

LRRR1 2 3 4

L1 Q.factor : C44 R R1

Note: i) Maxwell's inductance capacitance bridge is used only for coils having low Q factor.(1 < Q < 10) ii) Maxwell's inductance-capacitance At balance bridge uses variable capacitance. The ZZZZ1 4 2 3 value of this capacitance is difficult to (R jL)(R   j/  C)  RR determine accurately. 1 1 4 4 2 3 iii) Maxwell's inductance capacitance LR11    R4 R 1    j   L1 R 4   R2 R 3 bridge can be used for measurement for CC44   

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission Comapring the real and imp. Parts. The anderson's bridge is used to avoid the L use of variable capacitor. RRRR1 1 4 2 3 And it is used for the measurement of C4 inductance having RR L 23 1 At balance: R1  RCR4 4 4 vab = vad + vdc and L R  R /  C  0 (R1 + jL1)I1 = R2I2 = rIC…(i) 1 4 1 4 Also at balance RL11RR23 LR    vbc = vdc 14 CCRCR   2 4 4 4 4 4 I RI  c 1 RR 31 23 jC 4 LR14 2 2  2 CRCR 4 4 4 4 Ic j C 4 R 3 I 1 (ii)

RR23 2 (r1+R1+jL1)I1 = R2I2 = JC4 R3 rI1 CR44 CR44 [r1 + R1 + j(L1 -  C4R3r)] I1 = R2 I2 L1  2 2 2 (1 C44 R )

RRC2 3 4 L1  2 1 1  Q 1 is neglected for Q>10. (Q)2 Note From above equation we observed that Also at balance: balance equation depends upon the -Icr + I4R4 = I1R3 frequency ofsource. The balance can be I4 = I2 - Ic obtained by making it independent if -Icr + (I2 – Ic) R4 = I1 R3 frequency of Q factor is greater than 10.  -Ic(r + R4) + I2R2 = I1R3 Hey's bridge is used for measurement of -Ic(r + R4) + I1R2 = I1R3 inductance with quality factor (Q > 10) -jC4R3(r + R4)I1-I1 R3 = - I2 R4 j C4 R 3 (r  R 4 )  R 3 II21 3.4.6 ANDERSON’S BRIDGE R4

r1  R 1  j(  L 1   C 4 R 3 r) j R C R (r  R )  R R  2 4 3 4 2 3 R4 Comparing real and imaginary

RR23 rR11 R 4

RR23 Rr11 R 4

R2 C 4 R 3 (r R 4 ) L   C43 R r  R4 R C R (r R ) L  2 4 3 4  C R r 1 R 4 3 Note 4

At balance 3.5.1 INTRODUCTION Z1Z4 = Z2Z3 Alternating current bridge methods are of 3.4.8 WIEN’S BRIDGE outstanding importance for measurement of electrical quantities. Measurement of (1) freq. measurement inductance, capacitance, storage factor, loss (2) harmonic distortion analyzer factor may be made (3) notch filter (4) audio and HF oscillator 3.5.2 SOURCES AND DETECTORS

RR14 CR11 1 =R 2  + jCRR1 1 2 R C c For measurement at low frequencies, the 3 2 2 power line may act as the source of supply Comparing both sides to the bridge circuit. For higher frequencies RRCR1 4 1 1 electronics oscillators are universally used R 2 …(i) RC32 as bridge source supplies. These oscillators And have the advantage that the frequency is 1 constant, easily adjustable, and CRR 1 1 2 C determinable with accuracy. The waveform 2 is very close to a sine wave, and their 1  power output is sufficient for most bridge CCRR1 2 1 2 measurement. A typical oscillator has a 1 frequency range of 40 Hz to 125 kHz with a f. …(ii) power output of 7 W. 2 C C R R 1 2 1 2 The detectors commonly used for a.c. bridges are (i) Head phones, (ii) Vibration From Equation (i) galvanometers, and (iii) Tuneable amplifier detectors. RRC4 2 1  Head phones are widely used as detectors RRC 3 1 2 at frequencies of 250 Hz and over upto 3 or

whenC1 C 2 ,R 1 R 2 4 kHz. They are most sensitive detectors for this frequency range. R43 2R Vibration galvanometers are extremely 1 and f  useful for power and low audio frequency 2 RC ranges. Vibration galvanometers are manufactured to work at various Note: frequencies ranging from 5 Hz to 1000 Hz 1. Wein's bridge is used for measurement but are most commonly used below 200 Hz of frequency from 100 Hz to 100 KHz as below this frequency they are more Audio AndHF frequency range. sensitive than the head phones. 2. Wein's bridge can be used as Notch Tuneable amplifier detectors are the most filler in Harmonic distortion analyser. versatile of the detectors. 3. Harmonics in supply can disturb the This detector can be used, over a frequency balance. It is very sensitive towards range of 10 Hz to 100 kHz. harmonics in supply. 4. Wein's bridge can also be used for measurement of capacitance.

R3 R1  (R2 r 2 ) R 4 Maxwell’s Inductance – Capacitance Bridge

R4 (R1 j L 1 )  R2 R 3 or R 1 R 4 j L 1 R 4 1 j C44 R

R2 R 3 j R 2 R 3 C 4 R 4 General Equation for Bridge Balance. Impedance Z1, Z2, Z3 and Z4. E4 = E2 I1Z1 = I2Z2 E orI1 = I3 = ZZ13 E I2 = I4 = ZZ24 Z1Z4 = Z2Z3 Y1Y4 = Y2Y3

(Z1 1 )(Z 4  4 )(Z  2  2 )(Z 3  3 )

Z1Z4  1 + θ4 = Z2Z3  2 + θ3 Z1Z4 = Z2Z3

1 + 4 = 2 + 3

3.5.3 MAXWELL’S INDUCTANCE BRIDGE.

RR23 R1  R 4

L1 = R2R3C4

Q = ωL1/R1 = ωC4R4 ADVANTAGES 1. The two balance equations are independent 2. The frequency does not appear in any of the two equations. 3. Simple expression for unknowns L1 and R1 in terms of known bridge elements. 4. The Maxwell’s is inductance – capacitance

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission bridge is very useful for measurement of a ADVANTAGES wide range of inductance at power and 1. In case adjustments are carried out by audio frequencies. manipulating control over r1 and r2. This is a marked superiority over Disadvantages sliding balance conditions met with low 1. This bridge requires a variable standard Q coils when measuring with Maxwell’s capacitor which may be very expensive. bridge. It is much easier to obtain 2. The bridge is limited to measurement of balance in the case of Anderson’s bridge low Q coils. (1 < Q < 10). than in Maxwell’s bridge for low Q-coils. The Maxwell’s bridge is also unsuited for 2. A fixed capacitor can be used instead of coils with a very low value of Q (i.e. Q < 1). a variable capacitor as in the case of Maxwell’s bridge. 3.5.4 HAY’S BRIDGE 3. This bridge may be used for accurate determination of capacitance in terms ADVANTAGE of inducatance. 1. This bridge gives very simple expression DISADVANTAGES for unknown inductance for high Q 1. The Anderson’s bridge is more complex coils, than its prototype Maxwell’s bridge. Q> 10. 2. An additional junction point increase 2. This bridge also gives a simple the expression for Q factor. difficulty of shielding the bridge. 3. for high Q coils its value should be small. 3.5.6 OWEN’S BRIDGE This bridge requires only a low value This bridge may be used for measurement resistor for R4, whereas the Maxwell’s of an inductance in terms of capacitance. bridge requires a parallel resistor, R , of 4 11    a very high value. (R1 j L 1 )   R2   R3 j C42   j C 

DISADVANTAGE L1=R2R3C4 This bridge is not suited for measurement C RR 4 of coils having Q less than 10 and for these 13C applications a Maxwell’s bridge is more 2 suited. ADVANTAGES 3.5.5 ANDERSON’S BRIDGE 1. Examining the equations for balance, we This bridge, in fact, is a modification f the find that we obtain two independent Maxwell’s inductance-capacitance bridge. equations in case C2 and R2 are made In this method, the self – inductance is variable. Since R2 and C2, the variable measured in terms of a standard capacitor. elements, are in the same arm, This method is applicable for precise convergence measurement of self – inductance over a to balance conditions is much easier. very wide range of values. 2. The balance equations are quite simple RR and do not contain any frequency Rr23 component. 11R 4 3. The bridge can be used over a wide R3 range of measurement of inductances. L1  C [r(R4  R) 2  RR] 2 4 R4

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission DISADVANTAGES to obtain balance if both the capacitors are 1. This bridge requires a variable not free from dielectric loss. Thus with this capacitor method only loss – less capacitors like air which is an expensive item and also its capacitors can be compared. accuracy is about 1 percent. In order to make measurement 2. The value of capacitance C2 tends to onimperfect capacitors (i.e., capacitors become rather large when measuring having dielectric loss), the bridge is high Q coils. modified as shown in fig.

3.6 MEASUREMENT OF CAPACITANCE

3.6.2 SCHERING BRIDGE 3.6.1 DE SAUTY’S BRIDGE The bridge is the simplest method of The connections and phasor diagram of the comparing two capacitances. The bridge under balance conditions are shown connections and the phasor diagram of this in fig. bridge are shown fig. C1 = capacitor whose capacitance is to be measured, C2 = a standard capacitor, R3, R4 = non – inductive resistors. 11     RR43   j C12   j C  C1 = C2.R4/R3 The balance can be obtained by varying either R3 or R4. The advantage of this bridge is its simplicity. But this advantage is nullified by the fact that it is impossible

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission  Campbell’s Bridge  Carey Foster Bridge; Heydweiller Bridge This bridge was used basically by Carey Foster but was subsequently modified by Heydweiller for use a.c. Both names are associated with the bridge and is used for two opposite purpose: (i) It is used for measurement of capacitance in terms of a standard mutual inductance. The bridge in this case in known as Carey Foster’s bridge. Equating the real and imaginary terms. We (ii) It can also be used for measurement obtain r1 = R3C4/C2 of mutual inductance in terms of a C1 = C2 (R4/R3) standard capacitance and is then Two independent balance equations are known as Heydweilling bridge. obtained if C4 and R4 are chosen as the variable element. 3.7 MEASUREMENT OF FREQUENCY Dissipation factor D = tan δ = ωC r = ω. 1 1 1 Some bridges have balance equations (C R /R ) × (R C /C ) = ωC R ….(16.37) 2 4 3 3 4 2 4 4 which involve frequency directly in balance Therefore values of capacitance C , and its 1 equation. dissipation factor are obtained from the values of bridge elements at balance. 3.7.1 WIEN’S BRIDGE Let us say that the working frequency is 50 Hz and the value of R4 is kept fixed at The Wien’s bridge is primarily known as a 3,180 Ω. frequency determining bridge but also for Dissipation factor D1 = 2π × 50 × 3180 × its application in various other circuits. A C4 = C4 × 106. Wien’s bridge, for its application be Schering bridge is widely used for employed in a harmonic distortion capacitance and dissipation factor analyzer, where it is used as notch filter, measurements. In fact Schering bridge is discriminating against one specific one of the most important of the a.c. frequency. The Wien’s bridge also finds bridges. Measurement of the properties of applications in audio and HF oscillators as insulators, capacitor bushings, insulating the frequency determining device. oil and other insulating materials. This R1  1  measurement done on small capacitances  RRR4  2  3 1 j C R C suffer from many disadvantages if carried 1 1  2  out at low voltages. High voltage Schering R1 and R2 are mechanically R1 = R2. bridge is certainly preferable for such C1 and C2 are fixed capacitors equal in value measurements. and R4 = 2R3, the Wien’s bridge may be 3.6.3 MEASUREMENT OF MUTUAL used as a frequency determining device. INDUCTANCE This bridge is suitable for measurement of  Heaviside Mutual Inductance Bridge frequencies for 100 Hz to 100 kHz. It is  Campbell’s Modification of Heaviside possible to obtain an accuracy of 0.1 to 0.5 Bridge per cent.  Heaviside Campbell Equal Ratio Bridge

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission The bridge is not balanced for any harmonics present in the applied voltage. The difficulty can be overcome by connecting a filter in series with the null detector. A Wien’s bridge may be used for measurement of capacitance also.

3.7.2 UNIVERSAL IMPEDANCE BRIDGE

One of the most useful and versatile laboratory bridges is the Universal Impedance Bridge. This instrument is capable of measuring both d.c. and a.c. resistance, inductance and storage factor Q factor of an inductor, capacitance and dissipation factor D of a capacitor. The universal bridge consists of four basic bridge circuits. It has suitable a.c. and d.c. sources, a.c. and d.c. null detectors, and impedance standards. The Wheatstone bridge is used for both d.c. and a.c. resistance measurements.

3.7.3 WAGNER EARTHING DEVICE very high accuracy in measurement is made possible by the additional of a Wagner earthing device. This device removes all the earth capacitances from the bridge network.

Fig : Wagner Earthing Devise

Q.1 Kelvin double bridge is best suited a) R1342 R R / R for the measurement of b) R R R / R a) Resistance of very low value 1234 c) R R R / R b) Low value capacitance 1243 c) Resistance of very high value d) RRRR1 2  3  4 d) High value capacitance [GATE-2006] [GATE-2002] Q.5 Suppose that resistors R1 and R2 are Q.2 A dc potentiometer is designed to connected in parallel to give an measure up to about 2V with a slide equivalent resistor R. If resistors R1 wire of 800mm. A standard cell of and R2 have tolerance of 1% each, emf 1.18V obtains balance at the equivalent resistor R for 600mm. A test cell is seen to obtain resistors R1 = 300Ωand R2 = 200Ω balance at 680mm. The emf of the will have tolerance of test cell is a) 0.5% b) 1% a)1.00V b)1.34V c) 1.2% d) 2% c)1.50V d)1.70V [GATE-2014-2] [GATE-2004] Q.6 An unbalanced DC Wheatstone Q.3 The set-up in the figure is used to bridge is shown in the figure. At measure resistance R. The ammeter what value of p will the magnitude and voltmeter resistance are 0 . 0 1Ω of Vo be maximum? Ai‘ir1 and2000Ω , respectively Their Engineering SI reading are 2A and 180V, giving a [GATE-2015-1] measured resistance of 90Ω .The percentage error in the Q.7 The bridge most suited for measurement is measurement of a four-terminal resistance in the range of 0.001to0.1 is a) Wien’s bridge b) Kelvin double bridge c) Maxwell’s bridge d) Schering bridge a)2.25% b)2.35% [GATE-2015] c) 4.5% d)4.71% [GATE-2005] Q.8 A dc potentiometer, shown in figure below, is made by connecting fifteen 10  resistors and a 10 slide Q.4 R1 and R4 are the opposite arms of wire of length 1000 mm in series.

a Wheatstone bridge as are and R2 . The potentiometer is standardized The source voltage is applied across with the current Ip = 10.0000 mA. and R .Under balanced Balance for an unknown voltage is 3 obtained when the dial is in position conditions which one of the 11 (11 numbers of the fixed 10 following is true?

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission resistor are included) and the slide wire is on the 234th mm position. The unknown voltage (up to four decimal places) in volt is ______.

[GATE-2016]

Q.9 When the voltage across a battery is measured using a d.c. potentiometer, the reading shows 1.08V. But when the same voltage is measured using a Permanent Magnet Moving Coil (PMMC) voltmeter, the voltmeter reading shows 0.99V. If the resistance of the voltmeter is 1100  , the internal resistance of the battery, in , is ______. [GATE-2017]

ANSWER KEY: 1 2 3 4 5 6 7 8 9 (a) (b) (c) (b) (b) (a) (b) 1.1234 100

Q.1 (a)

Q.2 (b)

Estands1  call of emf1.18

l1 6 0 0 m m

Eemf2  of the test cell

l 62 8 0 m m The voltage of any point along the slide wire is proportional to the Adjustments are made in various length of slide wire. arms of the bridge so that the El voltage across the detector is zero El 11 and hence no current flows through El22 it, when no current flows through it, l2 680 when no current flows through EE1.181.34V21 l6001 detector the bridge is said to be balanced. Q.3 (c) Under conditions of balance Measured value of resistance R3 RR12  90Ω R4 Resistance of voltmeter

R2000v  Ω Q.5 (b) Voltage across voltmeter V=180 R1 = 250 ±1%

V RR12 Current through voltmeter = RT  R v RR12 180 R3001% R136.36 Ω 0.09A 2 T 2000 R % E100T Current through resistance RT RT RI2I20.09   Rv R ΔRRΔR =±.+.×100T1T2 IR 1.91A  RRRR1122 True value o resistance R.RR.R V 180 R =1 1 =2.5; R = 2 2 94.24Ω 12100 100 I 1.91 R 136.36 2.5 136.36 3 measured value True value   .  .%  1 %error 100  True value 250 250300 300 9094.24 100 94.24 Q.6 (a) 4.5% Q.7 (b) Q.4 (b) Q.8 1.1234 Slide wire resistance = 10  (for 1000 mm).

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission For 234 mm length, PMMC reads, 234 R =102.34  v0.99V.m  1000 ByKVL When dial is at position 11 then total resistance = 110  V= 1.080.99 Unknown voltage V=0.09Volts. VX = (110 + 2.34) 10 mA Vm 0.99 4 VX = 1.1234 Volt Im 910AMPS. So, the unknown voltage is 1.1234 V. R1100v V0.09 R 100 Q.9 100 i 4 I910m We use potentiometer to measure unknown voltages (very low) it is a Null type instrument

The Galvanometer reads zero when the voltage drop across slide wire and unknown Battery voltages are equal.

Given that potentiometer reading as 1.08V i.e., The Battery voltage will be 1.08 volts

Q.1 The items in List-I represents the a) First adjust R4 , and then adjust various types of measurements to R be made with reasonable accuracy 1 b) First adjust R , and then adjust using a suitable bridge. The items in 2

List –II represent the various R 3 bridges available for this purpose c) First adjust , and then adjust .Select the correct choice of the item in List –II for the corresponding item in List –I from the following d) First adjust , and then adjust List-I a) Resistance in the milli-ohm rage [GATE-2007] b) Low value of Capacitance c) Comparison of resistance which Q.3 The Ac Bridge shown in the fig. is are nearly equal used to measure the impedance Z. d) Inductance of a coil with a large time –constant List-II 1) Wheatstone Bridge 2) Kelvin Double Bridge 3) Schering Bridge 4) Schering Bridge 5) Hay’s Bridge 6) Carey –Foster Bridge If the bridge is balanced for Codes: oscillator frequency f=2 kHz, then A B C D the impedance Z will be a) 2 3 6 5 a) (260j0) Ω b) (0j200) Ω b) 2 6 4 5 c) (260j200) Ω d) (260j200) Ω c) 2 3 5 4 [GATE-2008] d) 1 3 2 6 [GATE-2003] Q.4 The Maxwell’s bridge shown in the figure is at balance, the parameters Q.2 A bridge circuit is shown in the of the inductive coil are figure below. Which one of the sequence given below is most suitable for balancing the bridge?

a) RRR/R,LCRR2 3 4 4 2 3

b) LRR/R,RCRR2 3 4 4 2 3

c) RR /RR,L42 3 1/ CRR 4 2 3 

d) L R/RR,R4 2 3 1/CRR 4 2 3  [GATE-2006]

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission Q.5 The bridge circuit shown in the figure is used for the measurement of an unknown elements Zx The bridge circuit is best suited when Zx is a

[GATE-2014-1]

a) low resistance b) high resistance Q.9 In the bridge circuit shown, the c) low Q inductor d) lossy capacitor capacitors are loss free. At balance, [GATE-2006] the value of capacitance C1 in microfarad is Q.6 The bridge method commonly used [GATE-2014-3] finding mutual inductance is a) Heaviside Campbell bridge Q.10 The resistance and inductance of an b) Schering bridge inductive coil are measured using an c) DeSauty bridge AC bridge as shown in the figure. d) Wien bridge The bridge is to be balanced by [GATE-2006] varying the impedance Z2.

Q.7 Three moving iron type voltmeters are connected as shown below.

Voltmeter readings are V,VandV12 as indicated. The correct relation among the voltmeter readings is

For obtaining balance, z2 should consist of elements: VV12 a) V  b) VVV12 (A) R and C (B) R and L 22 (C) L and C (D) Only C

c) VVV 12 d) VVV21 [GATE-2014] [GATE-2013] Q.11 A capacitor ‘C’ is to he connected Q.8 The reading of the voltmeter (rms) across the terminals ‘A’ and ‘B’ as in volts, for the circuit shown in the shown in the figure so that the figure is power factor of the parallel combination becomes unity. The value of the capacitance required μFis ______

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission Q.13 A high Q coil having distributed (self) capacitance is tested with a Q- 6 meter. First resonance at 1 10 rad/s is obtained with a capacitance of 990 pF. The second resonance at 6 2 2 10 rad/s is obtained with a 240 pF capacitance. The value of the inductance (in mH) of the coil is (up [GATE-2014] to one decimal place) ______. [GATE-2018] Q.12 The inductance of a coil is measured using the bridge shown in the figure. Balance (D = 0) is obtained with

C1 1nF, R1  2.2M  R2  22.2k  R4  10 k  The value of the inductance Lx (in mH) is ___.

[GATE-2014]

ANSWER KEY:

1 2 3 4 5 6 7 8 9 (a) (c) (a) (a) (c) (a) (d) 142 0.3 10 11 12 13 (b) 187 222 1

Q.1 (a) ω R22 R C R  234  Wheat stone bridge is used for 2 1 ω C222 R measurement of medium 44 Q factor of the coil resistance. ωL 1  Kelvin double bridge is used for Q 1 measurement of low resistance. R144 ω C R

 Schering bridge is used for R R234 C Therefore L1  2 ….(i) measurement of low value of 1 capacitances. 1  Q  Wein’s bridge is used for 22 measurement of the frequency ω R2 R 3 R 4 C 4 And R1  2 …(ii)  Hay’s bridge is used for 1 1  measurement inductance of a Q coil with a large time constant. For a value of greater than10, the  Carey- foster bridge is used for 2 comparison of resistances which term 1/  Q will be smaller than are nearly equal. 1/1000 and can be neglected Therefore eq (i) and (ii) reduces to

Q.2 (c) LRRC1234 (iii) 1 R  ωRRC22 (iv) x114ωL andx 1234 ωC4 R4 appears only in eq. (iv) and R2 zRjxRj ωL 11111 appears in both eq (iii) & (iv) zR22 So first is adjusted and then

zR33 is adjusted. 1 zRjx 444 R4 Q.3 (a) ωC4 Under balanced condition

z1 z 4 z 2 z 3

Rj1ωL 1 R 4  jx 4   R 2 R 3

LR11    R1 R 4   jωL1 R 4   R2 R 3 C44   ωC  Equating real and imaginary terms,

we obtain ZAB  500Ω L 1 ZZCD  RRRR1 4 2 3 C4 1 ZRBC BC R1 jωC ωL14 R0 ωC4 j 300 Solving above equations, we get 2π 2  100.39836 10  RRC2 3 4 Z 300 j200Ω L  and BC 1 1 ω2 C 2 R 2 44 ZAD R AD jωL

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission 33 The bridge is Maxwell Bridge. Z300j2AD  π21015.9110 3 0 0 j 2 0 0 Ω Element is an inductor Element is an inductor At balance Inductance  Lx effective resistance ZZZZABCDBCAD of the inductor =R x ZZCD  ωL ZZ Q x ω C R ….(i)  BCAD R 11 Z x AB The bridge is limited to 300 j200   300  j200  Z measurement of low Q inductor 500 (110 the bridge is unsuitable. The bridge is also unsuited for coils with very low values of Q (i.e. Q<1)

zRj1 ωL zR Q.6 (a) 22 Heaviside Campbell bridge method zR 33 commonly used for finding mutual j inductance. zR44 ||  ωC4 Q.7 (d) 1 R 4 V1   | j1Ω |  l R4 ||  ωC1jωC4 R 44  V2   | j2Ω |  l At balance V  j1Ω  l  j2Ω  l zzzz1423  VV21

R4 RjωLRR23 1j ωC44 R Q.8 (142)

RRj4  ωLR R1jωC23  R 44

RRj4 ωLRR4232344 RjωR R R C Equating real and imaginary terms,

RRRR423 RR R  23 R4 Net z=j1 - j1 = 0, acts as short circuit 100sin(ωt) ωLR4 ωR 2 R 3 R 4 C 4 i t = =200sin(ωt) LRRC 0.5 2 3 4 i(t) i = =100sin(ωt)=i vv122 Q.5 (c) V11 =(-j )100sin(ωt)

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission V21 = ( j ) 1 0 0 s i n ( ω t ) Q.12 222 Given figure, V=V-V=j200sin(12 ωt) V 200 V m 141.42Volts RMS 22

Q.9 (0.3) Bridge is balanced

C1 1nF,R2.2MR22.2kR101 2 k 4

Above bridge is the example of Maxwell inductance Capacitance 0.3μF Bridge. Bridge is balanced For a Maxwell bridge the value of Lx z1 z 4 = 2 3 z z is given by, 11 LRRC 35k.=105k. x 241 jω0.1μFjωc 39 1 L22.21010110222mHx 

C0.31  μF

Q.10 B Q.13 1

RR144 jL At balance,  66 Given :1012 ,2  10  , R32z C990pF, C240 pF R 12 zRjL 3  2 106 2  44 n = 2 2 R1 6  10 Thedistributed capacitance is given by, Q.11 187 2 Cn12 C Cd  2 When C is connected across terminal AB, n 1 990 22402 V C 10pF current, I= Vj c d 212  R + j L The inductance of the coil is given by, VRjL  1 =Vjc Lcoil  2 2 2 CC RL  11 d For unity power factor, 1 Lcoil   1mH 6 2 12 VL 10990  10 10 Vc RL2  2 1  c  7 1 c   187 F 314 17

4.1 CAPACITANCE MEASUREMENT Note: For the low frequency range, (upto 10 MHz) the ace. anode is not needed.(e)Focusing anode: this anode is used to focus the e-beam on the screen and this type of focus-sing is called, electrostatic focusing.and it is achieved by formulation of two concave lenses.

ii) deflecting plates: a) Horizontal def. plates: The horizontal def. plates are used to Block diagram of a general-purpose deflect the electron beam in oscilloscope horizontal direction. For the display of a waveform horizontal plates 4.2 CRT are given a sawtooth wave which result into continuous motion of e-beam from left to right on the screen.For the measurement of phase and frequency the horizontal def. plates is supplied with external signals. b) Vertical def. plates: These plates are i) Electron gun used todeflect the e-beam in vertical a) Heater: used to raise the direction. The volume waveform temperature of Cathode under study is connected across b) Cathode: Emits the electrons when these plates. heated, coated with Barium and strantium oxide. The cathode is cylindrical in shape which emits electrons at moderate temperature. c) Grid: electron from cathode passes Note:The upper frequency limit of through Grid, made up of Ni cylinder CRO. having a hole at center and placed v coaxially with tube. fc  0x Grid is given -ve potential and it 4ld

controls the no.of electrons emitted Vox velocity of e-beam in x from the cathode. direction before itenters in Hence the intensity of beam at deflecting plates. screen is in control of grid. Id  length of vertical deflection d) pre-accelerating & post accelerating plates. anodes These are positively charged electrodes iii) Screen of CRO: which increases the speed of electrons Screen of CRT is made up of optical emitted. fibre

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission  Inside the screen, the phosphor is 4.2.1 ANOTHER CLASSIFICATION OF coated. AMPLIFIERS:  To the phosphor, traces of other elements are added to increase i) Narrowband amp. luminous efficiency, spectralemissions ii) Wideband amp. and persistence of phosphor. Such elements are called "activators". 4.2.2 AMPLIFIERS USED IN CRO ARE Activators added are: CLASSIFIED (i) Silver Ag (ii) Manganese Mn i) Vertical amplifier (iii)Copper Cu ii) Horizontal amplifier (iv)Chromium Cr  Phosphor convert electrical energy i) vertical amp: the vertical amp. into light energy and light emitted determines the sensitivity and B.W. of is called. "Fluorescent" oscilloscope. Sensitivity is expressed in  A film of metal such as Aluminum is Volt/cm, at mid-band frequency. deposited on no viewing side of Note phosphor which has following As gain increases, the B.W. decreases. effects. The B.W. of oscilloscope (CRO)  it works like heat Sink determines the range of frequency that  the light scatter from phosphor can be accurately reproduced on screen is reduced because Al. reflect it of CRT. back towards viewer. Note

 The electrons which strike tr  B.W 0.35 phosphor release secondary tr 10% to 90% of the Vertical signal. electrons which are collected by ii) Horizontal Amp: the horizontal amp. Aquadag. Some secondary serves two purposes. electrons are still on screen Note: which decreases the accelerating i) in normal mode of the display of a voltage. signal, it simply amplifies the sweep So these electrons are prevented by All generator. which makes the contact with aquadag ii) is same as vertical amp. when and screen. oscilloscope is in X-Y mode, the signal applied to X inputterminal iv) Aquadagis used to collect the secondary will be amplified by horizontal amp. emitted electrons from screen. It is aquous solution of graphite and is 4.3 EXPRESSION OF ELECTROSTATIC connectedto anode. Amplifiers of CRO DEFLECTION (i) a.c. coupled amplifier (ii) d.c. coupled amplifier.

(i) a.c. coupled amp: a.c. coupled amp has lower cost and generally used in labs. (ii) d.c. coupled amp: the d.c. coupled amp. are expensive and can be used for both a.c. and d.c.application.

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission E l L standard resistance The voltage across D dd (m) 2E d standard resistance is displayed on a CRO. The voltage measured from CRO where divided by it gives value of current D = deflection on the fluorescent screen L = distance from center of deflection iii) Measurement of phase and frequency platesto screen (meters) Id = effective length «f the deflection plates (a) Measurement of phase difference (meters) between two signals: the two signals are d = distance between the deflection plates connected across vertical and horizontal (meters) deflecting plates. A pattern is obtained on Ed = deflection voltage (volts) the screen. And this pattern is called. Ea = accelerating voltage volts) Lissazous pattern. The deflection sensitivity S of a CRT is defined as the deflection on the screen (in 4.4.1DIFFERENT LISSAZOUS PATTERNS meters) per volt of deflection voltage. By AND PHASE DIFFICULT BETWEEN definition, therefore SIGNALS D Ll S d (m / V) Eda 2dE (i) where S is the defection sensitivity (m/v)- The deflection factor G. of a CRT by definition, is the reciprocal of the sensitivity S and is expressed as. 1 2dE G a (V / m) S Lld with all terms as defined above. The Phase diff. = 0 expressions for deflection sensitivity S and (ii) deflection factor Gindicate that the sensitivity of a CRT is independent of the deflection voltage but varies linearlywith accelerating potential.

4.4 MEASUREMENT USING CRO Phase diff. = 180 I) Voltage Measurement Note assumption in (i) and (ii) both is that Note: CRO always measures peak to peak signals are having same amplitude and voltage and voltage of the waveform frequency. displayed = (def. factor) No. of Div. from (iii) peak to peak)

ii) Current Measurement

Note: No current can be directly measured, i.e. itnever displays current waveform. Because it is a voltage controlled instrument.The current can be measured by passing it through a 90o to 180o

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission (iv) The two signals one of unknown frequency and another of Known frequency are connected Acrossx and y plates. the frequency of unknown signals is determined from the Lissazous pattern as follows. Let fx Known frequency f  unknown 180o to 270o frequency (v) Then Max.no.of Interscetion of a horizontal f Line with Lissazous pattern y  fx Max.no.of int ersec tion of a line with Lissozous pattern

Example 1. Note when voltage of unequal amp. and same Frequency are connected, the resultant pattern is ellipse (A)

f 2 y 1 f2x 2.

(B)

f 4 y 2 f2x 3.

Volume of unequal amplitude is Vy> Vx and phase cliff, is 90°unequal amp. and 90° phase diff.

Note (A) and (B) frequencies of both the signals are same f 3 y  f2 4.5 MEASUREMENT OF FREQUENCY x

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission 4. The normal form of a CRO uses a horizontal input voltage which is an internally generated ramp voltage called “Time Base”. CROs operate on voltages. However, it is possible to convert current, strain acceleration, pressure and other physical quantities into voltages with the help of 63  transducers and thus to present visual 42 representations of a wide variety of dynamic phenomena on CROs. 5. CROs are also used to investigate waveforms, transient phenomena, and other time varying quantities from a very low frequency range to the radio frequencies. Oscilloscopes have been evolved continuously, and they are now available f 6 which can measure frequencies upto 1 GHz, y  f2 and observer events as small as 20 Hz in x duration. Storage oscilloscopes can be used for 4.5.1 SPECIAL OSCILLOSCOPES capturing transient signals. The digital storage oscilloscope first converts the In the conventional CRT the persistence of analog signal to a digital form and stores it the phosphor ranges from a few in digital memory. The signal can ten be milliseconds to several seconds, so that an recalled for display as and when required. event that occurs only once will disappear from the screen after a relatively short 4.6.2 CATHODE RAY TUBE (CRT) period of time. A storage CRT can retain the display much longer, up to several hours A cathode ray oscilloscope consists of a after the image was first written on the cathode ray tube (CRT), which is the heart phosphor. of the tube, and some additional circuitry to operate the CRT. The main parts of a CRT 4.6 CATHODE RAY OSCILLOSCOP (CRO) are: (i) Electron gun assembly, 4.6.1 INTRODUCTION (ii) Deflection plate assembly, (iii)Fluorescent screen, The cathode ray oscilloscope (CRO) is a (iv) Glass envelope, very useful and versatile laboratory (v) Base, through which connections are instrument used for display, measurement made to various parts. and analysis of waveforms and other LeE lm Ll E phenomena in electrical and electronic D.d d d d md 2eE 2dE circuits. CROs are in fact very fast X – Y aa D plotters, displaying an input signal versus DeflectionsensitivityS time. The “stylus” of this “plotter” is a Ed luminous spot which moves over the Lld display area in response to an input  m / V 2dE voltage. The luminous spot is produced by a a beam of electrons striking a fluorescent screen.

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission The Deflection Factor of a CRT is defined as changing at a rate faster than the eye can the reciprocal of sensitivity follow, 1 If we are to be able to observe such rapid Deflection factor G S changes, the beam must retrace the same

2dEa pattern repeatedly. If the pattern is  V / m retraced in such a manner that the pattern Lld 1 always occupies the same location on the Upper limitingfrequencyf screen, the eye will see a stationary display. c 4t 1 The beam will retrace the same pattern at a V  ox rapid rate if the vertical input signal and 4l the sweep generator signal are synchronized, which means that the 4.6.3 AQUADAG frequency of vertical input signal must be equal to or an exact multiple of, the sweep The bombarding electrons, striking the generator signal frequency. screen, release secondary emission (i) Free Running Sweep electrons. These secondary electrons are (ii) Triggered Sweep collected by an aqueous solution of graphite called ‘Aquadag’ which is 4.7.2 TYPES OF SWEEPS connected to the second anode, collection of secondary electrons is necessary to keep There are four basic types of sweeps the CRT screen in a state of electrical (i) Free Running or Recurrent Sweep equilibrium. In the free or recurrent sweep, the sawthooth waveform is repetitive. A 4.6.4 TIME BASE GENERATORS new sweep is started immediately after the previous sweep is terminated and Oscilloscopes are generally used to display the circuit is not initiated by any a waveform that varies as a function of external signal. time. If the waveform is to be accurately (ii) Triggered Sweep reproduced, the beam must have a constant A waveform to be observed on the CRO horizontal velocity. Since the beam velocity may not be periodic but may perhaps is a function of the deflecting voltage, the occur at irregular intervals. The deflecting voltage must increase linearly triggered sweep is used for examination with time. A voltage with this characteristic of transients or one time signals and the is called a ramp voltage. If the voltage waveform is photographed for record. decreases rapidly to zero with the The trigger can be obtained from the waveform repeatedly reproduced, as signal under investigation or by an shown in Fig. the pattern is generally called external source. a saw tooth waveform. (iii)Driven Sweep In most cases, a driven sweep is used 4.7 VERTICAL INPUT AND SWEEP where the sweep is recurrent but GENERATOR SIGNAL triggered by the signal under test. (iv)Non Saw Tooth Sweep 4.7.1 SYNCHRONIZATION For some applications like comparison of two frequencies or for finding phase Most waveforms that we will have occasion shift between two voltages, non to observe with an oscilloscope will be sawtooth voltages are utilized for the

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission sweep circuit. Sweep frequencies vary fy number of times tan gent touches topor bottom with the type os oscilloscope. A  fx number of time tan gent toucheseitherside laboratory oscilloscope may have number of horizontal tan gencies sweep frequencies upto several MHz; a  number of vertical tan gencies simple oscilloscope for audiowork has an upper limit of 100 kHz. Most TV Where fy = frequency of signal applied to Y services require a sweep voltage plates, frequency upto 1 MHz. Fx = frequency of signal applied to X plates f number of intersectionsof thehorizontalline with thecurve y  4.7.3 SYNCHRONIZATION fx number of intersectionsof the verticalline with thecurve The applications of this rule to fig. gives a Whatever type of sweep is used, it must be f 5 frequency ratio y  synchronized with the signal being f2 measured. Synchronization has to be done x f number of horizontal tangencies to obtain a stationary pattern. This requires y  that the time base be operated at a sub fx number of vertical tangencies multiple frequency of the signal under 2 1/ 2 5  measurement (applied to Y plates). 12

4.7.4 SOURCES OF SYNCHRONIZATION 4.8.3 ACCESSORIES OF CATHODE RAY OSCILLOSCOPES (i) Internal: In this type of synchronization, the trigger is obtained from the signal The cathode-ray oscilloscope is one of the being measured through the vertical most useful instruments in the electronic amplifier. industry. The usefulness of the oscilloscope (ii) External: In this method, an external is further extended by provision of trigger source is also used to trigger or accessories or auxiliary equipment. Some initiate the signal being measured. of the accessories are described below. Line: In this case, the trigger is obtained from the power supply to the CRO (say 4.8.4 CALIBRATORS 230 V, 50 Hz). Many oscilloscopes have a built-in reference source of voltage which has 4.8 BLANKING CIRCUIT usually a square waveform with a frequency of 1kHz. 4.8.1 ASTIGMATISM 4.8.5 PROBES In most modern oscilloscopes there is an additional focusing control marked The probe performs the very important Astigmatism. function of connecting the test circuit to the The spot is then made as sharp as possible oscilloscope without altering, loading, or by successive adjustment of focus and otherwise the test circuit. astigmatism controls. The probes are of three different types: Measurement of Phase and Frequency 1. Direct Probe: This probe is simplest of (LissajousPatterns) all the probes and uses a shielded co- axial cable. It avoids stray pick-ups 4.8.2 FREQUENCY MEASUREMENT which may create problems when low level signals are being measured. It is

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission usually used for low frequency or low oscilloscopes except the highly impedance circuits. specialized ones. External high impedance probes are used to increase the input resistance 4.8.6 FREQUENCY METERS and reduce the effective input capacitance of an oscilloscope. The different types of frequency meters Supposing, it is intended to attenuate are: the signal by a factor of 10 1. Mechanical resonance type R1 = R2 (k -1) = (1 × 106) (10 – 1) = 9 2 Electrical resonance type MΩ 3. Electrodynamometer type C1 = C2j(k – 1) = 30 × 10-12/(10 – 1) 4. Weston type = 3.33pF. 5. Ratiometer type Ri = R1 + R2 = 10 MΩ 6. Saturable core type CC The frequency can also be measured and C 12 3pF i compared by other arrangement like CC12 Probe capacitance is adjusted to the electronic counters, frequency bridges, wrong value, the oscilloscope will stroboscopic methods and cathode ray exhibit a factor frequency response. The oscilloscope. adjustment of probe is usually checked by displaying a square wave on the CRT screen. If the probe is not properly compensated, the display of square waveform will be adversely affected as shown in Fig. If the value of C1 is too small, the leading edge of the square wave is rounded off but if value of C1 is too large, the leading edge of square wave overshoots. 2. Isolation Probe: Isolation probe is used in order to avoid the undesirable circuit loading effects of the shielded probe. The isolation of the probe, which is used along with a capacitive voltage divider, decreases the input capacitance and increases the input resistance of the oscilloscope. This way the loading effects are drastically reduced. 3. Detector Probe: When analyzing the response to modulated signals used in communication equipment like AM, and TV receivers, the detector probe functions to separate the low frequency modulation component from the high frequency carrier. This permits an oscilloscope capable of audio-frequency response to perform signal tracing tests on communication signals in the range of hundreds of MHz, a range, which is beyond the capabilities of all

Q.1 Two in phase 50Hz sinusoidal wave forms of unit amplitude are fed into channel -1 and channel -2 respectively of an oscilloscope Assuming that the voltage scale, time a)2kHz b)1kHz scale and other setting are exactly c)500Hz d)250Hz the same for both the channels. What [GATE-2003] would be observed if the oscilloscope is operated in x-y mode? Q.4 List-I represents the figures obtained a) A circle of unit radius on a CRO screen when the voltage b) An ellipse signals c) A parabola VVsin ωtandVVsin(ωtΦ) d) A straight line inclined at 45° xxm yym with respect to the x-axis are given to its X and Y plates [GATE-2002] respectively and Φ is changed. Choose the correct value of Φ is Q.2 A reading of 120 is obtained when changed. Choose the correct value of standard inductor was connected. from list-I to match The circuit of a Q- mater and the corresponding figure of List –II variable capacitor is adjusted to a List-I value of 300 pF .A lossless capacitor A. Φ=0 of unknown value C is then B. Φ = π/2 x C. π< Φ<3π/2 connected in parallel with the variable D. Φ = 3π/2 capacitor and the same reading was List –II obtained when the variable capacitor 1. is readjusted to a value of 200pF. The value of in pF is a) 100 b) 200 c) 300 d) 500 [GATE-2003] 2. Q.3 The simplified block diagram of a 10- bit A/D converter of duel slop integrator type is shown in figure. The 10-bit counter at the output is 3. clocked by a 1MHz clock. Assuming negligible timing overhead for the control logic that can be converted using this A/D converter is approximately 4.

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission Q.8 The simultaneous application of signals x (t) and y (t) to the horizontal and vertical plates respectively, of an oscilloscope, 6. produces vertical figure –of -8 displays. If P and Q are constants and x (t) =P sin (4t+30), then y(t) is equal to a) Qsin(4t 30) b) Q s i n ( 2 t 1 5 ) Codes : c) Q s i n ( 8 t 6 0 ) d) Qsin(4t 30) A B C D [GATE-2005] a) 1 3 6 5 b) 2 6 4 5 Q.9 The time /div and voltage /div axes c) 2 3 5 4 of an oscilloscope have been erased. d) 1 5 6 4 A student connects a 1 kHz 5V p-p [GATE-2004] square wave calibration pulse to channel 1 of the scope and observes Q.5 A CRO probe has an impedance of the screen to be as shown in the 5 0 0 kΩ in parallel with a capacitance upper trace of the figure. An of 10 pF .The probe is used to unknown signal is connected to measure the voltage between P and channel 2 (lower trace) of the scope. Q as shown in figure. The measured It the time /div and V/div on both voltage will be channels are the same, the amplitude (p-p) and period of the unknown signal are respectively

a)3.53V b)4.37V c)4.54V d)5.00V [GATE-2004]

Q.6 The Q-meter works on the principle a) 5V,1ms b) 5V, 2ms of c) 7.5V, 2ms d) 10V, 1ms a)mutual inductance [GATE-2006] b) self inductance c) series resonance Q.10 The probes of a nonisolated, two d)parallel resonance channel oscilloscope are clipped to [GATE-2005] points A, B and C in the circuit of the adjacent figure. Vin is a square wave Q.7 A digital –to –analog converter with of a suitable low frequency. The

a full scale output voltage of 3.5V has display on Ch1 and Ch2 are as a resolution close to 14m. V its bit shown on the right. Then the “Signal” size is and “Ground “probes a) 4 b) 8 S1 ,G 1 andS 2 G 2 andCh 2 respectively c) 16 d) 32 are connected to points: [GATE-2005]

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission the X-Y mode. The screen shows a figure which changes from ellipse to circle and back to ellipse with its major axis changing orientation slowly and repeatedly. The following inference can be made from this a) The signals are not sinusoidal b) The amplitudes of the signals are a) A, B, C, A b) A, B,C, B very close but not equal c) C, B, A, B d) B, A,B, C c) This signals are sinusoidal with [GATE-2007] their frequencies very close but Q.11 Two 8-bit ADCs, one of single slope not equal integrating type and other of d) There is a constant but small successive approximate type. Take phase difference between the T a n d T times to convert 5V analog signals. AB [GATE-2009] input signals to equivalent digital output. If the input analog signal is Q.14 An average –reading digital multi reduced to 2.5V, the approximate meter reads 10V when fed with a time taken two ADCs will triangular wave, symmetric about respectively, be the time –axis .For the same input an a) T ,T b) T / 2 ,T AB AB rms –reading meter will read c) T,T/2AB d) T/2,T/2AB 20 10 a) V b) V [GATE-2008] 3 3 c) 2 0 3 V d) 1 0 3 V Q.12 Two sinusoidal signals [GATE-2009] ρω 1, tAsinω t and1, qωt  2, are applied to x and Y inputs of a dual Q.15 A duel trace oscilloscope is set to channel CRO. The Lissajous figure operate in the Alternate mode. The displayed on the screen is shown control input of the multiplexer use below: in the Y-circuit is fed with a single having a frequency equal to The signals qωt2,  will be a) The highest frequency that the represented as multiplexer can operate properly b) Twice the frequency of the time base (sweep) oscillator c) The frequency of the time base (sweep) oscillator d) Half the frequency of the time a) qω tAsinω  t,ω2ω base (sweep) oscillator 2 221 [GATE-2011] b) qω2 tAsinω  t,ωω221 / 2 1 Q.16 A 4 digit DMM has the error c) qω2 t  Acosω2 t,ω 2 2ω 1 2 d) qω tAcosω  t,ωω / 2 specification as: 0.2% of reading 2 221 +10counts. If a dc voltage of 100V is [GATE-2008] read on its 200V full scale, the maximum error that can be expected Q.13 The two inputs of a CRO are fed with in the reading is two stationary periodic signals. In

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission a) 0.1% b) 0.2% Q.19 An air cored coil has a Q of 5 at a c) 0. 3% d) 0. 4% frequency of 100 kHz. The Q of the [GATE-2011] coil at 20 kHz (neglecting skin effect) will be______. Q.17 In an oscilloscope screen, linear [GATE-2016] sweep is applied at the Q.20 A coil is tested with a series type Q a) Vertical axis meter. Resonance at a particular b) Horizontal axis frequency is obtained with a c) Origin capacitance of 110 pF. When the d) Both horizontal and vertical axis frequency is doubled, the [GATE-2014-1] capacitance required for resonance is 20 pF. The distributed capacitance Q.18 The two signals 51 and S2, shown in of the coil in pico farad is ______. figure, are applied to Y and X [GATE-2016] deflection plates of an oscilloscope. Q.21 A voltage of 6cos100t V is fed as y- input to a CRO. The waveform seen on the screen of the CRO is shown in the figure. The Y and X axes settings for the CRO are respectively

The waveform displayed on the screen is a) b)

a) 1 V/div and 1 ms/div b) 1 V/div and 2 ms/div c) 2 V/div and 1 ms/div d) 2 V/div and 2 ms/div [GATE-2018] c) d)

[GATE-2014-3]

ANSWER KEY:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 (d) (a) (b) (d) (b) (c) (b) (b) (c) (b) (b) (d) (c) (a) 15 16 17 18 19 20 21 (d) (c) (b) (a) 1 10 (d)

Q.1 (d) But for Φ 0° the trace has positive

Phase difference 0 ° A l s o f fxy slope and for Φ 1 8 0 ° the trace has negative slope. Q.2 (a) When the two voltages has phase Q of the coil =120 displacement of 90° the trace is a ω L 1 circle. If the direction of the trace is Q  in the clockwise direction then the R ω R C phase difference is Φ 9 0 ° If the Case-I Q=120 is obtained for C=300pF direction of the trace is anti clockwise direction the phase Case-II difference is ππ For same reading i.e. Q=120 2πΦ2π3  Effective capacitance of the circuit 22 should be 300pF When the phase difference is not Effective capacitance of parallel equal to 0° or the trace is an capacitor 3π ellipse. For πΦ the trace is Ceff C Cx 2 an ellipse is anti-clockwise direction. CCCxeff 300200 Q.5 (b) 1 0 0p F 1 X  c 2πfC Q.3 (b) 1 The wave form for duel slope  2π1001010103 12 integrator is shown .The maximum X159.15k Ω frequency can be attained when c

T21 T 0 and as

N T2T1CC (Tclock period) Taking supply voltage as the 1 f reference. f   C max NN V100Vs  2 .TC 2 Using KCL 106 1kHz V 10 V V V 1024 p p p  p  0 100 103 100  103 500  103  j159.15  103

Q.4 (d) V4.3715.94Vp  When the two voltages are in phase i.e [Φ 0°or180°] , the trace is Q.6 (c) straight line ωL Q  0 R

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission Where ω0 is the resonant angular θ s i n ( 2 t 1 5 ) has angular frequency frequency L is the inductance and R ω 2 r a d / s e c is the effective resistance of the coil. The principle of working of Q –meter Q.9 (c) is based upon series resonance of R, Peak-peak (p-p) division of upper L, C circuit. trace voltage =2 and value of (p-p) voltage =5V Q.7 (b) V o l t a g e s 2 . 5 V Resolution of digital to analog D i v i s i o n converter Now it will be same for unknown V R 1 4 m0 V voltage (p-p) division of unknown 2N voltage =3 Where p  p voltage  3  2.5  7.5V V0 =Full scale output voltage =3.5V Frequency of upper trace =1 kHz N= bit size 1 Time period1ms V 3 0 1 4 m V 10 2N Division of x-axis (upper) =4 N 3.5 Division of x-axis (lower) =8 2 250 1410 3 ∴ Period of unknown signal =2ms N8 Q.10 (b) Q.8 (b) Square wave is of low frequency, .So it can be assumed that time during fy  frequency of signal applied to y which the wave forms are displayed plates on the screen, the voltage across R f  frequency of signal applied to X x and L is V plates in xtPsin(4t30)  4 So, fHz x 2π

V/ S ls  in RLs V ls  in R Lss L f no.of times tangent touches top or bottom  y  Vin 11L fx no of time s tanfent touches eithe side  R 1 LsRs   L 2 f 4 1 2π  f x    V 11 y  ls in 22π 2 2   R Rss  2π L ωyy 2πf  2π  2rad / sec 2 V i t in 1 eRt/L R  

Maximum number of intersection of So, S is connected to point A a horizontal line with 1 ω Lissajous patten And G is connected to point B y  1 ω maximum number of intersectin ofa vertical line with di x Voltage across inductor VL Lissajous pattern BC dt ωy 21 d Vin Rt/L    L1e   ω 4 2 dtR x Rt/L ωxy 2 ω VBC V in e ω12 2 ω

And q ωt2, will lead ρ ω  t1, by 90° as trace is a circle

q ωtAsinωt90°2,   2

qωtAcosωt2,  2

So S2 is connected to point C. Q.13 (c)

And G2 is connected top point B. If the phase difference between the two signals is then the trace is a Q.11 (b) circle. Signal slope integrating type ADC If the phase difference between the utilizes digital counter techniques to two signals is not equal to 0° or , measure time required for a voltage then the trace is an ellipse. ramp to rise from zero to the input As the figure change from ellipse to voltage. circle and back to ellipse, it means If conversion time for input voltage phase difference is constant but it varies with time which I possible 5V= TA so, conversion time for input when frequency both the signals are voltage 2.5V= T / 2 A not equal. Conversion time in successive type As the variation is slow, it means the ADC does not depend on input signals a sinusoidal with their voltage 2.5V is also TB frequencies very close but not equal.

Q.12 (d) Q.14 (a)

Here ρ ω11 t   Asinω t For triangular wave Vm y1  line cut ‘4’ times the Lissajous Avg value  pattern 2 Vm x1 -line cut ‘2’ times the Lissajous RMS value  pattern 3

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission V Error corresponding to 0.2% of m 10VV20 2 m reading 100 Vm 20 RMS value V E0.20.2V2  33 100 Total error EE0.10.212 Q.15 (d)  0 . 3 V i . e . 0 . 3 % Alternate mode is used to display two wave forms simultaneously by Q.17 (b) single CRT. As fluorescent material stores light for some time and eye Q.18 (a) sensing time is 20ms. By using multiplexer alternatively two waves are connected to y plates. In this mode the frequency of control signal to multiplexer is equal to half off X- time base generator. In one sweep display 1st wave form and in the half record sweep display 2nd waveform connected to Y-plates .For law frequency at high frequency that the multiplexer can operate. This is called chopping mode.

Q.16 (c) 1 4 digit. 2

No of full digits in case of digit display =4 So, maximum count with digit display =19999 Full scale reading o=200V 200V 1count  19999

EError1  corresponding to10Counts 200V 10   0.1V 19999 Reading =100V

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission Q.19 1 Q.21 (d)  L 2 f L Given: Q 1 1 RR 2 100K L  R Sincef =100kHz  5 L5 v 6 c o s1 0 0 t  ....i  y R 2 100K v 1peak 2 V to peak  2L 5 Q2   2  20K Number of vertical division = 6 R 2 100K Vertical sensitivity from eqn. i  12  V/div2V/div 1 6 2 Time period  T20msec Q.20 10 100 From given data: Number of horizontal division = 10 C1 = 110 pF Horizontal sensitivity C2 = 20 pF msec20 2f 2msec/div n 2 div10 f C  nC2 110420 C 12 d n2 141 11080 30pF  10pF 33 So the distributed capacitance of the coil is 10 picofarad.

5.1 DIGITAL VOLTMETERS

The DVM's outstanding qualities can best be illustrated by quoting some typical operating and performance characteristics. The following specifications do not all apply to one particular instrument, but they do represent valid information on the present state of the art: (a) Input Range: From ± 1.000000 V to = 1.000,000 V, with automatic range selectionand overload indication. (b) Absolute Accuracy: As high as ± 0.005 per cent of the reading. (c) Stability: Short term, 0.002 per cent of the reading for a 24-hr period: long term, 0.008per cent of the reading for a 6-month period (d) Resolution: 1 part in 106 (1 V can be read on the 1 -V input range) (e) Input Characteristics: Input resistance typically 10M; input capacitance typically 4) pF (f) Calibration: Internal calibration standard allows calibration independent of die measuring circuit; derived from stabilized reference source (g) Output Signals: print command allows output to printer : BCD ( binary-coded- decimal output for digital processing or recording, Optional features may include additional Circuit to measure current, resistance, and voltage ratios, 5.1.1 RAMP TYPE DVM other physical variables may bemeasured by using suitable transducers. Digital voltmeters can be classified according to the following broad categories: (a) Ramp-type DVM (b) Integrating DVM (c) Continuous-balance DVM (d) Successive-approximation DVM Block diagram of ramp type digital voltmeter

A very effective and relatively inexpensive method of analog-to-digital conversion is the methods of successive approximation. This is an electronic implementation of a technique called binary regression. Assume that one is to determine the value of a number and is allowed to make estimates. Each estimate would be evaluated and it would be known if the estimate was (1) equal to or less than or (2) greater than the number to be determined. The maximum and minimum value of the possible number is also known. 6.1.3 DUAL SLOPE DVM Estimate Result 256 Equal to or less than 256 + 128 = 384 Equal to or less than 384 + 64 = 448 Equal to or less than 448 + 32 = 480 Equal to or less than 480 + 16 = 496 Equal to or less than 496 + 8 = 504 Greater than 496 + 4 = 500 Greater than 496 + 2 = 498 Equal to or less than 498 + 1 =499 Correct The electronic implementation of the successive-approximation technique is relatively straightforward and is shown in Block diagram of a dual slope DVM Fig. A D/A converter is used to provide the estimates. The “equal to or greater than” or 6.1.4 SUCCESSIVE APPROXIMATION-DVM “less than” decision is made by a comparator. The D/A converter provides the estimate and is compared to the input signal. A special shift register called a successive-approximation register (SAR) is used. The sequence of events performs, electronically, the same estimating procedure that was outlined previously. An estimate is made on the edge of the SAR clock. Dor an N-bit conversion after N clock, the actual value of the input is known. The least significant bit is the state of the comparator. In some systems an additional clock is used to store the last in the SAR and thus N + 1 clocks are required for a conversion.

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission The operating principle is to measure the time that a linear ramp takes to change the input level to the ground level, or vice- versa. This time period is measured with an electronic time-interval counter and the count is displayed as a number of digits on an indicating tube or display.

5.3 DIGITAL VOLTMETERS

Digital voltmeters are measuring instruments that convert analog voltage signals into a digital or numeric readout. The ramp may be positive or negative; in The DVM displays ac and dc voltages as this case a negative ramp has been selected. discrete numbers, rather than as a pointer The ramp voltage is continuously on a continuous scale as in an analog compared with the voltage that is being voltmeter. A numerical readout is measured. At the instant these two voltage advantageous because it reduces human become equal, a coincidence circuit error, eliminates parallax error, increases generates a pulse which opens a gate, i.e. reading speed and often provides output in the input comparator generates a start digital form suitable for further processing pulse. The ramp continues until the second and recording. With the development of IC comparator circuit senses that the ramp modules, the size, power requirements and has reached zero value. When the ramp cost of DVMs have been reduced, so that voltage equals zero or reaches ground DVMs compete with analog voltmeters in potential, the ground comparator generates portability and size. a stop pulse. The time duration of the gate 1. Input range form + 1.000 V to + 1000 V opening is proportional to the input voltage with automatic range selection and value. overload indication 2. Absolute accuracy as high as  0.005% of the reading 3. Resolution 1 part in million (1 μV reading can be read or measured on 1 V range) 4. Input resistance typically 10 MΩ, input capacitance 40 pF 5. Calibration internally from stabilized reference sources. 6. Output in BCD form, for print output and further digital processing In the time interval between the start and 5.4 RAMP TECHNIQUE stop pulses, the gate opens and the oscillator circuit drives the counter. The

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission magnitude of the count indicates the magnitude of the input voltage, which is displayed by the readout. Therefore, the voltage is converted into time and the time count represents the magnitude of the voltage.

5.4.1 ADVANTAGES & DISADVANTAGES

The ramp technique circuit is easy to design and its cost is low. Also, the output The discharge time t2 is now proportional pulse can be transmitted over long feeder to the input voltage. The counter indicates lines. However, the single ramp requires the count during time t2. When the negative excellent characteristics regarding linearity slope of the integrator reaches zero, the of the ramp and time measurement. Large comparator switches to state 0 and the gate errors are possible when noise is closes, i.e. the capacitor C is now superimposed on the input signal. Input discharged with a constant slope. As soon filters are usually required with this type of as the comparator input (zero detector) converter. finds that ea is zero, the counter is stopped. The pulses counted by the counter thus 5.5 DUAL SLOPE INTEGRATING have a direct relation with the input TYPE DVM(VOLTAGE TO TIME voltage. CONVERSION) In ramp techniques, superimposed noise can cause large error. In the dual ramp technique, noise is averaged out by the positive and negative ramps using the process of integration.

5.5.1 PRINCIPLE OF DUAL SLOPE TYPE DVM

As illustrated in fig, the input voltage ‘ei’ is integrated, with the slope of the integrator output proportional to the test input During charging t1 voltage. After a fixed time, equal to t1, the 1 e t e  e dt   i1 input voltage is disconnected and the 0iRC RC integrator input is connected to a negative 0 voltage –er. The integrator output will have During discharging a negative slope which is constant and t2 1 er2 t proportional to the magnitude of the input e0r   e dt   RC RC voltage. 0 At the start a pulse resets the counter and t ee2 the F/F output to logic level ‘0’. Si the irt capacitor begins to charge. As soon as the 1 integrator output exceeds zero, the comparator output voltage changes state, 5.5.2 INTEGRATING TYPE DVM which opens the gate so that the oscillator (VOLTAGETO FREQUENCYCONVERSION) clock pulses are fed to the counter.

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission The principle of operation of an integrating type DVM is illustrated in fig. A constant input voltage is integrated and the slope of the output ramp is proportional to the input voltage. When the output reaches a certain value, it is discharged to 0 and another cycle begins.

5.5.3 MOST COMMONLY USED PRINCIPLES OF ADC (ANALOG TO The advantages of a staircase type DVM are DIGITALCONVERSION) as follows. 1. Input impedance of the DAC is high Direct Compensation when the compensation is reached. 2. The accuracy depends only on the The Staircase Ramp stability and accuracy of the voltage and DAC. The clock has no effect on the accuracy. The disadvantages are the following. 1. The system measures the instantaneous value of the input signal at the moment compensation is reached. This means the reading the rather unstable, i.e. the input signal is not a pure dc voltage. 2. Until the full compensation is reached, The basic principle is that the input signal the input impedance is low, which can Vi is compared with an internal staircase influence the accuracy. voltage, Vc, generated by a series circuit consisting of a pulse generator (clock), a 5.6 SUCCESSIVE APPROXIMATIONS counter counting the pulses and a digital to analog converter, converting the counter The successive approximation principle can output input a dc signal. As soon as Vc is be easily understood using a simple equal to Vi, the input comparator closes a example; gate between the clock and the counter, the counter stops and its output is shown on 5.6.1 3 – 1/2 DIGIT the display. (DAC) is also 0. If Vi is not equal to zero, the input comparator applies an output voltage that opens the gate so that clock pulses are passed on to the counter through the gate. Starts counting and the DAC starts to produce an output voltage increasing by one small step at each count of the counter. This process continues until the staircase voltage is equal to or slightly greater than The number of digit positions used in a the input voltage V . At that instant t , the i 2 digital meter determines the resolution. output voltage of the input comparator Hence a 3 digit display on a DVM for a 0 – 1 changes state or polarity, so that the gate V range will indicate values from 0 – 999 closes and the counter is stopped. mV with a smallest increment of 1 mV.

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission Normally, a fourth digit capable of A 4½ digit voltmeter is used for voltage indicating 0 or 1 (hence called a Half Digit) measurements is placed to the left. This permits the digital (i) Find its resolution meter to read values above 999 up to 1999, (ii) How would 12.98 V be displayed on a to give overlap between ranges for 10 V range? convenience, a process called over – (iii)How would 0.6973 be displayed o 1 V ranging. This type of display is called a 3½ and 10 V ranges. digit display, shown in fig. Solution (i) Resolution = 1/10n = 1/104 = 0.0001 5.7 RESOLUTION AND SENSITIVITY Where the number of full digits is n = 4 OF DIGITAL METERS (ii) There are 5 digit places in 4½ digits, therefore 12.98 would be displayed as Resolution 12.980. If n = number of full digits, then resolution Resolution on 1 V range is 1 V ×0.0001 (R) is 1/10n. = 0.0001 1 1 Any reading up to the 4th decimal can be If n = 3, R =  .0 001 or %1.0 10n 103 displayed. Sensitivity of Digital Meters Hence 0.6973 will be displayed as Sensitivity is the smallest change in input 0.6973. which a digital meter is able to detect. (iii)Resolution on 10 V range = 10V × Hence, it is the full scale value of the lowest 0.0001 = 0.001V voltage range multiplied by the meter’s Hence decimals up to the 3rd decimal resolution. place can be displayed. Sensitivity S = (fs)min × R Therefore on a 10 V range, the reading Where (fs)min= lowest full scale of the will be 0.697 instead of 0.6973. meter .8 BLOCK DIAGRAM OF SA DVM R= resolution expressed as decimal 5 5.8.1 BASIC Q METER CIRCUIT Example What is the resolution of a 3½ digit display on 1V and 10V ranges? Solution Number of full digits is 3. Therefore resolution is 1/10n where n = 3. Resolution R = 1/103= 1/1000 = 0.001 Hence the meter cannot distinguish between values that differ from each other by less than 0.001 of full scale. For full scale range reading of 1V, the 5.8.2 SERIES CONNECTION resolution is 1 × 0.001 = 0.001 V. For full scale reading of 10V range, the resolution is 10V × 0.001 = 0.01 V. Hence on 10 V scale, the meter cannot distinguish between readings that differ by less than 0.01 V.

Example

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission Q meter measurement of a Low Impedance resonated, by using a suitable work coil, to component in series connection establish reference values for Q and C(Q1 Series connection: Low impedance and C1).Then when the component under components, such a low-value resistors, test is connected to the circuit, the small coils and large capacitors, are capacitor is readjusted for resonance, and a measured in series with the measuring new value for the tuning capacitance (C2) circuit. The above figure shows the is obtained and a change in the value of connection. The component to be circuit Q(Q) from Q1 to Q2. measured, here indicated by [Z] is placed in series with a stable work coil across the test terminals. (The work coil is usually supplied with the instrument). Two measurements are made: In the First measurement the unknown is short- circuited by a small shorting strap and the circuit is resonated, establishing reference condition. The values of the tuning capacitor (C1) and the indicated Q (Q1) are noted. In the second measurement the shorting strap is removed and the circuit is returned, giving a no value for the tuning capacitor (C2) and a change in the Q value from Q1, to Q2.

C1 CQQ 2  1 2 Qs  CQ1 1 CQ 2 2

CC1 Cs  CC2 The Q of the capacitor may be found by using above equation

5.8.3 PARALLEL CONNECTION:

High-impedance components, such as high- value resistors, certain inductors, and small capacitors, are measured by connecting them in parallel with the measuring circuit. Figure shows the connections. Before the unknown is connected, the circuit is

Q.1 A 500A/5A, 50Hz current a) 0,0,30 b)-0.5, 35 transformer has a bar primary. The c) -1.0, 030 d)-1.0, 25 secondary burden is a pure [GATE-2006] resistance of 1Ω and it draws a current of 5A if the magnetic core Q.5 The power delivered to a single requires 250 AT for magnetization, phase inductive load is measured the percentage ratio error is with a dynamometer type a)10.56 b)-10.56 wattmeter using a potential c) 11.80 d)-11.80 transformer (PT) of turns ratio [GATE-2003] 200:1 and the current transformer (CT) of turns ratio 1:5. Assume both Q.2 A 50 Hz, bar primary CT has a the transformers to be ideal. The secondary with 500 turns. The power factor of the load is 0.8. If the secondary supplies 5 A current into wattmeter reading is 200W, then a purely resistive burden of The the apparent power of the load in magnetizing ampere –turns is 200. kVA is ______. The phase angel between the [GATE-2016] primary and secondary current is a) 4 . 6 ° b) 8 5 . 4 ° Q.6 A 3 ½ digit DMM has an accuracy c) 9 4 . 6 ° d) 1 7 5 . 4 ° specification of ±1% of full scale [GATE-2004] (accuracy class 1). A reading of 100.0 mA is obtained on its 200 mA Q.3 The core flux in the CT of Prob, full scale range. The worst case under the given operating conditions error in the reading in a) 0 b) 45.0μWb milliampere is ± ______. c)22.5mWb d)100.0mWb [GATE-2004] 1 Q.7 A 200 mV full scale dual-slope 3 2 Q.4 A 200/1 Current transformer (CT) is digit DMM has a reference voltage of wound with 200 turns on the 100 mV and a first integration time secondary on a toroid core. When it of 100 ms. For an input of carries a current of 160A on the [100+10cos(100πt)]mV, the primary, the ratio and phase errors conversion time (without taking the of the CT are found to be-0.5% and auto-zero phase time into 30 minutes respectively. If the consideration) in millisecond is number of secondary turns is ______. reduced by 1 the new ratio error (%) and phase error (min) will be respectively

ANSWER KEY:

1 2 3 4 5 6 7 (b) (a) (b) (a) 250 2 200

Q.1 (b) Magnetizing ampere turn l  500 m Nominal ratio 100 Np 5 200 Number of turn in primary N=1 2 0 0 A 1 (primary bar) 180  200  Magnetizing current θ     mmf π  500 5  l  m no.ofturns  4 . 6 ° 250 250 Q.3 (b) 1 Z B u r d e n 1 Ω Secondary current s l 5 A Voltage induced in the secondary, s ElZ515V 500 sss n 1 0 0 E 4.44fΦN 5 s m s Primary current Es Φm 2 4.4fN l n l l   2 s psm 5 22  1005250 4.4450500  45μ W b l559.017Ap Actual ratio Q.4 (a) l p 559.017 200  Nominal ratio k200 55 n 1 111.803 Primary current l160A Ratio error p Nomial RatioActual ratio l 100 Actual ratio Rn1 e …(i) 11 Actual ratio lp 100 111.803  100   10.56% kRn1 111.803 % ratio error  1000.5 R1 200R Q.2 (a) 1 100 Phase angle between primary and R1

secondary current Actual ratio R2011

180 lm nturn1  ratio200 θ  degree π nls l R 200 1 e …(ii) No. of turns in primary N1 1  p lp No. of turns in secondary Ns 500 When no. of secondary is reduced by N 1 N=turn ratio s 500 ns  199 Np

n2  199 ls  Secondary widing current =5A Magnetizing ampere turn =200

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission l VI11 R n 1e 200=0.8 22 2005 lp 200 3 l VI=10=25011 kVA 1 9 9 1 e …(iii) 0.8  lp Q.6 2 Dividing eq.(ii) and (iii) Since all information are given n in R 200 mA unit assume the scale in mA unit. 1  R 12 9 9 199 RR21 200 199 201 → Since it is given that error is ±1% 200 of full scale So, error =±1%of 1 9 9 . 9 9 5 2 0 0 200mA=±2mA. % ratio Error →So if it measures 100mA then the kR n2100 reading will be in the range (100 ± R2 2)mA 200200 → The worst source error is ±2mA.  1000 200 Q.7 200 180 l Phase angle error 0 m In dual slope converter total  πlp conversion time Reduction of one or two turns of the T= 1st integration period secondary winding, no doubt, + 2nd integration period reduces the ratio error but is has no = T1 + T2 = 100 msec T2 To obtain T2 we can use effect on the phase angle error. Vin T1 = Vref T2 ⟹ 100mv × 100msec = 100mv × T2 Q.5 250 ⟹ T2 = 100msec IN Exp: 12 ⟹ T = 100 + 100 = 200 msec IN21

N1 II21 N2 I I  1 2 5 VN 22 VN11 V V  1 2 200

I through C.CI 2

V/g crossP.CV 2 Power measured by w/m will be

200 = V22 I cos

Q.1 A Wheatstone bridge requires a change of 6 ohms in the unknown arm of the brigeto produce a change in deflection of 3 mm of the galvanometer. The sensitivity of the instrument is a) 0.5 percent b) 2.0 percent c) 0.5 mm/ohm d)2.0ohm/mm

Q.2 A digital voltmeter has a read-out a) R = R b) C = C range from 0 to 0000 counts. When 1 3 1 3 c) R = 2 R d) R = R full scale reading is 0.999 V, the 2 4 2 4 resolution of the full scale reading is Q.6 Consider the following statements in a) 0.001 b) 1000 connection with deflection and null c) 3 digit d) 1 mv type instruments: 1. Null type instrument is more is Q.3 The resistance of a circuit is found more accurate than the by measuring current flowing and deflection type one. the power fed into the circuit. If the 2. Null type instrument can be limiting errors in the measurement highly sensitive as compared of power and current are 1.5% with deflection type instrument. and 1.0% 3. Under dynamic consideration, a) 1% b) null type instrument is not c) 2.5% d) 3.5% proffered to deflection type instrument. Q.4 A simple dc potentiometer is to be 4. Response is faster in null type standardized by keeping the slider instrument as compared to wire setting at 1.0183 V. If by deflection type instrument. mistake, the setting is at 1.0138 V Which of these statements are and the standardization is made to correct? obtain a source voltage of 1.0138 V, a)1, 2 and 3 only b)1, 2 and 4 only then the reading of the c)2, 3 and 4 only d)1, 2, 3 and 4. potentiometer will be a) 1.0138 V b) 1.0183 V Q.7 In the statement “the wattmeter (1.0138)2 commonly used to power c) V d) (1.0138)2 V 1.0183 measurement atcommercial frequencies is of the X-type. This Q.5 Which of the following conditions meter consists of two coil systems, are to be satisfied so that the the fixed system being the Y-coil and common variableshaft of resistance moving system being the Z-coil”. X, Y R1 and R3 can be graduated in and Z stand respectively for frequency to measure thefrequency a) dynamometer, voltage & current of under balanced condition b) dynamometer, current & voltage c) induction, voltage and current d) induction, current and voltage

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission Q.8 Two-wattmeter method is employed Q.13 A Lissajous pattern on an to measure power in a 3-phase oscilloscope has 5 horizontal balanced system with the current tangencies and 2 vertical tangencies. coils connected in the A and C lines. The frequency of the horizontal The phase sequence is ABC. If the input is 100 Hz. What is the wattmeter with its current coil in A- frequency of the vertical inout? phase line reads zero, then the a) 400 Hz b) 2500 Hz power factor of the 3-phase load c) 4000 Hz d) 5000 Hz will be a) zerolaggin b) zero leading Q.14 The resistance of a thermistor is c) 0.5 lagging d) 0.5 leading 5000 Ω at 20° C and its resistance temperature coefficient is 0,04/° C. Q.9 In a particular form of frequency A measurement with a lead meter, a 1 mF capacitor is connected resistance of 10 Ω will cause an across a symmetrical square wave error of signal of 1 volt peak value. If the a) 0.05° C b) 0.1° C average value of the current taken c) 0.4° C d) 0.8° C by the capacitor, after full wave rectification is measured as 2 mA, Q.15 In a digital voltmeter, the oscillator then the frequency of the signal will frequency is 400 kHz and the ramp be voltage falls from 8 V to 0 V in 20 m a) 1000/pHz b) 500 Hz sec. The number of pulses counted c) 1000 Hz d) 1000 pHz by the counter is a) 800 b) 2000 Q.10 The meter constant of a single- c) 400 d) 8000 phase 240 V induction watt-hour meter is 400revolutions per kWh. Q.16 A zero to 300 V voltmeter has an The speed of the meter disc for a error of ±2% of the full-scale current of 10 amperes at 0.8 p.f, deflection. If the true voltage is 30 V, lagging will be then the range of readings on this a) 12.8 rpm b) 16.02 rpm voltmeter would be c) 18.2 rpm d) 21.1 rpm a) 20 V to 40 V b) 24 V to 36 V Q.11 A digital voltmeter uses a 10 MHz c) 29.4 V to 30.6 V clock and has a voltage controlled d) 29.94 V to 30.06 V generator which provides a width of 10 m sec per volt of unit signal. 10 Q.17 If Qeis the effective Q of the coil, C is volt of input signal would the resonance capacitance and Cd is correspond to a pulse count of the distributed capacitance, then the a) 500 b) 750 true Q in a Q.meter will be c) 1000 d) 1500 a) Qe[(C + Cd)/C)] b) Qe[C/(C + Cd))] Q.12 When reading is taken at half scale c) Qe[(Cd/(C + Cd)] in the instrument, the error is d) Qe[(C + Cd)/Cd)] a) exactly equal to half of full – scale error. Q.18 A first order instrument is b) equal to full – scale error. characterized by c) less than full – scale error. a) time constant only. d) more than full – scale error.

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission b) static sensitivity and time a) 111.11 Ω b) 105.2 Ω constant. c) 100 Ω d) 90.9 Ω c) static sensitivity and damping coefficient. Q.23 A current i = (10 + 10 sin t) amperes d) static sensitivity, damping is passed through an ideal moving coefficient and natural frequency iron type ammeter. Its reading will of oscillations. be a) zero b) 10 A Q.19 The voltmeter of choice for c) 150A d) 10 2A measuring the emf of a 100 V dc source would be Q.24 An indicating instrument is more a) 100 V, 1 mA sensitive if its torque to weight ratio b) 100 V, 2 mA is c) 100 V, 10 kW/V a) much larger than unity. d) 100 V, 100 W/V b) of the order of unity c) much less the unity. Q.20 A piezoelectric transducer has the d) made deflection dependent. following parameters values Crystal capacitance = 10-9 F Q.25 In PMMC instrument, the central Cable capacitance = 2 × 10-10 F spring stiffness and the strength of Charge sensitivity = 4 × 10-6 F the magnet decrease by 0.04% and Columb/cm 0.02% respectively due to a rise in If the oscilloscope used for read-out temperature by 1°C. With a rise in has an input resistance of 1 MΩ in temperature of 10° C, the parallel with C = 4 × 10-10 F, then the instrument reading wil voltage sensitivity constant will be a) increase by 0.2% a) 2500 V/cm b) 3334 V/cm b) decrease by 0.2% c) 4000 V/cm d) 4500 V/cm c) increase by 0.6% d) decrease by 0.7% Q.21 A high frequency a.c. signal is applied to a PMMC instrument. If the Q.26 Standard call rms value of the a.c. signal is 2 V, a) Will have precise and accurate then the reading of the instrument constant voltage when current will be drawn from it is few a) zero b) 2 V microamperes only. c) 2 2V d) 4 b) Will have precise and accurate constant voltage when few Q.22 In the circuit shown in the figure, if microamperes are drawn from it. the ammeter indicates 1 A and the c) Will continue to have constant voltmeter having an internal voltage irrespective of loading resistance of 1 kΩ indicated 100 V, conditions. then the value of R would be d) Can supply voltages up to 10 V

Q.27 In a Q.meter, an inductor tunes to 2 MHz with 450 pF and to 4 MHz with 90 pF. Thedistributed capacitance of the inductor is a) 30 pF b) 45 pF c) 90 pF d) 360 pF

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission Q.28 If the reading of the two wattmeters Q.33 A voltage of are equal and positive in two- {200 2 sin314t 6 2 sin(942i 30 ) wattmeter method, the load pf in a 8 2 cos(1570t 30 )}V is given to a balanced 3-phase 3-wire circuit will be harmonic distortion meter. The a) zero b) 0.5 meter will indicate a total harmonic c) 0.866 d) unity distortion of approximately a) 4.55% b) 6.5% Q.29 The disc of a house service energy c) 7.5% d) 8.5% meter of 230 V, 50 Hz, 5 A, 2400 rev per kWh creeps at a 1 rev. Per min. Q.34 Ana.c. voltmeter using full-wave The creep error (in percent) of full rectification and having a sinusoidal load unity pF is input has an a.c. sensitivity equal to 60 a) 1.414 times dc sensitivity a) 100 b) dc sensitivity 2400 c) 0.90 times dc sensitivity 60 b) 100 d) 0.707 times dc sensitivity 2400 60 c) 100 Q.35 A spring controlled moving iron 1.15 2400 voltmeter draws a current of 1 mA 60 for full scale value of 100 V. If it d) 100 1.15 2400 draws a current of 0.5 mA. The meter reading is a) 25 V b) 50 V Q.30 which one of the following decided c) 100 V d) 200 V the time of response of an indicating instrument? Q.36 The difference between the a) deflecting system. indicated value and the true value of b) controlling system. a quantity is c) Damping system.. a) gross error d) pivot and jewel bearings. b) absolute error. c) dynamic error. Q.31 A wattmeter has a range of 100 W d) relative error. with an error of ±1% of full scale deflection. If the true power passed Q.37 In the measurement of power on through it is 100 W, then the balanced load by two-wattmeter relative error would be method in a 3- phase circuit, a) ±10% b) ±5% the readings of the wattmeter are 3 c) ±1% d) ±0.5% kW and 1 kW respectively. The letter being obtained after reversing Q.32 A resistance strain guage is fastened the connections to the current coil. to a beam subjected to a stain of 1 × The power factor of the load is 10-6yielding a resistance change of a) 0.277 b) 0.554 240 μΩ. If the original resistance of c) 0.625 d) 0.866 the strain guageis 120 Ω, the guage factor would be Q.38 A first order instrument of power a) 5 b) 2 on balanced Od by two-Wattmeter c) 1 d) 0.2 method in a 3-phase circuit, the readings of the Wattmeter’s are 3

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission kW and 1 kW respectively, the CRO when voltages of latter being obtained after reversing frequencies fx the connections to the current coil. and fy are applied to the x and y The power factor of the load is plates respectively. fx :fy a) Time constant only b) Static sensitivity and time constant c) Static sensitivity and damping coefficient. d) Static sensitivity, damping coefficient and natural fervency is then equal to of oscillations. a) 3 : 2 b) 1 : 2 c) 2 : 3 d) 2 : 1 Q.39 A CRO screen has ten divisions on the horizontal scale. If a voltage Q.44 If an energy meter disc makes 10 signal 5 sin (314 t + 450) is revolution in 100 seconds where a examined with a line base setting of load 450 W is connected to it, the 5 msec/div, the number of cycles of meter constant (in rev/kWh) is signal displayed on the screen will a) 1000 b) 500 be c) 1600 d) 800 a) 0.5 cycles b) 2.5 cycles c) 5 cycle d) 10 cycles Q.45 The minimum number of wattmeter (s) required to measure 3-phase, 3- Q.40 A metal strain gauge factor of 2. Its wire balanced and unbalanced nominal resistance is 120 ohms. If it power is undergoes a strain of 10-5, the value a) 1 b) 2 of change of resistance in response c) 3 d) 4 to the strain is a) 240 ohms Q.46 A 150 mA meter has accuracy of ±2 b) 2 × 10-5 ohms percent. Its accuracy while reading c) 2.4 × 10-3 ohms 75 mA will be d) 1.2 × 10-3 ohms a) ±1% b) ±2% c) ±4% d) ±20% Q.41 A 0 – 10 mA PMMC ammeter reads 4 mA in a circuit. Its bottom control Q.47 A resistor of 10 k-ohm with 5 % spring snaps suddenly. The meter tolerance is connected in series with will now read nearly a 5 k-ohms resistor of 10% a) 10 mA b) 8 mA tolerance. What is the tolerance c) 2 mA d) Zero limit of the series network? a) 5% b) 6.67% Q.42 The difference between the c) 10% d) 8.33% measured value and the true value of a quantity is called Q.48 The voltage across an impedance is a) gross error b) relative error. measured by a voltmeter having c) probable error d) absolute error input impedance competence comparable with the impedance Q.43 A Lissajous pattern, as shown in causing an error in the reading. figure below, is observed on the What is this error called? screen of a a) Random error.

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission b) gross error. 1. The smallest change in the input c) Systematic error. quantity which can be detected d) Loading effect error. with its certainty 2. Closeness of the reading with its Q.49 Two voltmeter have the same range true value 400 V. The internal impedances are 3. Measure of reproducibility of the 30,000 ohms and 20,000 ohms. If measurements. they are connected in series and 600 4. Ratio of infinitesimal change V be applied across them the sensitivity in output to readings are infinitesimal change sensitivity a) 360 V and 240 V in output to infinitesimal change b) 300 V and 300 V in input c) 400 V and 200 V Codes: d) None of these A B C D a) 3 2 1 4 Q.50 A meter has a full-scale angle of 900 b) 2 3 1 4 at a current of 1 A. This meter has c) 2 3 4 1 perfect square-law response. What d) 3 2 4 1 has perfect square-law response. What is the current when the Q.53 Match List-I (Error parameters) deflection angle is 450? with List-II (Values) and select the a) 0.5 A b) 0.65 A correct answer using the codes c) 0.707 A d) 0.87 A given below the lists (σ is the standard deviation of Gaussian Q.51 Which of the following electronic error) instruments (or equipment) can be List – I used to measure correctly the A. Precision index fundamental frequency components B. Probable error of a waveform and its higher C. Error limit harmonics? D. Peak probability density of error 1. Cathode ray oscilloscope List – II 2. Vacuum tube voltmeter 1. 0.67 σ 3. Spectrum analyser 2. 3 σ 4. Distortion factor meter 3. 0.39/ σ Select the correct answer using the 4. 0.71/ σ codes given below Codes: a) 1 and 2 b) 2 and 3 A B C D c) 3 and 4 d) 1 and 4 a) 4 2 1 3 b) 4 1 2 3 Q.52 Match List-I with List-II and select c) 3 1 2 4 the correct answer using the codes d) 3 2 1 4 given below the lists: List – I Q.54 The error introduce by an A. Precision instrument fall in which category? B. Accuracy (a) Systematic error. C. Resolution (b) random error. D. Static (c) Gross Error. List – II (d) Environment errors.

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission Q.55 A dc circuit can be represented by when it reads 222 V. The actual an internal voltage source of 50 V voltage with an output resistance of 100 kΩ. a) lies between 217.56 V and In order to achieve accuracy better 226.44 V than 99% for voltage measurement b) lies between 217.4 V and 226.6 V across its terminals, the voltage c) lies between 216 V and 228 V measuring device should have a d) is exactly 222 V. resistance of at least a) 10 MΩ b) 1 kΩ Q.61 A spring controlled moving iron c) 10 kΩ d) 1 kΩ voltmeter draws a current of 1 mA for full scale value of 100 V. If it Q.56 An analogue voltage signal whose draws a current of 0.5 mA, the meter highest significant frequency is 1 reading is kHz is to be coded with a resolution a) 25 V b) 50 V of 0.01 percent for a voltage range of c) 100 V d) 200 V 0 – 10 V. The minimum number of bits should respectively be Q.62 Sensitivity of potentiometer can be a) 1 kHz and 12 b) 1 kHz and 14 increased by c) 2 kHz and 12 d) 2 kHz and 14 a) Decreasing the length of potentiometer wire Q.57 Two meters X and Y require 40 mA b) Increasing the length of and 50 mA, respectively, to give full- potentiometer wire scale deflection, then c) Decreasing the current in a) sensitivity cannot be judged with potentiometer wire given information d) Decreasing the resistance in the b) both are equally sensitive rheostat in series with the c) X is more sensitive battery. d) Y is more sensitive Q.63 Match List-I (Instrument) with List- Q.58 What is the correct sequence of the II (Measurand) and select the following types of ammeters and correct answer using the codes voltmeters with increasing accuracy? given below the lists 1. Moving iron List – I 2. Moving-coil permanent magnet A. McLeod gauge 3. Induction B. Turbine meter Select the correct answer using the C. Pyrometer codes given below D. Synchros a) 1, 3, 2 b) 1, 2, 3 List – II c) 3, 1, 2 d) 2, 1, 3 1. Temperature 2. Pressure Q.59 The total current l = l1 + l2 in a 3. Flow circuit is measured as l1 = 150 ± 1 A, 4. Displacement l2 = 250 ± 2 A, where the limits of Codes: error are given as standard A B C D deviations. l is measured as a) 1 4 2 3 a)(400 ± 3) A b)(400 ± 2.24) A b) 2 3 1 4 c)(400 ± 1/5) A d)(400 ± 1) A c) 1 3 2 4 d) 2 4 1 3 Q.60 A 300 V full – scale deflection voltmeter has an accuracy of ±2%,

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission Q.64 In a stroboscopic method of Q.69 In digit voltmeter ‘over ranging’ rotational speed measurement of a implies that machine shaft, a) next 4 digit are switched ON N = the machine shaft speed of b) ½ digit is switched OFF rotation of the shaft in c) ½ digit is switched ON revolutions/min d) an indicator short growing n = No. of points on the circuit pattern Q.70 A C.R.O. is operated with X and Y F = No. of flash per min. settings of 0.5 mV/cm and 100 The speed of rotation N will be mV/cm. The screen of the C.R.O is a) N = F + n b) N = F - n 10 cm × 8 cm (X and Y). A sine wave c) N = F/n d) N = F.n of frequency 200 Hz and r.m.s. amplitude of 300 mV is applied to Q.65 To reduce the effect of noise level, the Y-input. The screen will show 100 sets of data are averaged. The a) One cycle of the undistorted sine averaged data set will have a noise wave level reduced by a factor of b) Two cycles of the undistorted a) 10 b) 10 2 sine wave c) 50 2 d) 100 c) One cycle of the sine wave with clipped amplitude Q.66 The “accuracy” of a measuring d) Two cycle of the sine wave with instrument is determined by the clipped amplitude a) closeness of the value indicated by it to the correct value of the Q.71 A Wien-bridge is used is used to measured. measure the frequency of the input b) repeatability of the measured signal. However, the input signal has value. 10% third harmonic distortion. c) speed with which the Specifically the signal is 2 sin 400 πt instrument’s reading approaches + 0.2 sin 1200 πt (with t in sec.). the final value. With this input the balance will d) last change in the value of the a) Lead to a null indication and measured that could be detected setting will correspond to a by the instrument. frequency of 200 Hz b) Lead to a null indication and Q.67 A 1 cm piezoelectric transducer setting will correspond to 260 having a g-coefficient of 58 V/kg/m2 Hz is subjected to a constant pressure c) Lead to a null indication and of 10-3 kg/m2 for about 15 minutes. setting will correspond to 400 The piezoelectric voltage developed Hz by the transducer will be d) not lead to null indication a) 116 mV b) 58 mV c) 29 mV d) 0 mV Q.72 Accuracy is defined as the a) measured of the consistency or Q.68 The output of a piezoelectric crystal reproducibility of the has measurement. a) low amplitude & low impedance b) closeness with which an b) high amplitude & high impedance instrument reading approaches c) low amplitude & high impedance the true value of the quantity d) high amplitude & low impedance being measured.

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission c) smallest measurable input A. Least accurate change. B. More accurate d) ratio of the change in output C. Much more accurate signal of an instrument to a D. Highest possible accurate change in the input. List – II 1. Primary Q.73Match List-I (Parameter) with List-II 2. Secondary (Transducer) and select the correct 3. Working answer using the codes given below 4. International the lists Codes: List – I A B C D A. Pressure a) 3 4 1 2 B. Temperature b) 1 4 3 2 C. Displacement c) 3 2 1 4 D. Stress d) 1 2 3 4 List – II 1. Thermistor Q.77 Measurement of an unknown 2. Piezoelectric crystal voltage with a d.c. Potentiometer 3. Capacitance transducer loses its advantage of open circuit 4. Resistance strain gauge measurement when 5. Ultrasonic waves a) primary circuit battery is Codes: changed A B C D b) standardisation has to be done a) 1 2 5 3 again to compensate for drifts. b) 2 1 4 3 c) Voltage larger than the range of c) 1 2 5 4 the potentiometer are measured. d) 2 1 3 4 d) range reduction by a factor of 10 is employed in the Q.74 Measurement of flow, thermal potentiometer to improve conductivity and liquid level using resolution. thermistors make use of a) Resistance decrease with Q.78 considered the following statement temperature regarding a moving coil instrument. b) Resistance increase with 1. The sensitivity of a moving coil temperature voltmeter is specified in terms of c) Self-heating phenomenon ohms per volt. d) Solar cell, LVDT 2. A higher range moving coil voltmeter has higher sensitivity. Q.75 Pair of active transducers is 3. Higher sensitivity meter give a) Thermistor, Solar cell more reliable result. b) Thermocouple, Thermistor Which of the statement are correct? c) Thermocouple, Solar cell a) 1, 2 and 3. b) 1, 3 and 4. d) Solar cell, LVDT c) 1, 2 and 4. d) 2, 3 and 4.

Q.76 Match List-I (Accuracy) with List-II Q.79 Match List-I (instruments) with List- (Type of the standard) and select II (application) and select the the correct answer using the codes correct answer using the codes given below the lists given below the lists List – I List – I

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission A. Dynamometer instrument List – II B. Thermocouple based instrument 1. Head phone C. Ramp generator 2. D’Arsonval galvanometer D. Weston Standard Cell 3. Cathode ray oscilloscope List – II 4. Vibration galvanometer 1. True r.m.s. value meter 5. Ballistic galvanometer 2. Transfer instrument between a.c Codes: and d.c A B C D 3. Time based of CRO a) 2 1 5 3 4. Standard of Electromotive b) 3 4 1 2 force(Emf) c) 2 4 1 3 Codes: d) 3 1 5 2 A B C D a) 4 1 3 2 Q.83 The secondary winding of a current b) 4 3 1 2 transformer is open when current is c) 2 1 3 4 following in the primary then. d) 2 3 1 4 a) there will be high current in primary. Q.80 A set of independent current b) there will be very high secondary measurements taken by four voltage. observes was recorded as: 117.02 c) the transformer will burn out mA, 117.11 mA, 117.08 mA and immediately. 117.03 mA. What is the range of d) the meter will burn out. error? a) ±0.045 b) ±0.054 Q.84 which one of the following c) ±0.065 d) ±0.056 statements is not correct? a) It is not possible to have precise Q.81 Which of the following bridges can measurement which are not be used for inductance accurate. measurement? b) Correctness in measurements 1. Maxwell’s bridge requires both accuracy and 2. Schering bridge precision. 3. Wein-bridge c) Reproducibility and consistency 4. Hay’s bridge are expressions that best 5. Wheatstone bridge describe precision in Select the correct answer using the measurements. codes given below d) An instrument with 2% accuracy a) 1 and 2 b) 2 and 3 is better than another with 5% c) 3, 4 and 5 d) 1 and 4 accuracy.

Q.82 Match List-I (frequency) with List-II Q.85 A 12 bit A/D convert has a range 0- (Detector) and select the correct 10V. What is the approximate answer using the codes given below resolution of the converter? the lists a) 1 mV b) 2.5 mV List – I c) 2.5 μV d) 12 m V A. Zero frequency B. 50 Hz Q.86 In ananalog data acquisition unit, C. 1200 Hz what is correct sequence of the D. 10 KHz blocks starting from the unit?

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission a) Transducer-Recorder-Signal b) 2 & 3 represent greater condition precision than 1. b) Transducer-Signal condition- d) 1, 2 & 3 represent the same Recorder precision c) Signal condition-Transducer- Recorder Q.91 Match List-I (Parameter to be d) Signal condition-Recorder- measured) with List-II (Instrument Transducer to be Used) and select the correct answer using the codes given below Q.87 Which one of the following digital the lists voltmeters is most suitable to List – I eliminate the effect of period noise? A. Average value of current a) Ramp type digital voltage B. RMS value of current b) Integrating type digital C. Frequency of a wave voltmeter D. Strain gauge resistance c) Successive approximation type List – II digital voltmeter 1. Self-balancing bridge d) Servo type digital voltmeter 2. Wien Bridge 3. PMMC ammeter Q.88 A moving-coil instrument gives full- 4. Moving-iron ammeter scale deflection for 1 mA and has a Codes: resistance of 5Ω. If a resistance of A B C D 0.55Ω is connected in parallel to the a) 3 4 2 1 instrument, what is the maximum b) 2 1 3 4 value of current it can measure? c) 3 1 2 4 a) 5 mA b) 10 mA d) 2 4 3 1

c) 50 mA d) 100 mA Q.92 Match List-I with List-II and select the correct answer using the codes Q.89 A signal slide wire is used for the given below the lists measurement of current in a circuit. List – I The voltage drop across a standard A. Digital Counter resistance of 1.0Ω is balanced at 70 B. Schering Bridge cm. What is the magnitude of the C. Megger current, if the standard cell having is D. Spectrum Analyser balanced at 50 cm? List – II a) 3.09 A b) 2.65 A 1. Measurement of harmonics c) 2.03 A d) 1.45 A 2. Measurement of frequency 3. Measurement of dielectric loss Q.90 A resistance of 105 ohms is 4. Measurement of insulation specified using significant figure as resistance indicated below: Codes: 1. 105 ohms A B C D 2. 105.0 ohms a) 1 3 4 2 3. 0.000105 ohms b) 2 4 3 1 Among these c) 1 4 3 2 a) 1 represent greater precision d) 2 3 4 1 than 2 and 3 b) 2 represent greater precision but Q.93 Match List-I (Instrument) with List- 1 & 3 represent same precision. II (Error) and select the correct

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission answer using the codes given below b) 2 and 3 represent greater the lists precision than 1. List – I d) 1, 2 and 3 represent the same A. PMMC voltmeter precision B. AC ammeter C. Current transformer Q.97 The meter constant a signal phase D. Energy meter 240 V induction wattmeter meter is List – II 400 revolution per KWh. The speed 1. Eddy current error of the meter disc for a current of 10 2. Phase angle error Amps of 0.8 p.f. lagging will be 3. Braking system error a) 12.8 rpm b) 16.02 rpm 4. Temperature error c) 18.2 rpm d) 21.1 rpm Codes: A B C D Q.98 A force with which the plates of a a) 2 3 4 1 parallel plate capacitor having b) 4 1 2 3 charge Q and area of each plate A, c) 2 1 4 3 attract each other is d) 4 3 2 1 1. Directly proportional to Q 2. Directly proportional to Q2 Q.94 What is the series resistance 3. Inversely proportional to A required to extend the 0-100V range a) 1 and 2 only b) 2 and 3 only of a 20000 Ω/V meter to 0-1000V? c) 1 and 3 only d) 1, 2 and 3 a) 10 MΩ b) 16 MΩ c) 18 MΩ d) 20 MΩ Q.99 A 10 bit A/D converter is used to digities an analog signal in the 0 and Q.95 which of the following can be used/ 5 range. The maximum peak to peak modified for measurement of ripple voltage that can be allowed in angular speed? the D.C. voltage is 1. LVDT a) nearly 100 mV b) nearly 50 mV 2. Magnetic pick-up c) nearly 25 mV d) nearly 0.5 mV 3. Tacho-generator 4. Strain gauge Q.100 The sensitivity of voltmeter using 0 Select the correct answer using the to 5 mA meter movement is code given below a) 50 Ω/volt b) 100 Ω/volt a) Only 1 and 2 b) Only 2 and 3 c) 200 Ω/volt d) 500 Ω/volt c) Only 3 d) Only 2, 3 and 4 Q.101 Twomillimetres, with a full scale Q.96 A resistance of 108 Ω is specified current of 1 mA and 10 mA are using significant figure as indicated connected in parallel and they read below: 0.5 mA and 2.5 mA respectively. 1. 108 Ω Their internal resistance are in the 2. 108.0 Ω radio of 3. 0.000108 MΩ a) 1 : 10 b) 10 : 1 Among these c) 1 : 5 d) 5 : 1 a) 1 represent greater precision than 2 and 3 Q.102 Which one of the following b) 1 represent greater precision statement is correct? than 1 and 3 represent same The application of the instrument in precision. wrong manner in the procedure of measurement result in a/an

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission a) systematic error. a) 57500 pulses b) 5750 pulses b) random error. c) 575 pulses d) 57.5 pulses c) gross error. d) instrument error Q.108 What are the causes of gross error in the instruments? Q.103 The relation which related the gauge 1. Misreading of instrument factor ‘K’ to Poisson ratio ‘μ’ is given 2. Incorrect adjustment of as instrument a) μ = 1 + 2 K b) μ = 1 – 2 K 3. Error due to defective c) K = 1 – 2 μ d) K = 1 + 2 μ instrument 4. Error due to effect environment Q.104 A Wien Bridge oscillator has on the instrument a) two feedback paths, both positive Q.109 In a CRT, 3 × 1017 electrons are b) two feedback paths, both accelerated through a potential negative difference of 10,000 V over a c) one positive and one negative distance of 40mm per minute. feedback, positive greater than Calculate the average power negative feedback supplied to the beam of electrons. d) one positive and one negative a) 2 W b) 4 W feedback, positive less than c) 6 W d) 8 W negative feedback Q.110 Calculate the maximum velocity of Q.105 The full scale deflection current of a the beam of electrons in a CRT meter is 1 mA and its internal having a cathode anode voltage of resistance is 100Ω. This meter is to 1000 V. Assume the electrons to have full deflection when 100 V is leave the cathode with zero velocity. measured. What is the volume of Charge of electron = 1.6 × 10-19 C series resistor to be used? and mass of electron = 1.9 × 10-13 kg. a) 99.99 kΩ b) 100 kΩ a) 0.1875 × 106 m/s c) 99.99 Ω d) 100 Ω b) 0.1875 × 107 m/s c) 0.1875 × 108 m/s Q.106 A bridge type rectification meter d) 0.1875 × 109 m/s and a thermocouple meter employ moving coil movement for Q.111 A zero to 300 V voltmeter has a indication. Both are calibrated on a guaranteed accuracy of 1% full scale 100 Hz sinusoidal wave from, if a reading. The voltage measured by 100 Hz rectangular waveform is the instrument is 83 V. The percent applied to each, the ratio of their limiting error i readings will be a) 0.95 b) 1.81 a) 2 : 1 b) 1.11 : 1 c) 3.62 d) 4.85 c) 1.41 : 1 d) 1.21 : 1 Q.112 A utility type voltmeter with an Q.107 Pulses from the clock of frequency accuracy of ±3% of full scale (at 100 KHz pass through the counter of 250C) is used on 300 V scale to digital multi meter during a gate measure 230 V. (a) What is the period 5.75 m sec. The number of possible percentage error? (b) What pulses counted by the counter will range will the actual voltage fall be

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission within if the instrument reads 200 V? a) 3.9%, 200 V b) 3.9%, 191-209 V c) 7.6%, 221-239 V d) 7.6%, 200 V

Q.113 In a dual slope integrating type digital voltmeter the first integration is carried out for 10 a) 375 Ω, 75 mH b) 75 Ω, 150 mH periods of the supply frequency of c) 37.5 Ω, 75 mH d) 75 Ω, 75 mH 50 Hz. If the reference voltage used is 2 V the total conversion time for Q.117 The current flowing through the an input of 1 V is galvanometer having an internal a) 0.01 sec b) 0.05 sec resistance of 1.25 k Ω as shown in c) 0.1 sec d) 1 sec Fig. is

Q.114 Consider the following. 1. Human error 2. Improper application of instrument 3. Error due to worn part of instrument 4. Error due to effects of environment. 1 1 Which of the above come under the a) mA b) mA type of systematic error? 3 5 a) 1 and 2 b) 2 and 3 1 c) mA d) 0 mA c) 3 and 4 d) 1 and 4 8

Q.115 When testing a coil having a Q.118 If two ac signals of same frequency resistance of 10 Ω, resonance are applied to the X and Y plates of a occurred when the oscillator CRO and the display shows a frequency was 10 MHz and the straight line with a negative slope, rotating capacitor was set at 500/2π the phase shift between the signals pF. The effective value of the Q of is the coil is a) 45° b) 90° a) 20 b) 254 c) 135° d) 180° c) 314 d) 542 Q.119 The bridge circuit shown in Fig. Q.116) In the Maxwell bridge as shown in the figure below, the values of resistance Rx and inductance Lx of a coil are to be calculated after balancing the bridge. The component values are shown in the figure at balance. The values of Rx and Lx will respectively

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission a) cannot be balanced Q.120 Which one of the following type of b) can be balanced but the error come under systematic error? frequency of excitation must be 1. Irregular spring tension. known 2. Improper readings of an c) can be balanced for only one instrument. frequency 3. Loading effects. d) can be balanced at any 4. Error due to the presence of frequency. electric filed or magnetic field a) 1 and 2 b) 2 and 3 c) 3 and 1 d) 4 and 1 ANSWER KEY:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 (c) (d) (d) (a) (d) (a) (b) (c) (a) (a) (c) (c) (d) (a) 15 16 17 18 19 20 21 22 23 24 25 26 27 28 (d) (b) (b) (b) (c) (a) (a) (a) (c) (a) (a) (a) (a) (d) 29 30 31 32 33 34 35 36 37 38 39 40 41 42 (d) (c) (a) (b) (a) (c) (a) (b) (a) (b) (b) (c) (a) (d) 43 44 45 46 47 48 49 50 51 52 53 54 55 56 (c) (d) (b) (c) (b) (b) (a) (c) (c) (a) (b) (a) (a) (d) 57 58 59 60 61 62 63 64 65 66 67 68 69 70 (c) (c) (b) (c) (a) (b) (b) (c) (d) (a) (b) (c) (c) (a) 71 72 73 74 75 76 77 78 79 80 81 82 83 84 (d) (a) (d) (a) (c) (c) (c) (c) (c) (a) (d) (c) (b) (a) 85 86 87 88 89 90 91 92 93 94 95 96 97 98 (b) (b) (d) (b) (c) (b) (a) (d) (b) (c) (b) (b) (a) (b) 99 100 101 102 103 104 105 106 107 108 109 110 111 112 (d) (c) (d) (c) (d) (c) (a) (b) (c) (a) (d) (c) (c) (b) 113 114 115 116 117 118 119 120 (c) (c) (a) (a) (b) (d) (d) (c)

Q.1 (c) 768 = rpm = 12.8 rpm 3 Sensitivity = mm/ohm 60 6 Q.11 (c) Q.2 (d) 9.999 Q.12 (c) Resolution = = 1mV 9999 Q.13 (b) Q.3 (d) fy No.of horizontal tangent 2 = P = l R fx No.of vertical tangle P R = fy 5 I2 = δR δP 2δI 1000 2  ± fy = 2500 Hz RPI = ±1.5×(2×1) Q.14 (a) δR = ± 3.5% R Q.15 (d)

Q.4 (a) Q.16 (b) δV = 2% Q.5 (d) V 2 Q.6 (a) δV = 300 = 6 V 100 Q.7 (b) So range of reading = 30 ± 6 In dynamometer type wattmeter, = 24 V to 36 the fixed coil is current coil and moving coil us voltage coil or Q.17 (b) pressure coil. Q.18 (b)

Q.8 (c) Q.19 (c) When power factor cos = 0.5 then one wattmeter reads zero. The load Q.20 (a) is lagging in this case. Q.21 (a) Q.9 (a) Because PMMC reads only d.c. value or average value. Q.10 (a) Meter constt.=400 revolution parkwh Q.22 (a) 240 10 0.8 = 400 revolutions per 1000 hour = 768 revolution per hour

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission V = I1R Q.32 (b) 103 R But I1 = .I 103  R  Gauze factor = R I = 1 A and V = 100 V L 103 L 100 = .R 3 6 10  R 240 10 = ∴ R = 111.11  120 106 Gauze factor = 2 Q.23 (c) Moving iron type ammeter reads Q.33 (a) average value Total harmonic distortion 102 Totalharmonics ∴ Reading = 102  100 2 Totalrms Reading = 150 A 6822 100 2 2 2 Q.24 (a) 6 8 200 T.H.D. = 4.55% Q.25 (a) For 10℃ spring stiffness K’ = K- Q.34 (c) 0.4% of K K’ = 0.996 K Q.35 (a) For 10℃ New B’ = B-0.2% of B In Moving iron voltmeter deflection = 0.998 B α I2 2 Kθ NBAI 100 1 =  K'θ' NB'AI  V1  0.5  .999K B = V1 = 25 V ' K 0.998B Q.36 (b) Θ’ = 1.002 Θ So the instrument reading increase Q.37 (a) by 0.2% PP tanθ = 3 12 PP Q.26 (a) 12 The makers specify the maximum P1= 3 kW value as 100 μA. This means that the P2= -1 kW current drawn from the cell should 4 tanθ = 3  be less than 100 μA and this current 2 should flow momentarily. tanθ = 23 θ = 73.89 Q.27 (a) Power factor =cos θ = 0.277

Q.28 (d) Q.38 (b)

Q.29 (d) Q.39 (b) Line base setting = 5 m sec./div. Q.30 (c) for 10 division = 50 m sec. ω = 314 Q.31 (a) 2πf = 314

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission f = 50Hz ∴ Accuracy while reading 72 mA ∴ No. of cycles = 50×10-3×50 3 = 100   4% = 2.5 cycles 75

Q.40 (c) Q.47 (b) R Tolerance for 10 k R 5 Gauze factor = = 10K 0.5K L 100 L Tolerance for 5 k = R 10 5K 0.5K 2 = 120 100 105 Total tolerance = 0.5 + 0.5 = 1 K ∆R = 2.4×10-3  Total resistance in series = 10 + 5 = 15 K Q.41 (a) ∴ Tolerance limit = When control spring snaps it given 1 100 6.67% full scale deflection. Because there is 15 no controlling torque present. Q.48 (b) Q.42 (d) Q.49 (a) Q.43 (c) Total impedance = 30000+20000 fy No.of horizontal tangent = = 50000 fx No.of vertical tangle ∴ Current through them 1 600 = =  .012A 1.5 50000 2 Voltage across 1st voltmeter = 3 = .012 × 30000 = 360 V Q.44 (d) Voltage across IInd voltmeter Revolution per kW = = 0.012×20000 10 104 = 240 V 3  450 10 450 Q.50 (c) 4 10 3600 2 Revolution per kWh = ∝ I 450 100 2 11I = 800  2 22I  Q.45 (b) 2 1  Two wattmeter method will be 2   2 used to measure 3-phase, 3 wire I2 balanced and unbalanced power. 4 ∴ I2= 0.707 Q.46 (c) Error while reading 150mA Q.51 (c) 2 Both spectrum analyzer and = 150 100 distortion factor meter are single = 3 mA analyzers. A spectrum analyzer

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission sweeps the single frequency band and displays a plot of amplitude Q.60 (c) versus frequency. Distortion factor metcs.er tunes out the fundamental Q.61 (a) 2 signal and gives an indication of the 100 1 harmonics. ∝ I2   0.5 Q.52 (a)    25 V

Q.53 (b) Q.62 (b)

Q.54 (a) Q.63 (b)

Q.55 (a) Q.64 (c) E 49.5 1 L  Z  10M  Q.65 (d) E 50 100K L 0 1 Z L Q.66 (a)

Q.56 (d) Q.67 (b) Minimum sampling frequency = V =g.p Nyquist V = 58×10-3 = 58 mV Sampling Rate = 2kHz and resolution Q.68 (c) = 0.01 1 = 100 Q.69 (c) 21n  n ≈ 14 Q.70 (a)

Q.57 (c) Q.71 (d) Refer static sensitivity. Q.72 (a) Q.58 (c) Induction principle is more Q.73 (d) generally used for Watt-hour meter than for ammeter and voltmeter Q.74 (a) owing to their comparatively high Thermistors have negative cost and inaccuracy of induction resistance instruments of the latter types. temperature coefficients.

Q.59 (b) Q.75 (c) 22 II      22   Q.76 (c) 1  I12   I II12    II Q.77 (c) 1 II 12 Q.78 (c) 2 2 2 2 ∴ 1 (1) (1)  (1) (2)  2.24A ∴ I = (400±2.24)A Q.79 (c)

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission 2.03 ∴ Current through resistor = Q.80 (a) 1 Average current, = 2.03 A 117.02 117.08  117.11  117.03 = 4 Q.90 (b) = 117.06mA as Imax = 117.11 mA &Imin Q.91 (a) = 117.02 mA ∴ range of error Q.92 (d) IIII      = ± max av av min 2 Q.93 (b) 0.05 0.04 = ± Q.94 (c) 2 Initial resistance = 20000 × 100 = = ±0.045 mA 2M  Final resistance = 20000 × 100 Q.81 (d) = 20M ∴ Series resistance = 20 – 2 = 18 M Q.82 (c) Q.95 (b) Q.83 (b) LVDT and strain gauge measure linear displacement. Q.84 (a) Q.96 (b) Q.85 (b) Approximate resolution Q.97 (a) 10 =  2.5 mV 400 rev → 1 kw 12 21  400 20 Rpm speed =  60 3 Q.86 (b) 240 10 0.8 Power is = 1000 Q.87 (d) = 1.92 kw Refer potentiometric type digital 20 required speed = × 1.92 voltmeter 3 = 12.8 rpm Q.88 (b) V = 5 × 1 = 5 mV Q.98 (b) 5 .55 55 New resistance =  5.55 111 Q.99 (d) 5 111 The smallest incremental change is ∴ Imax = 10 mA 55 11 =  210 1024 Q.89 (c) 5 For 5 V, = nearly 5 mV. Voltage drop per unit length 1024 = 1.45/50 = 0.029 V/cm Voltage drop across 70 cm. length Q.100 (c) = 0.029 × 70 = 2.03 V 1 Sensitivity (I) = 200 N 5mA

© Copyright Reserved by Gateflix.in No part of this material should be copied or reproduced without permission 2 1.6  1019  1000 Q.101 (d) = 9.1 1031 1 1∝ = 0.1875 108 m/s R RI2.5 5 ∴ 12   Q.111 (c) R21 I 0.5 1 1 % accuracy means that a 300 1 maximum possible error of Q.102 (c) 100 = 3 may be present in any reading. Q.103 (d) Since the deflection is 83 V the 3 present limiting error is 100 = Q.104 (c) 83 3.62. Q.105 (a) Series resister Q.112 (b) 1 3 = 100K  1  K  = 99.99 K  Error = 300 = 9V 100 100 (a) Possible % error to measure 230 Q.106 (b) V In bridge type rectifier meter 9 = 100 = 3.9% Reading =Vms = 1.11 Vav 230 In Thermocouple meter for square (b) Range = 230 ± 9 = 191 – 209 V wave Reading =Vms = Vav Q.113 (c) ∴ Ratio = 1.11 : 1 In a dual slope integrating type digital voltmeter Q.107 (c) ∴ Vin =Vref (t2/t1) No. of pulses = 5.75 × 100 = 575 Where t1 is the first integration time pulses t1 = 10 × 1/50 = 0.2 sec

Vm = 1 V Q.108 (a) Vref= 2

t1 Q.109 (d) t2 = Vin × V Total energy supplied by the source ref 0.2 in one minute. = 1 = 0.1 sec W = 3 × 1017 × 10-19 × 10000 2 = 4.8 × 102 J = 480 J ∴ Average power supplied to the Q.114 (c) beam = 480/60 = 8 W Q.115 (a) L 1 Q = 0  Q.110 (c) RCR0 Work done by the electric field = eV 1 1 = Kinetic energy = mv2 = eV 500 / 2  1012  2  107  10 2 4 2eV 10 10000 V = = 20 m 500 500

R3 750 R1 = R2  2000   375 W R4 4000 L1 = R2R3C4 = 2000×750×0.05×10-5 = 75 mH

Q.117 (b)

Q.118 (d)

Q.119 (d)

Q.120 (c)