Measurement and Instrumentation Unit 1-standards and Instruments

Functions of Instruments and Measurement Systems Instruments or measurement system are classified based upon the function they performed.

1. Indicating Function:- Different kinds of methods for supplying information concerning the variable quantity under measurement 2. Recording Function:- Stores or write the value of quantity under measurement. 3. Controlling Function:- In this case the information is used by the instrument or the system to control the original measured

History of Instruments The history of development of instrument encompasses three phases of instruments

 Mechanical Instruments Very reliable for static and stable condition Unable to respond rapidly to measurements of dynamic and transient condition Due to rigid, heavy and bulky parts have large mass hence cannot faithfully follow the rapid change are potential source of noise pollution  Electrical Instruments Electrical instrument are more rapid than mechanical type An electrical system normally depends upon a mechanical meter movement as indicating device.  Electronic Instruments Today’s requirement of measuring instrument is very fast response Electronic instrument uses semiconductor devices Since in electronic devices, the only movement involved is that of electrons the response time is very small

Application of measurement Systems 1. Monitoring of process and operation- simply indicating the value or condition of parameter under study. For example- water and electricity meter 2. Control of process and operations- automatic control system a very strong association between measurement and control for example: refrigeration with thermostatic control 3. Experimental Engineering analysis: engineering problem, theoretical and experimental methods may be used depending upon the nature of the problem

Units: A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same quantity.[1] Any other value of that quantity can be expressed as a simple multiple of the unit of measurement.

INTERNATIONAL SYSTEM OF UNITS:

The International System of Units (French: Système international d'unités pronounced abbreviated as SI) is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units.

The system was published in 1960 as the result of an initiative that began in 1948. It is based on the metre-kilogram-second system of units (MKS) rather than any variant of the centimetre- gram-second system (CGS). SI is intended to be an evolving system, so prefixes and units are created and unit definitions are modified through international agreement as the technology of measurement progresses and the precision of measurements improves.

SI Units are category as follows:

1.Fundamental-6 2.Supplementry-2 3.Derived -27

FUNDAMENTAL UNITS:

SI base units

Unit Dimensio Unit Quantity symbo Definition (incomplete)[n 1] n name name

l symbol

 Original (1793): 1/10000000 of the meridian through Paris between the North Pole and the Equator.FG  Interim (1960): 1650763.73 wavelength s in a vacuum of the radiation corresponding to the L

metre m length transition between the 2p10 and 5d5 quantum levels of the krypton- 86 atom.  Current (1983): The distance travelled by light in vacuum in 1/299792458 second.  Original (1793): The grave was defined kilogram[ as being the weight [mass] of one cubic n 2] kg mass decimetre of pure water at its freezing M

point.FG  Current (1889): The mass of the international prototype kilogram.

 Original (Medieval): 1/86400 of a day.  Interim (1956): 1/31556925.9747 of the tropical year for 1900 January 0 at 12 hours ephemeris time.

second s time T  Current (1967): The duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.  Original (1881): A tenth of the electromagnetic CGS unit of current. The [CGS] electromagnetic unit of current is that current, flowing in an arc 1 cm long of a circle 1 cm in radius, that creates a field of one oersted at the electric centre.[39] IEC ampere A I

current  Current (1946): The constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 m apart in vacuum, would produce between these conductors a force equal to 2×10−7 newtons per metre of length.  Original (1743): The centigrade scale is obtained by assigning 0 °C to the freezing point of water and 100 °C to the boiling point of water. thermodynam kelvin K  Interim (1954): The triple point of Θ ic temperature water (0.01 °C) defined to be exactly 273.16 K.[n 3]  Current (1967): 1/273.16 of the thermodynamic temperature of the triple point of water  Original (1900): The molecular weight of a substance in mass grams.ICAW amount of mole mol  Current (1967): The amount of N substance substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12.[n 4]  Original (1946): The value of the new candle is such that the brightness of the full radiator at the temperature of solidification of platinum is 60 new luminous candles per square centimetre. candela cd J  intensity Current (1979): The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 5.4×1014 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

SUPPLEMENTARY UNITS

 Unit of plane angle : radian ( rad)

 Unit of solid angle : steradian (sr)

DERIVED UNITS

The derived units in the SI are formed by powers, products or quotients of the base units and are unlimited in number.[22]:103[33]:3 Derived units are associated with derived quantities, for example velocity is a quantity that is derived from the base quantities of time and length, so in SI the derived unit is metres per second (symbol m/s). The dimensions of derived units can be expressed in terms of the dimensions of the base units.

Named units derived from SI base units[33]:3

Expressed in Expressed in

Name Symbol Quantity terms of terms of other SI SI base units units

−1

radian rad angle m·m

2 −2

steradian sr solid angle m ·m

−1

hertz Hz frequency s

−2 newton N force, weight kg·m·s

2 −1 −2 pascal Pa pressure, stress N/m kg·m ·s

2 −2 joule J energy, work, heat N·m kg·m ·s

2 −3 watt W power, radiant flux J/s kg·m ·s

electric charge or quantity of coulomb C s·A electricity

voltage (electrical potential 2 −3 −1 volt V W/A kg·m ·s ·A difference), electromotive force

−1 −2 4 2

farad F electric capacitance C/V kg ·m ·s ·A

electric 2 −3 −2 ohm Ω V/A kg·m ·s ·A resistance, impedance, reactance

−1 −2 3 2

siemens S electrical conductance A/V kg ·m ·s ·A

2 −2 −1

weber Wb magnetic flux V·s kg·m ·s ·A

2 −2 −1

tesla T magnetic flux density Wb/m kg·s ·A

2 −2 −2

henry H inductance Wb/A kg·m ·s ·A degree °C temperature relative to 273.15 K K

Celsius

lumen lm luminous flux cd·sr cd

2 −2

lux lx illuminance lm/m m ·cd

−1 becquerel Bq radioactivity (decays per unit time) s

2 −2 gray Gy absorbed dose (of ionizing radiation) J/kg m ·s

2 −2 sievert Sv equivalent dose (of ionizing radiation) J/kg m ·s

−1

katal kat catalytic activity mol·s

Standard In measurements

• International standards

• Primary

• Secondary

• Working

Functional Elements of an Instrumentation system An Instrument may be defined as a device or a system which is designed to maintain a functional relationship between prescribed properties of physical variables and must include ways and means of communication to a human observer

Most of the measurement system contains following main functional elements as shown in figure

1. Primary Sensing Element. 2. Variable Conversion Element 3. Variable Manipulation Element 4. Data Transmission Element 5. Data Presentation Element

Primary Sensing Element: - The Measurand is first detected by primary sensing element. The primary sensing element transfers the measurand to variable conversion element for further processing. The output signal of a primary sensing element is a physical variable such as displacement or voltage.

Variable Conversion Element: - The output signal of a primary sensing element may require to be converted to more suitable variables while preserving its information content. This function is performed by variable conversion element and it may be considered as an intermediate transducer

Variable Manipulation Element: - This element is an intermediate stage of a measuring system. It modifies the direct signal by amplification, filtering, etc; so that a desired output is produced the physical nature of the variable remains unchanged during this stage.

Data Transmission Element: - when the functional elements of the measuring system are spatially separated then it becomes necessary to transmit signals from one element to another. This function is performed by data transmission element. It is an essential functional element where remote control operation is desired.

Data Presentation Element: - usually information about the quantity being measured is to be communicated to human observer for monitoring control and analysis purpose. This is therefore, to be presented in form of human sensory capability. This function is done by data presentation element.

STATIC & DYNAMIC CHARACTERISTICS OF MEASUREMENT SYSTEM: The performance characteristics of an instrument are mainly divided into two categories: i) Static characteristics ii) Dynamic characteristics

Static characteristics:

The set of criteria defined for the instruments, which are used to measure the quantities which are slowly varying with time or mostly constant, i.e., do not vary with time, is called ‘static characteristics’.

The various static characteristics are: i) Accuracy ii) Precision iii) Sensitivity iv) Linearity v) Reproducibility vi) Repeatability vii) Resolution viii) Threshold ix) Drift x) Stability xi) Tolerance xii) Range or span

Accuracy:

It is the degree of closeness with which the reading approaches the true value of the quantity to be measured. The accuracy can be expressed in following ways: a) Point accuracy:

Such accuracy is specified at only one particular point of scale. It does not give any information about the accuracy at any other Point on the scale. b) Accuracy as percentage of scale span:

When an instrument as uniform scale, its accuracy may be expressed in terms of scale range. c) Accuracy as percentage of true value:

The best way to conceive the idea of accuracy is to specify it in terms of the true value of the quantity being measured. Precision: It is the measure of reproducibility i.e., given a fixed value of a quantity, precision is a measure of the degree of agreement within a group of measurements. The precision is composed of two characteristics: a) Conformity:

Consider a resistor having true value as 2385692 , which is being measured by an ohmmeter. But the reader can read consistently, a value as 2.4 M due to the nonavailability of proper scale. The error created due to the limitation of the scale reading is a precision error. b) Number of significant figures:

The precision of the measurement is obtained from the number of significant figures, in which the reading is expressed. The significant figures convey the actual information about the magnitude & the measurement precision of the quantity. The precision can be mathematically expressed as:

Where, P = precision Xn = Value of nth measurement Xn = Average value the set of measurement values

Sensitivity:

The sensitivity denotes the smallest change in the measured variable to which the instrument responds. It is defined as the ratio of the changes in the output of an instrument to a change in the value of the quantity to be measured. Mathematically it is expressed as,

Thus, if the calibration curve is liner, as shown, the sensitivity of the instrument is the slope of the calibration curve. If the calibration curve is not linear as shown, then the sensitivity varies with the input. Inverse sensitivity or deflection factor is defined as the reciprocal of sensitivity. Inverse sensitivity or deflection factor = 1/ sensitivity

Reproducibility:

It is the degree of closeness with which a given value may be repeatedly measured. It is specified in terms of scale readings over a given period of time.

Repeatability:

It is defined as the variation of scale reading & random in nature Drift: Drift may be classified into three categories: a) zero drift:

If the whole calibration gradually shifts due to slippage, permanent set, or due to undue warming up of electronic tube circuits, zero drift sets in. b) span drift or sensitivity drift

If there is proportional change in the indication all along the upward scale, the drifts is called span drift or sensitivity drift. c) Zonal drift:

In case the drift occurs only a portion of span of an instrument, it is called zonal drift.

Resolution:

If the input is slowly increased from some arbitrary input value, it will again be found that output does not change at all until a certain increment is exceeded. This increment is called resolution.

Threshold:

If the instrument input is increased very gradually from zero there will be some minimum value below which no output change can be detected. This minimum value defines the threshold of the instrument.

Stability:

It is the ability of an instrument to retain its performance throughout is specified operating life.

Tolerance:

The maximum allowable error in the measurement is specified in terms of some value which is called tolerance.

Range or span:

The minimum & maximum values of a quantity for which an instrument is designed to measure is called its range or span.

Dynamic characteristics: The set of criteria defined for the instruments, which are changes rapidly with time, is called ‘dynamic characteristics’.

The various static characteristics are: i) Speed of response ii) Measuring lag iii) Fidelity iv) Dynamic error

Speed of response:

It is defined as the rapidity with which a measurement system responds to changes in the measured quantity.

Measuring lag:

It is the retardation or delay in the response of a measurement system to changes in the measured quantity. The measuring lags are of two types: a) Retardation type:

In this case the response of the measurement system begins immediately after the change in measured quantity has occurred. b) Time delay lag:

In this case the response of the measurement system begins after a dead time after the application of the input. Fidelity: It is defined as the degree to which a measurement system indicates changes in the measurand quantity without dynamic error.

Dynamic error:

It is the difference between the true value of the quantity changing with time & the value indicated by the measurement system if no static error is assumed. It is also called measurement error.

GALVANOMETER

Galvanometer is an electromechanical instrument which is used for the detection of electric currents through a circuit. Being a sensitive instrument, Galvanometer can not be used for the measurement of heavy currents. A galvanometer works as an actuator, by producing a rotary deflection (of a "pointer"), in response to electric current flowing through a coil in a constant magnetic field.

Sensitive galvanometers have been essential for the development of science and technology in many fields. For example, they enabled long range communication through submarine cables, such as the earliest Transatlantic telegraph cables, and were essential to discovering the electrical activity of the heart and brain, by their fine measurements of current.

D'ARSONVAL GALVANOMETER

D’Arsonval Principle :  An action caused by electromagnetic deflection, using a coil of wire and a magnetized field. When current passes through the coil, a needle is deflected.  Whenever electrons flow through a conductor, a magnetic field proportional to the current is created.  This effect is useful for measuring current and is employed in many practical meters.Since most of the meters in use have D’Arsonval movements, which operate because of the magnetic effect, only this type will be discussed in detail.  The basic dc meter movement is known as the D’Arsonval meter movement because it was first employed by the French scientist, D’Arsonval, in making electrical measurement.  This type of meter movement is a current measuring device which is used in the ammeter, voltmeter, and ohmmeter.  Basically, both the ammeter and the voltmeter are current measuring instruments, the principal difference being the method in which they are connected in a circuit. While an ohmmeter is also basically a current measuring instrument, it differs from the ammeter and voltmeter in that it provides its own source of power and contains other auxiliary circuits. Construction of D’Arsonval galvanometer: This instrument is very commonly used in various methods of resistance measurement and also in d.c. potentiometer work.

1) Moving Coil:  It is the current carrying element. It is either rectangular or circular in shape and consists of number of turns of fine wire. This coil is suspended so that it is free to turn about its vertical axis of symmetry.

 It is arranged in a uniform, radial, horizontal magnetic field in the air gap between pole pieces of a permanent magnet and iron core.

 The iron core is spherical in shape if the coil is circular but is cylindrical if the coil is rectangular.  The iron core is used to provide a flux path of low reluctance and therefore to provide strong magnetic field for the coil to move in this increases the deflecting torque and hence the sensitivity of the galvanometer.

2) Damping:  There is a damping torque present owing to production of eddy currents in the metal former on which the coil is mounted.

 Damping is also obtained by connecting a low resistance across the galvanometer terminals. Damping torque depends upon the resistance and we can obtain critical damping by adjusting the value of resistance.

3) Suspension:  The coil is supported by a flat ribbon suspension which also carries current to the coil. The other current connection in a sensitive galvanometer is a coiled wire. This is called the lower suspension and has a negligible torque effect.

 The upper suspension consists of gold or copper wire of nearly 0.012-5 or 0.02-5 mm diameter rolled into the form of a ribbon. This is not very strong mechanically; so that the galvanometers must he handled carefully without jerks.

 Sensitive galvanometers are provided with coil clamps to the strain from suspension, while the galvanometer is being moved.

4) Indication:  The suspension carries a small mirror upon which a beam of light is cast. The beam of light is reflected on a scale upon which the deflection is measured.

 This scale is usually about 1 meter away from the instrument, although ½ meter may be used for greater compactness.

5) Zero Setting: A torsion head is provided for adjusting the position of the coil and also for zero setting.

Galvanometer to Voltmeter ,Ammeter and ohm meter :

Torque Equation:

TYPES OF ANALOG INSTRUMENTS

1. Moving coil type

 Permanent magnet Moving coil Type –used for DC measurement only

 Dynamometer Type- used for DC & AC measurement

2.Moving Iron Instruments

 Permanent magnet Moving coil Type –used for DC measurement only

Working Principle:

Permanent Magnet Moving Coil Mechanism (PMMC) In PMMC meter or (D’Arsonval) meter or galvanometer all are the same instrument, a coil of fine wire is suspended in a magnetic field produced by permanent magnet.

According to the fundamental law of electromagnetic force, the coil will rotate in the magnetic field when it carries an electric current by electromagnetic (EM) torque effect. A pointer which attached the movable coil will deflect according to the amount of current to be measured which applied to the coil.

The (EM) torque is counterbalance by the mechanical torque of control springs attached to the movable coil also. When the torques are balanced the moving coil will stopped and its angular deflection represent the amount of electrical current to be measured against a fixed reference, called a scale.

If the permanent magnet field is uniform and the spring linear, then the pointer deflection is also linear.

Construction:

A coil of thin wire is mounted on an aluminum frame (spindle) positioned between the poles of a U shaped permanent magnet which is made up of magnetic alloys like alnico.

The coil is pivoted on the jewelled bearing and thus the coil is free to rotate. The current is fed to the coil through spiral springs which are two in numbers. The coil which carries a current, which is to be measured, moves in a strong magnetic field produced by a permanent magnet and a pointer is attached to the spindle which shows the measured value.

Mathematical Representation of PMMC Mechanism:

Assume there are (N) turns of wire and the coil is (L) in long by (W) in wide. The force (F) acting perpendicular to both the direction of the current flow and the direction of magnetic field is given by: where N: turns of wire on the coil I: current in the movable coil

Applications:

The PMMC has a variety of uses onboard ship. It can be used as:

1) Ammeter:

When PMMC is used as an ammeter, except for a very small current range, the moving coil is connected across a suitable low resistance shunt, so that only small part of the main current flows through the coil.

The shunt consists of a number of thin plates made up of alloy metal, which is usually magnetic and has a low temperature coefficient of resistance, fixed between two massive blocks of copper. A resistor of same alloy is also placed in series with the coil to reduce errors due to temperature variation.

2) Voltmeter:

When PMMC is used as a voltmeter, the coil is connected in series with high resistance. Rest of the function is same as above. The same moving coil can be used as an ammeter or voltmeter with an interchange of above arrangement

3) Galvanometer:

Galvanometer is used to measure small value of current along with its direction and strength. It is mainly used onboard to detect and compare different circuits in a system.

5) Ohm Meter:

The ohm meter is used to measure resistance of the electric circuit by applying a voltage to a resistance with the help of battery. A galvanometer is used to determine the flow of current through the resistance. The galvanometer scale is marked in ohms and as the resistance varies, since the voltage is fixed, the current through the meter will also vary.

Advantages:

– The PMMC consumes less power and has great accuracy.

– It has uniformly divided scale and can cover arc of 270 degree. – The PMMC has a high torque to weight ratio.

– It can be modified as ammeter or voltmeter with suitable resistance.

– It has efficient damping characteristics and is not affected by stray magnetic field.

– It produces no losses due to hysteresis.

Disadvantage:

– The moving coil instrument can only be used on D.C supply as the reversal of current produces reversal of torque on the coil.

– It’s very delicate and sometimes uses ac circuit with a rectifier.

– It’s costly as compared to moving coil iron instruments.

– It may show error due to loss of magnetism of permanent magnet.

Errors in PMMC

 Frictional Error

-Avoided by winding of coil carefully

 Temperature Error

 Due to weakening of permanent magnet

- Eliminated by attaching symmetrical iron or steel needle to the coil

 Stray magnetic field error

-iron cover for moving part of system

Moving Iron Instrument Working Operation

Moving Iron Instruments or MI Instruments

In our previous article we have discussed PMMC Instrument Working Opeartion. In this tutorial on Moving Iron Instrument Working Operation we go through the construction & basic principle of MI type instrument.

The moving iron instruments are classified as: i) Moving iron attraction type instruments ii) Moving iron repulsion type instruments

Moving Iron Attraction Type Instrument Construction & Working Operation CONSTRUCTION:

1.Coil

2.Soft iron

(oval shape)

3.Pointer

Moving Iron Instrument Working Principle : The basic working principle of these instruments is very simple that a soft iron piece if brought near magnet gets attracted by the magnet.

The construction of the attraction type moving iron instrument is shown in the below figure.lt consists of a fixed coil C and moving iron piece D. The oil is flat and has narrow slot like opening. The moving iron is a flat disc which is eccentrically mounted on the spindle. The spindle is supported between the jewel bearings. The spindle carries a pointer which moves over a graduated scale.The number of turns of the fixed coil are dependent on the range of the instrument. For passing large current through the coil only few turns are required.The controlling torque is provided by the springs but gravity control may also be used for vertically mounted panel type instruments.

The damping torque is provided by the air friction. A light aluminium piston is attached to the moving system. it moves in a fixed chamber. The chamber is closed at one end. it can also be provided with the help of vane attached to the moving system.

The operating magnetic field in moving iron instruments is very weak. Hence eddy current damping is not used since it requires a permanent magnet which would affect or distort the operating field.This is the reason Why why eddy current damping is not used in moving iron instrument.

Moving Iron Repulsion Type Instrument CONSTRUCTION:

1.Coil

2.Soft iron

(oval shape)

3.Pointer

Principle

Moving iron repulsion Type instruments have two vanes inside the coil. the one is fixed and other is movable. When the current flows in the coil, both the vans are magnetized with like polarities induced on the same side. Hence due to the repulsion of like polarities, there is a force of repulsion between the two vanes causing the movement of the moving vane. The repulsion type instruments are the most commonly used instruments.

The two different designs of repulsion type instruments are: i) Radial vane type and ii) Co-axial vane type

Torque Equation of Moving Iron Instruments Consider a small increment in current supplied to the coil of the instrument. due to this current let dθ be the deflection under the deflecting torque Td. Due to such deflection, some mechanical work will be done.

Mechanical Work = Td .dθ There will be a change in the energy stored i the magnetic field due to the change in inductance. This is because the vane tries to occupy the position of minimum reluctance. The inductance is inversely proportional to the reluctance of the magnetic circuit of coil.

Let I = initial current

L = instrument inductance

θ = deflection dI = increase in current ,dθ = change in deflection, dL = change in inductance

In order to effect an increment dL in the current, there must be an increase in the applied voltage given by, e = d(L*I)/dt

= I * dL/dt + T * dI/dt as both I and L are changing.

The electrical energy supplied is given by eIdt = { I * dL/dt + T * dI/dt }Idt

=I²dL + ILdI

The stored energy increases from 1/2*(LI²) to 1/2*[(L+dL)(I+dI)²]

Hence the change in stored energy is given by,

1/2*[(L+dL)(I+dI)²] - 1/2*(LI²)

Neglecting higher order terms,this becomes ILdI + 1/2 * I² dL

The energy supplied in nothing but increase in stored energy plus the energy required for mechanical work done.

I²dL + ILdI = ILdI + 1/2*(I²)dL +Td.dθ

Td.dθ = 1/2( I².dL )

Td = 1/2 I²dL/dθ While the controlling torque is given by,

Tc = Kθ where K = spring constant

Kθ = 1/2 I²dL/dθ

θ = 1/2 I²dL/dθ * 1/K under equilibrium

Thus the deflection is proportional to the square of the current through the coil. And the instrument gives square law response.

Application:

Measurement of Electric Voltage and Current

• Moving iron instruments are used as Voltmeter and Ammeter only. • Both can work on AC as well as on DC.

Modern Application:

Accurate measurements in electric power systems.

Advantages:

• The instruments are suitable for use in AC and DC circuits.

• The instruments are robust, owing to the simple construction of the moving parts.

• The stationary parts of the instruments are also simple.

• Instrument is low cost compared to moving coil instrument.

• Torque/weight ratio is high, thus less frictional error.

Disadvantages:

• Scale is not uniform

• For low voltage range, the power consumption is higher

• In case of AC measurements, change in frequency causes serious error

Errors in MI:

Error in DC and AC,

1.Hytersis –

Mumetal or perm-Alloy

2.Stray magnetic field

iron shield over the working Parts

3.Temperature

manganin, Higher value for series resistance

Error in AC only,

4.Frequency

Due to chances in Reactance of the coil

5.Eddy Current Affect Deflection torque

Dynamometer Type Instrument

he electrodynamometer type instrument is a transfer instrument. A transfer instrument is one which is calibrated with a D.C source and used without any modifications for A.C measurements. Such a transfer instruments has same accuracy for A.C and D.C measurements. The electro-dynamometer type instruments are often used in accurate A.C voltmeters and ammeters, not only at the power line frequency but also in the lower audio frequency range with some little modifications, it can be used as a wattmeter for the power measurements.

Principle: Electro-dynamometer type instruments are very similar to PMMC type instrument in which the operating field is produced, not by a permanent magnet but by another fixed coil (usually two fixed air cored coils are used).

The PMMC instrument cannot be used on A.C currents or voltages. If A.C supply is given to these instruments, an alternating torque will be developed. Due to moment of inertia of the moving system, the pointer will not follow the rapidly changing alternating torque and will fail to show any reading. In order that the instrument should be able to read A.C quantities, the magnetic field in the air gap must change along with the change in current. This principle is used in the electro-dynamometer type instrument.

Construction: The below fig shows the construction of the electro-dynamometer type instrument.

The various parts of the dynamometer type instrument are:

Fixed coil: The necessary field required for the operation is produced by the fixed coil. This coil is divided into two halves to give a more uniform field near the centre and to allow passage of the instrument shaft. The fixed coils re usually air cored to avoid hysteresis, eddy currents and other errors when the instrument is used on A.C fixed coils are wound with fine wire for using as voltmeter, while for ammeters and wattmeter’s it is wound with heavy wire ( i.e. stranded heavy wire). The coils are usually varnished and baked to form a solid assembly. They are then clamped in place against the coil supports. This makes the construction rigid.

The mounting supports are preferably made of ceramic. If the metal parts would have been used when it would weaken the field of the fixed coil.

Moving coil: the moving coil is wound either as a self-sustaining coil or else on a non-metallic former. Metallic former cannot be used because eddy currents would be induced in it by the alternating field. Light but rigid construction is used for the moving coil. It is also air cored.

Controlling: the controlling torque is provided by tow control springs. These springs acts as leads to the moving coil.

Moving system: The moving coil is mounted on an aluminium spindle. It consist of counter weights and pointer sometimes a suspension may be used, in case a high sensitivity is desire.

Damping: The damping torque is provided by air friction, by a pair of aluminium vanes which are attached to the spindle at the bottom. These vanes move in sector shaped chambers. Eddy current damping cannot be used in these instruments as the operating field is very weak (or would be destroyed).

Shielding: The field produced by these instruments is very weak. Even earth’s magnetic field considerably affects the readings in D.C measurements. So shielding is done to protect it from stay magnetic fields. It is done by enclosing in a casing of high permeability alloy.

Cases and Scales: laboratory standard instruments are usually contained in highly polished wooden cases which usually contained in highly polished wooden cases which are rigid. The cases are son constructed as to remain stable over long periods of time. The case is supported by adjustable levelling screws. A pririt level also provided to ensure proper levelling.

The scales are hand drawn, using machine sub-dividing equipment. Diagonal lines for fine sub- divisor are usually drawn for marking on the scale. Most of high-precision instruments have a 300 mm scale with 100, 120 or 150 divisions.

Torque Equation

Let i1 = Instantaneous value of current in fixed coil i2 = Instantaneous value of current in moving coil L1 = Self inductance of fixed coil L2 = self inductance of moving coil M = Mutual inductance between fixed and moving coils The electrodynamometer instrument can be represented by an equivalent circuit as shown in the Fig.2.

Fig. 2

From the principle of conversation of energy,

Energy input = Energy stored + Mechanical energy ... Mechanical energy = Energy input - Energy stored Substraction (2) from equation (1),

The self inductance L1 and L2 are constant and hence dL1 and dL2 are zero. Mechanical energy = i1 i2 dM

If Ti is the instantaneous deflecting torque and dθ is the change in the deflection then Mechanical energy = Mechanical workdone = Ti dθ i1 i2 d M = Ti dθ

This is the expression for the instantaneous deflection torque. Let us see its operation on a.c. and d.c.

D.C. operation : For d.c current of I1 and I2,

The controlling torque is provided by springs hence

Thus the deflection is proportional to the product of the two currents and the rate of change of mutual inductance. A.c. operation : In a.c. operation, the total deflecting torque over a cycle must be obtained by integrating Ti over one period.

Average deflecting torque over one cycle is,

Now if two currents are sinusoidal and displaced by a phase angle then

where i1, i2 are the r.m.s. values of the two currents as,

Thus the deflection is decided by the product of r.m.s. values of two currents, cosine of the phase angle (power factor) and rate of change of mutual inductance.

For d.c. use, the deflection is proportional to square of current and the scale is nonuniform and crowded at the ends. For a.c. use the instantaneous torque is proportional to the square of the instantaneous current. The i2 is positive and as current varies, the deflecting torque also varies.

But moving system, due to inertia cannot follow rapid variations and thus finally meter shows the average torque.

Thus the deflection is the function of the mean of the squared current. The scale is thus calibrated in terms of the square root of the average current squared i.e. r.m.s value of the a.c. quantity to be measured.

If an electrodynamometer instrument is calibrated with a d.v. current if 1 A and pointer indicates 1 A d.c. on scale then on a.c., the pointer will deflect upto the same mark but 1A in this case will indicate r.m.s value.

Thus as it is a transfer instrument, there is direct connection between a.c. and d.c. Hence the instrument is often used as a calibration instrument.

The instrument can be used as an ammeter to measure currents upto 20 A while using as a voltmeter it can have low sensitivity of about 10 to 30 Ω/v

The Fig. 3(a), (b) and (c) shows the connections of the electrodynamometer instrument as ammeter, voltmeter and the wattmeter.

Advantages 1) As the coils are air cored, these instruments are free from hysteresis and eddy currentlosses. 2) They have a precision grade security.

3) These instruments can be used on both a.c. and d.c. They are also used as a transfer instruments.

4) Electrodynamometer voltmeter are very useful where accurate r.m.s values of voltage, irrespective of waveforms, are required.

5)Freefromhysteresis. 6)LowpowerConsumption. 7)Lightinweight.

Disadvantages

1) These instruments have a low sensitivity due to a low torque to weight ratio. Also it introduces increased frictional losses. To get accurate results, these errors must be minimized.

2) They are more expensive than other type of instruments.

3) These instruments are sensitive to overload and mechanical impacts. Therefore can must be taken while handling them.

4) They have a nonuniform scale.

5) The operation current of these instruments is large due to the fact that they have weak magnetic field.

Errors in Electrodynamometer Instruments

The various errors in electrodynamometer instruments are,

1. Torque to weight ratio : To have reasonable deflecting torque, mmf of the moving coil must be large enough. Thus m.m.f. = NI hence current through moving coil should be high or number of turns should be large. The current cannot be made very high because it may cause excessive heating of springs. Large number of turns hence is the only option but it increases weight of the coil. This makes the system heavy reducing torque to weight ratio. This can cause frictional errors in the reading.

2. Frequency errors : The changes in the frequency causes to change self inductances of moving coil and fixed coil. This causes the error in the reading. The frequency error can be reduced by having equal time constants for both fixed and moving coil circuits. 3. Eddy current errors : In metal parts of the instrument the eddy current gets produced. The eddy current interacts with the instrument current, to cause change in the deflecting torque, to cause error. Hnec metal parts should be kept as minimum as possible. Also the resistivity of the metal parts used must be high, to reduce the eddy currents.

4. Stray magnetic field error : Similar to moving iron instruments the operating field in electrodynamometer instrument is very weak. Hence external magnetic field can interact with the operation field to cause change in the deflection, causing the error. To reduce the effect of stray magnetic field, the shields must be used for the instruments.

5. Temperature error : The temperature errors are caused due to the self heating of the coil, which causes change in the resistance of the coil. Thus temperature compensating resistors can be used in the precise instrument to eliminate the temperature errors.

ERRORS IN MEASUREMENT:

Classification of Errors

In order to understand the concept of errors in measurement, we should know the two terms that defines the error and these two terms are written below:

True Value

It is not possible to determine the true of quantity by experiment means. True value may be defined as the average value of an infinite number of measured values when average deviation due to various contributing factor will approach to zero.

Measured Value

It may be defined as the approximated value of true value. It can be found out by taking means of several measured readings during an experiment, by applying suitable approximations on physical conditions. Now we are in a position to define static error. Static error is defined as the difference of the measured value and the true value of the quantity. Mathematically we can write an expression of error as, dA = Am - At where, dA is the static error Am is measured value and At is true value. It may be noted that the absolute value of error cannot be determined as due to the fact that the true value of quantity cannot be determined accurately. Let us consider few terms related to errors.

Types of Errors

Basically there are three types of errors on the basis; they may arise from the source.

Gross Errors

This category of errors includes all the human mistakes while reading, recording and the readings. Mistakes in calculating the errors also come under this category. For example while taking the reading from the meter of the instrument he may read 21 as 31. All these types of error are come under this category. Gross errors can be avoided by using two suitable measures and they are written below:

1. A proper care should be taken in reading, recording the data. Also calculation of error should be done accurately.

2. By increasing the number of experimenters we can reduce the gross errors. If each experimenter takes different reading at different points, then by taking average of more readings we can reduce the gross errors.

Systematic Errors

In order to understand these kinds of errors, let us categorize the systematic errors as

Instrumental Errors

These errors may be due to wrong construction, calibration of the measuring instruments. These types of error may be arises due to friction or may be due to hysteresis. These types of errors also include the loading effect and misuse of the instruments. Misuse of the instruments results in the failure to the adjust the zero of instruments. In order to minimize the gross errors in measurement various correction factors must be applied and in extreme condition instrument must be re-calibrated carefully.

Environmental Errors

This type of error arises due to conditions external to instrument. External condition includes temperature, pressure, humidity or it may include external magnetic field. Following are the steps that one must follow in order to minimize the environmental errors:

 Try to maintain the temperature and humidity of the laboratory constant by making some arrangements.

 Ensure that there should not be any external magnetic or electrostatic field around the instrument.

Observational Errors

As the name suggests these types of errors are due wrong observations. The wrong observations may be due to PARALLAX. In order to minimize the PARALLAX error highly accurate meters are required, provided with mirrored scales. Random Errors

After calculating all systematic errors, it is found that there are still some errors in measurement are left. These errors are known as random errors. Some of the reasons of the appearance of these errors are known but still some reasons are unknown. Hence we cannot fully eliminate these kinds of error.