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Electrical and Electronic Measurements Contents Manual for K-Notes ................................................................................. 2 Error Analysis .......................................................................................... 3 Electro-Mechanical Instruments ............................................................. 6 Potentiometer / Null Detector .............................................................. 15 Instrument Transformer ....................................................................... 16 AC Bridges ............................................................................................. 18 Measurement of Resistance ................................................................. 21 Cathode Ray Oscilloscope (CRO) ........................................................... 25 Digital Meters ....................................................................................... 28 Q–meter / Voltage Magnifier ................................................................ 30 © 2014 Kreatryx. All Rights Reserved. 1 Error Analysis Static characteristics of measuring system 1) Accuracy Degree of closeness in which a measured value approaches a true value of a quantity under measurement. When accuracy is measured in terms of error : Guaranteed accuracy error (GAE) is measured with respect to full scale deflation. Limiting error (in terms of measured value) GAE * Full scale deflection LE Measured value 2) Precision Degree of closeness with which reading in produced again & again for same value of input quantity. 3) Sensitivity Change the output quantity per unit change in input quantity. qo S qi 4) Resolution Smallest change in input which can be measured by an instrument 5) Threshold Minimum input required to get measurable output by an instrument 6) Zero Drift Entire calibration shifts gradually due to permanent set 3 7) Span Drift If there is proportional change in indication all along upward scale is called span drift. 8) Dead zone & Dead time The range of input for which there is no output this portion is called Dead zone. To respond the pointer takes a minimum time is called dead time. TYPES OF ERROR a) Gross Error : Error due to human negligency, i.e. due to loose connection, reading the value etc. b) Systematic error : Errors are common for all observers like instrumental errors, environmental errors and observational errors. c) Random errors : Error due to unidentified causes & may be positive or negative. Absolute Errors : A AAmr Am Measured value Ar True value Relative Errors : AbsoluteErrors A r = Truevalue AT Am ATT A Amr 1 1r 4 Composite Error : i) Sum of quantities XXX12 x x1 x2 ii) Difference of quantities XXX12 x x1 x2 So for sum & difference absolute errors are added. iii) Multiplication of quantities XXXX1 2 3 X XX12X3 XXXX1 2 3 iv) Division of quantities X X 1 X2 X XX12 XXX12 So, for multiplication & division, fractional or relative errors are added. mm XX12 If X p X3 X XX12X3 m n p XXXX1 2 3 Precision Index Indicates the precision for a distribution 1 h 2 5 Probable Error r = 0.6745 0.4769 r h Standard deviation of combination of quantities 2 2 2 XXX 2 2 ...... 2 x x12 x xn XXX12 n Probable Error 2 2 2 XXX 22 2 r r r ...... r x x12 x xn XXX1 2 n Electro-Mechanical Instruments 1) Permanent magnet moving Coil (PMMC) Deflecting Torque Td = nIAB Where n = no. of turns I = current flowing in coil A = Area of coil B = magnetic flux density G Deflection I k G = NBA & K = Spring constant Eddy current damping & spring control torque in used. For pure AC signal, the pointer vibrates around zero position. It is used to measured DC or average quantity. It can directly read only up to 50mV or 100mA. 6 Enhancement of PMMC i) Ammeter For using PMMC as an ammeter with wide range, we connect a small shunt resistance in parallel to meter. I m multiplication factor Im Basically, ‘m’ is ratio of final range (as an ammeter) to initial range of instrument. R R m ; R = meter resistance sh m1 m ii) Voltmeter A series multiples resistance of high magnitude is connected in series with the meter. M = multiplication factor V m Vm Rsm R m 1 Sensitivity of voltmeter 1 RRsm S/Vv IVfsd Application of PMMC 1) Half wave rectifier meter I IIm avg 7 2VRMS RRRsmf 0.45VRMS Iavg ; For Ac input RRRsmf For DC input VDC Iavg RRRsmf I 0.45 I (Assuming VV ) avg AC avg DC DC RMS (Sensitivity)AC 0.45(Sensitivity) DC 2) Full wave rectifier meter 2 2VRMS I avg AC Rsm R 2Rf 0.9VRMS Rsm R 2Rf VDC I avg DC Rsm R 2Rf I 0.9 I (Assuring VV ) avg AC avg DC RMS DC SensitivityAC 0.9 SensitivityDC 2) Moving iron meter 1 dL Deflecting torque, TI 2 d 2d I = current flowing throw the meter L = Inductance = deflection Under steady state 8 1 dL KI 2 2d I2 MI meter measures both ac & dc quantities. In case of AC, It measures RMS value. 1 1 T 2 I i2 t dt RMS T 0 If i t I0 I 1 sinwt I 2 sin2wt ....... 21 2 2 IRMS I 0 I 1 I 2 ....... 2 Air friction Damping is used Condition for linearity dL constant d MI meter cannot be used beyond 125Hz, as then eddy current error is constant. 3) Elector dynamometer dM Deflecting Torque, T i i d 1 2 d For DC, i12 i I dM TI 2 d d I2 For AC, i1 I m1 sin t i2 I m2 sin t dM T I I cos d avg 12 d I I2 Where I m1 & I 1 2 2 2 9 Applications of dynamometer 1) Ammeter Fixed coils are connected in series. III12 0 (Angel between I&I12) dM TI 2 d d At balance, TTc d dM KI 2 d I2 It reads both AC & DC & for AC it reads RMS. 2) Voltmeter Rs Series multiplier resistance V II21 , 0 Rs cos 1 V2 dM Td 2 Rs d At balance, TTd c 2 V dM 2 K 2 V Rs d It reads both AC & DC & for AC it reads RMS. 10 3) Wattmeter Fixed coils carry same current as load & as called as current coils. Moving coil is connected across voltage and thus current voltage, a high non-inductive load is connected in series with MC to limit the current. dM T I I cos d 1 2 d V dMPavg dM I cos Rss d R d At balance, kT d Pavg Symbol : Two wattmeter method W1 VRY I R cos V RY & I R VLL I cos 30 W2 VBY I B cos V BY & I B VLL I cos 30 Where VL is line to line voltage 11 IL is line current These expression remain same for -connected load. PWW3 12 3VLL I cos Q3 3 W21 W 3VLL I sin Q 3 3 W21 W tan PWW3 12 3 W W tan1 21 for lag load WW 12 3 W W tan1 21 for lead load WW 12 = Remember, In our case W1 is wattmeter connected to R-phase and W2 is wattmeter connected to B-phase. = If one of the wattmeter indicates negative sign, then pf < 0.5 Errors in wattmeter a) Due to potential coil connection 2 IrL c %r * 100 PT IL = load current rC = CC Resistance PT = True Power V2 %r *100 RPs T V = voltage across PC 12 Rs = Series multiplier resistance PT = True Power b) Due to self inductance of PC If PC has finite inductance Zp R p R s jwLp RRps Zps R jwLp %r tan tan *100 = load pf angle Lp tan1 R s 4) Energy meter Energy = Power * Time VIcos t W * kwhr T 1000 3600 WT = True energy It is based on principle of induction. It is an integrating type instrument. t W VIsin * kwhr m 3600 Where Wm = measured Energy = angle between potential coil voltage & flux produced by it. = load pf angle Error = WWm T No.ofRe voluations N Energy constant = kwhr P.t Totalno.ofrevolutions Measured Energy = W m K 13 VIcos t True Energy = W * kw.hr T 1000 3600 WWmT Error = %r *100 WT Creeping Error in energy meter If friction is over compensated by placing shading loop nearer to PC, then disc starts rotating slow with only PC excited without connecting any load is creeping. Otherwise if over voltage is applied on pressure coil then also creeping may happen due to stray magnetic fields. To remove creeping holes are kept on either side of disc diametrically opposite & the torque experienced by both holes is opposite & they stop creeping. TotalNo.ofRe w / kwhr due to creeping % creeping error = * 100 TotalNo.ofRe w / kwhr due to load Thermal Instruments These instruments work on the principle of heating and are called as Thermal Instruments. These are used for high frequency measurements. They can measure both AC & DC. In case of AC, they measure RMS value. Electrostatic voltmeter 12 dc Deflecting torque, TV d 2d At Balance, TTd c 1 dc Vk2 2d V2 Condition for linearity 14 dc constant d For increasing the range, we connect another capacitor in series To increase the range from Vm to V Cm V Cs ; m m1 Vm Potentiometer / Null Detector Iw = working current VB Iw _____________(1) Rh l.r Switch at (A) If I0g Vsw I l1 r Vs Iw _____________(2) lr1 Switch at (B) Vxw I l2 r Vx Iw ________(3) lr2 Vs Vx l12 r l r l2 VVxs l1 15 r = resistance of slide wire (Ω/ m) l = Total length of slide wire (m) l1 = length at which standard cell ( Vs ) is balanced l2 = length at which test voltage ( Vx ) is balanced Measuring a low resistance VR RS Vs Instrument Transformer Current transformer Equivalent circuit N Turns Ratio = Nominal Ratio n 2 N1 1 XXls tan RRls I cos I sin R = Actual Ratio n Is 16 Errors in current transformer 1) Ratio Error : I Current ratio p is not equal to turns ratio due to no-load component of current. Is KR %r * 100 R K = n = Nominal Ratio R = Actual Ratio 2) Phase Angel Ratio : 0 Ideally, Phase difference between I&Ips should be 180 but due to no-load component of current, it deviates from that value.
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