I) Measurement of Resistance

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Electrical MeasurementsMeasurement of Resistances;Potentiometers;AC Bridge Methods for Measurement of Inductance & Capacitance;Magnetic MeasurementsMeasurement of Resistances1. Low Resistance: Up to 1;2. Medium Resistance: 1to 100K;3. High Resistance: Above 100K.Measurement of Medium Resistances:1. Ammeter-Voltmeter Method;2. Substitute Method;3. Wheatstone Bridge Method;4. Ohmmeter Method.aa Rm R RIV VIVR + =+= =1VV RmRRRI IVR+=+=12||.|

\| =11 1mamRRR R||||.|

\|=VmmRRR R22111. Ammeter-Voltmeter Method:2. Substitution Method:Accuracy of this method is greatly affected if there is any change inthe battery emf.This method is not widely used for medium resistancemeasurements and is used in a modified form for measurement ofhigh resistances.3. Wheatstone Bridge Method:SRQP=R I P I 2 1 =Q PEI I+= = 3 1S REI I+= = 4 2Sensitivity of BridgeQ PEPP I Eab+= = 1 ( ) ( )( ) S R RR R ER R I Ead+ + += + = 2((

++ + += =Q PPS R RR RE E E e ab adS RRQ PP+=+( ) ( ) S R R S RR ESe+ + + = 2( )2S RR ESe+=SVbe the voltage sensitivity of Galvanometer ( )2S RR ESS e S V V+= = SB is the Bridge SensitivityRRSB= RSSRE SS VB+ +=2 4E SS VB =4. Ohmmeter Method:(i) Series Type Ohmmeter:RX= Unknown Resistance;Rm= Internal Resistance of the meter;Rh= Half scale position Resistance;Ih= Half-full scale deflection;Ifm= Full scale deflection current of the meter;If = Full scale deflection battery currentm shm shse hR RR RR R++ =hhRVI2=hh fRVI I = = 2fm f sh I I I = m fm sh sh R I R I =h fmh m fmfm fm fmshR I VR R II IR IR==VR R IRR RR RR R h m fmhm shm shh se =+ =(ii) Shunt Type Ohmmeter:RX= Unknown Resistance;Rm= Internal Resistance of the meter;Rh= Half scale position Resistance;IB= Battery Current;Ifm= Full scale deflection current of the meter;If = Full scale deflection battery currentm sefmR RVI+=X mX mseBR RR RRVI++=X mXX mX msemR RRR RR RRVI+++= .( )( ) X m X m sem se XfmmR R R R RR R RIIS+ + += =P XXR RRS+=(iii) Crossed Coil Type Ohmmeter:(a) Fixed Magnetic Moving Coil (b) Crossed Coil Moving MagneticMeasurement of Low Resistances:Measured ResistanceContact Resistance% error1000.002 Negligible0.02 10%Methods for Measurement of Low Resistance1. Ammeter-Voltmeter Method;2. Kelvin Double Bridge Method;3. Potentiometer Method.Kelvin Double Bridge Method:QPrr=21Q PPr rr+=+ 2 11rQ PPr+=1 rQ PQr+=2||.|

\|++ =||.|

\|++ rQ PQSQPrQ PPRSRQP=ac ab EQ PPE+= ((

+ +++ + =r q pr q pS R I Eac) (((

)`+ ++++ =r q pr q pq ppR I Eamd) (((

+ ++ =r q pprR I Eamd((

+ ++ =((

)`+ +++ ++ r q pprR Ir q pr q pS R IQ PP ) (((

+ ++ =qpQPr q pqrSQPRSRQP=Measurement of High Resistances:1. Insulation resistance of cables;2. Resistance of high resistance circuit elements;3. Volume resistivity of a material;4. Surface resistivity.Difficulties in Measurement of High Resistances1. Due to leakage current;2. Due to electrostatic effect;3. Definite ratios in potential distribution with respect to surroundings;Use Guard CircuitMethods for Measurement of High Resistance:1. Prices Guard-wire Method;2. Loss of Charge Method;3. MegohmBridge Method;4. Megger Method.Prices Guard Wire Method:Measurement of Volume and Surface Resistivityd1= Diameter of the upper electrode d1;d2= Diameter of the lower electrode d2;t = Thickness of the specimen sheet;V1 , V2= Reading of voltmeter;I1= current through galvanometer G1;I2= current through galvanometer G2Volume resistivity of specimen:1121214 4 IVtdRtd = =Surface Resistivity:22 222IVtdRtds = =Loss of Charge Method:dtdvCdtdqi = =Again,' R'R' across drop PotentialRVi = =dtdvCRV =' ' CRdtVdv = =21 0 'VVtCRdtVdv'1 2CRte V V =''11R RR RR=MegohmBridge Method:Megger Method:Detail Circuit Diagram: