Electrical Measurements

Measurement of Resistances;

Potentiometers;

AC Bridge Methods for Measurement of Inductance &

Capacitance;

Magnetic Measurements

Measurement of Resistances

1. Low Resistance: Up to 1Ω;2. Medium Resistance: 1Ω to 100KΩ;3. High Resistance: Above 100KΩ.

Measurement of Medium Resistances:

1. Ammeter-Voltmeter Method;2. Substitute Method;3. Wheatstone Bridge Method;4. Ohmmeter Method.

aaR

m RRI

VVIVR +=

+==1

V

VRm

RR

RII

VR+

=+

=1

2

−=

11 1

m

am R

RRR

−=

V

mm

RRRR

22

1

1

1. 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:

SR

QP=

RIPI 21 =

QPEII+

== 31

SREII+

== 42

Sensitivity of Bridge

QPEPPIEab +

== 1 ( ) ( )( )SRR

RRERRIEad +∆+∆+

=∆+= 2

+

−+∆+

∆+=−=

QPP

SRRRREEEe abad SR

RQP

P+

=+

( ) ( )SRRSRRESe

+∆++∆

= 2 ( )2SRRESe

+∆

=

SV be the voltage sensitivity of Galvanometer ( )2SR

RESSeS VV +∆

==θ

SB is the Bridge Sensitivity

RRSB ∆

=θ

RS

SR

ESS VB

++=

2 4ESS V

B =

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 current

msh

mshseh RR

RRRR+

+=

hh R

VI2

=h

hf RVII == 2

fmfsh III −= mfmshsh RIRI =

hfm

hmfm

fmf

mfmsh RIV

RRIII

RIR

−=

−=

VRRI

RRR

RRRR hmfmh

msh

mshhse −=

+−=

(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 current

msefm RR

VI+

=

Xm

Xmse

B

RRRRR

VI

++

=

Xm

X

Xm

Xmse

m RRR

RRRRR

VI+

++

= .

( )( ) XmXmse

mseX

fm

m

RRRRRRRR

IIS

+++

==

PX

X

RRRS+

=

(iii) Crossed Coil Type Ohmmeter:

(a) Fixed Magnetic Moving Coil (b) Crossed Coil Moving Magnetic

Measurement of Low Resistances:

Measured Resistance

Contact Resistance % error

100Ω0.002Ω

Negligible

0.02Ω 10%

Methods for Measurement of Low Resistance

1. Ammeter-Voltmeter Method;

2. Kelvin Double Bridge Method;

3. Potentiometer Method.

Kelvin Double Bridge Method:

QP

rr=

2

1

QPP

rrr

+=

+ 21

1

rQP

Pr+

=1 rQP

Qr+

=2

+

+=

+

+ rQP

QSQPr

QPPR

SR

QP=

acab EQP

PE+

=

++

+++=

rqprqpSRIEac

)(

+++

++=

rqprqp

qppRIEamd

)(

++

+=rqp

prRIEamd

++

+=

+++

+++ rqp

prRIrqprqpSRI

QPP )(

−

+++=

qp

QP

rqpqrS

QPR

SR

QP=

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 Resistances

1. Due to leakage current;

2. Due to electrostatic effect;

3. Definite ratios in potential distribution with respect to

surroundings;

Use Guard Circuit

Methods for Measurement of High Resistance:

1. Price’s Guard-wire Method;2. Loss of Charge Method;3. Megohm Bridge Method;4. Megger Method.

Price’s Guard Wire Method:

Measurement of Volume and Surface Resistivity

d1 = 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 G2

Volume resistivity of specimen:

1

12

12

1

44 IV

tdR

td ππρ ==

Surface Resistivity:

2

222

2

IV

tdR

td

sππρ ==

Loss of Charge Method:

dtdvC

dtdqi −=−=

Again,'R'

R' across drop PotentialRVi ==

dtdvC

RV

−=' 'CR

dtVdv

−=

∫ ∫−=2

1 0 '

V

V

t

CRdt

Vdv

'12

CRt

eVV −=

''

1

1

RRRRR−

=

Megohm Bridge Method:

Megger Method:

Detail Circuit Diagram: