The connection diagram for substitution method is shown in fig. below. R is the unknown resistance to be measured, S is the standard variable resistance, ‘r’ is the regulating resistance and ‘A’ is an ammeter. There is a switch for putting S and R in a circuit.

Firstly switch is at position 1 and R is connected in a circuit. The regulating resistance ‘r’ is adjusted till ammeter pointer is at chosen scale. Now switch is thrown to position ‘2’ and now ‘S’ is in a circuit. The value of standard variable resistance ‘S’ is varied till the same deflection as was obtained with R in the circuit is obtained. When the same deflection obtained it means same current flow for both the resistances. It means resistances must be equal. Thus we can measure the value of unknown resistance ‘R’ by substituting another standard variable resistance ‘S’. Therefore this method is called Substitution method.

This is more accurate method than ammeter-voltmeter method. The accuracy of this method is greatly affected if the emf of the battery changes during the time of readings. Thus in order to avoid errors on this account, a battery of ample capacity should be used so that the emf remains constant.

See also: Ammeter voltmeter method.

The accuracy of the measurement naturally depends upon the constancy of the battery emf and of the resistance of the circuit excluding R and S, upon the sensitivity of the instrument, and upon the accuracy with which standard resistance S is known.

This method is not widely used for simple resistance measurements and is used in a modified form for the measurement of high resistances. The substitution principle, however, is very important and finds many applications in bridge methods and in high-frequency a.c. measurements.

## Example

In a measurement of resistance by substitution method, a standard 0.5MO resistor is used. The galvanometer has a resistance of 10KO and gives deflections as follows:

1) With standard resistor, 41 divisions,

2) with unknown resistance, 51 divisions.

Find the unknown resistance.

## Solution

The deflection of the galvanometer is directly proportional to the current passing through the circuit and hence is inversely proportional to the total resistance of the circuit. Let S, R, and G be respectively the resistances of the standard resistor, unknown resistor and galvanometer. Also, let ?1 be the deflection with a standard resistor in the circuit and ?2 with an unknown resistor in the circuit.

Hence unknown resistance R=(S+G)*?1/?2-G

= (0.5*10^6+10*1000)*(41/51)-10*1000

=0.4*10^6O

=0.4 MO.

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