In Substitution Method, the
Resistance whose value is to be measured is compared with the Standard
Resistance by some technique which is described in this section. The connection
diagram for Substitution Method is given below.

Here, R is the unknown
Resistance, S the Standard variable Resistance, A is Ammeter and r is
Regulating Resistance.

When we put the Switch at
position 1 then R is connected in the circuit. The Regulating Resistance r is
adjusted till the reading of Ammeter is at a chosen scale mark. Now the Switch
is thrown to position 2 putting the Standard variable Resistance S in the
circuit. Now the variable Resistor S is adjusted till the reading of Ammeter is
same as when R was in the circuit. The setting of dial of S is read. Since the
substitution of one resistance for another has left current unaltered, and
provided that EMF of battery and position of Regulating Resistance r remain
unaltered, the two Resistance R and S must be equal. Thus the value of unknown
Resistance R is equal to the dial setting of Standard Resistance S.

This method of measurement
is more accurate as compared to the Ammeter Voltmeter Method as in this method
measurement is not affected by the accuracy of Ammeter. However, the accuracy
of this method is greatly affected if there is any change in the Battery EMF
during the time when the reading in two settings is taken. Therefore to avoid
the error because of change of EMF of Battery, a Battery of enough capacity is
used so that it remains constant during the entire period of testing.

The accuracy of this method
also depend on resistance of circuit excluding R and S, upon the sensitivity of
instrument and upon the accuracy with which the Standard Resistance S is known.

This method is not widely
used for simple Resistance measurement and is used in modified form for the
measurement of High Resistance. The Substitution Method is however very
important as it finds its use in application of bridge method and in high
accuracy A.C measurement.

**Example:**In measurement of Resistance by Substitution Method, a standard 0.5 MOhm resistor is used. The Galvanometer has a resistance of 10 KOhm and gives raeding as follows:

- With
Standard Resistor, 41 division
- With
unknown resistor, 51 division.

What will be the value of
unknown resistance?

**Solution:**As the deflection of Galvanometer is directly proportional to the current flowing through the circuit which in turn depends on the net resistance in the circuit. Current through the circuit is inversely proportional to the net resistance. Let say a1 is the deflection of Galvanometer when standard Resistor S is in circuit and a2 when unknown Resistance R is in circuit.

So, a1/a2 = (R+G)/(S+G) where
G is Galvanometer resistance.

So, 41/51= (R+G)/(S+G)

R = (S+G)×41/51 = 0.4×10

^{6 }Ohm = 0.4 MOhm
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