# Substitution Method for Measuring Medium Resistance - Circuit & Procedure

The various methods used for measuring the resistance of medium values (i.e., 1Ω to 100kΩ) are,

#### Ammeter-voltmeter methodOhmmeter methodSubstitution methodWheatstone bridge methodCarry-foster bridge method

Let us see how unknown resistance of value lying between 1Ω to 100kΩ can be measured using the substitution method.

## Substitution Method for Measuring Medium Resistance :

The connection diagram for the substitution method of measurement of medium resistance is shown below.

#### In the above figure,V = Voltage sourceR = Rheostat to limit or adjust the ammeter currentS = Standard variable resistanceX = Unknown resistance

The Single Pole Double Throw (SPDT) switch is thrown to position 'b' which connects the unknown resistance (X) into the circuit. The current through the ammeter is adjusted to some value (I) and it is noted. Now the SPDT switch is thrown to position 'a' which connects standard variable resistance (S) into the circuit.

The rheostat is kept unaltered and S is varied until the ammeter reads the previously noted value (I). The value of X is taken as this particular resistance of S, because when the currents through two resistors are equal in similar conditions (i.e., applied voltages are equal) then their resistances will be equal.

The following are the factors on which the accuracy of this method depends upon,

#### Stability in battery voltageThe accuracy with which the standard resistance (S) is knownAmmeter sensitivityStability in rheostat resistance (R).

Compared to the ammeter-voltmeter method, substitution method is quite accurate. Where the errors due to ammeter voltage drop and voltmeter shunts are eliminated in the substitution method. The substitution method gives accurate results if the battery emf and circuit resistance are kept constant throughout the operation. Otherwise, errors are introduced due to variations in battery emf and sensitivity of the instrument.

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