Question

Derive condition of balance of a Wheatstone bridge. 

OR 

Draw a circuit diagram showing balancing of Wheatstone bridge. Use Kirchhoff’s rules to obtain the balance condition in terms of the resistances of four arms of wheat stone Bridge.

Answer 1

Condition of balance of a Wheatstone bridge:

The circuit diagram of Wheatstone bridge is shown in fig.

P, Q, R and S are four resistance forming a closed bridge, called Wheatstone bridge. A battery is connected across A and C, while a galvanometer is connected between B and D. When the bridge is balanced, there is no current in galvanometer. 

Derivation of Formula: Let the current flowing in the circuit in the balanced condition be I. This current on reaching point A is divided into two parts I₁ and I₂. As there is no current in galvanometer in balanced condition, current in resistances P and Q is I₁ and in resistances R and S it is I₂. 

Applying Kirchhoff’s I law at point A

This is the condition of balance of Wheatstone bridge.