Question

Write Kirchhoff's first rule (law of junction). Drawing a circuit diagram of Wheatstone bridge, derive condition for zero deflection in the bridge.

Answer 1

According to Kirchoff's current law, in an electrical circuit, total current entering a node equals the total current exiting the node. It is in accordance with the law of conservation of charge.

Circuit diagram of a Wheatstone bridge is shown in the attached figure.

For zero deflection in the galvanometer, no current should flow through it. This happens when voltage across it is zero.

$V_{P_1}=V_{P_2}............\left(i\right)$

Now since no current flows through galvanometer,

$I_1=I_3$

Using ohm's Law,

$\frac{V_{P_1}-V_A}{R_1}=\frac{V_{P_1}-V_B}{R_2}...........\left(ii\right)$

Similarly,

$I_2=I_4$

$\frac{V_{P_2}-V_A}{R_3}=\frac{V_{P_2}-V_B}{R_4}...........\left(iii\right)$

Dividing (ii) from (iii), we get:

$\frac{\frac{V_{P_2}-V_A}{R_3}}{\frac{V_{P_1}-V_A}{R_1}}=\frac{\frac{V_{P_2}-V_B}{R_4}}{\frac{V_{P_1}-V_B}{R_2}}$

Using (i) and rearranging terms we get,

$\frac{R_1}{R_3}=\frac{R_2}{R_4}$

The above is a necessary and sufficient condition for the galvanometer to show no deflection.