A galvanometer of resistance G is shunted by a resistance S ohm. To keep the main current in the circuit uncha

Question

A galvanometer of resistance G is shunted by a resistance S ohm. To keep the main current in the circuit unchanged, the resistance to be put in series with the galvanometer is

Accepted Answer

1. **Initial Condition:** The resistance of the circuit component is simply the resistance of the galvanometer, $G$.
2. **Shunted Condition:** When a shunt resistance $S$ is connected in parallel with the galvanometer, the equivalent resistance of this parallel combination ($R_p$) is:
   $$R_p = \frac{GS}{G+S}$$ .
3. **Problem Statement:** To keep the main current in the circuit unchanged, the total resistance of the modified circuit (galvanometer + shunt + series resistance) must equal the original resistance ($G$).
4. **Calculation:** Let $R$ be the resistance added in series. The total resistance becomes $R_{total} = R_p + R$.
   Equating to the original resistance:
   $$G = \frac{GS}{G+S} + R$$
   $$R = G - \frac{GS}{G+S}$$
   $$R = \frac{G(G+S) - GS}{G+S}$$
   $$R = \frac{G^2 + GS - GS}{G+S}$$
   $$R = \frac{G^2}{S+G}$$

Step-by-Step Solution

Practice All PHYSICS Questions