Question

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

• A. $\frac{S^2}{(S+G)}$
• B. $\frac{SG}{(S+G)}$
• C. $\frac{G^2}{(S+G)}$
• D. $\frac{G}{(S+G)}$

Answer 1

The correct option is C $\frac{G^2}{(S+G)}$

To keep the main current in the circuit unchanged, the resistance of the galvanometer should be,
$G=\frac{GS}{G+S}+S^{\prime }$

$G-\frac{GS}{G+S}=S^{\prime }$

$\frac{G^2}{G+S}=S^{\prime }$

$\therefore S^{\prime }=\frac{G^2}{G+S}$