A galvanometer of resistance, $G$ is shunted by a resistance $S \mathrm{~ohm}$. 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

  $\frac{S G}{(S+G)}$
• Correct answer
  C

  $\frac{G^2}{(S+G)}$
• D

  $\frac{G}{(S+G)}$

Solution

Current will be unchanged if resistance remains same so
$$ \begin{aligned} & G=\frac{G S}{G+S}+R \\ & R=G-\frac{G S}{G+S} \\ & R=\frac{G^2}{G+S} \end{aligned} $$

Hence, the correct answer is option: 'C'.