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A galvanometer of resistance ' $G$ ' is shunted by a resistance of $5 \Omega$. To keep the main current in the circuit unchanged, the resistance to be put in series with the same galvanometer is
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The correct answer is:
$\frac{\mathrm{G}^2}{\mathrm{~S}+\mathrm{G}}$
Current will be unchanged if resistance remains same to
$\begin{aligned} & G=\frac{G S}{G+S}+R \\ & \Rightarrow R=G-\frac{G S}{G+S}=\frac{G^2}{G+S}\end{aligned}$
$\begin{aligned} & G=\frac{G S}{G+S}+R \\ & \Rightarrow R=G-\frac{G S}{G+S}=\frac{G^2}{G+S}\end{aligned}$
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