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
AIPMT 2011, Medium
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Let resistance $R$ is to be put in series with galvanometer $G$ to keep the main current in the circuit unchanged.
$\therefore \frac{G S}{G+S}+R=G$
$R=G-\frac{G S}{G+S} \Rightarrow R=\frac{G^{2}+G S-G S}{G+S}$
$R=\frac{G^{2}}{G+S}$
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