A galvanometer of resistance, $G,$ is connected in a circuit. Now a resistance $R$ is connected in series of galvanometer. To keep the main current in the circuit unchanged, the resistance to be put in parallel with the series combination of $G$ and $R$ is
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$\mathrm{G}^{\prime}=\mathrm{G}$
$\frac{(\mathrm{G}+\mathrm{R}) \mathrm{S}}{\mathrm{G}+\mathrm{R}+\mathrm{S}}=\mathrm{G} \quad$ or $\mathrm{S}=\frac{\mathrm{G}^{2}}{\mathrm{R}}+\mathrm{G}$
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