Physics - Current Electricity Question with Solution | TestHub

Initial resistance of the galvanometer is $G$.

When the galvanometer is shunted with a resistance $S$, the equivalent resistance of the parallel combination becomes $R_{eq}=\frac{GS}{G+S}$.

To keep the main current in the circuit unchanged, the total resistance of the circuit must remain the same. Therefore, a resistance $R$ must be connected in series with the shunted galvanometer such that the new equivalent resistance equals the original resistance $G$.

$R+\frac{GS}{G+S}=G$

$R=G-\frac{GS}{G+S}$

$R=\frac{G(G+S)-GS}{G+S}$

$R=\frac{G^2+GS-GS}{G+S}$

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

Answer: $\frac{{\mathrm{G}}^2}{\mathrm{S}+\mathrm{G}}$