A galvanometer of resistance G is shunted by | vedclass

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(A) Let the original resistance of the galvanometer be $G$. When a shunt resistance $S$ is connected in parallel,the equivalent resistance of the comb

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

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(A) Let the original resistance of the galvanometer be $G$. When a shunt resistance $S$ is connected in parallel,the equivalent resistance of the combination is $R_{eq} = \frac{GS}{G + S}$.To keep the main current unchanged,the total resistance of the circuit must remain equal to the original resistance $G$.Let $S'$ be the resistance connected in series with the galvanometer. The new equivalent resistance is $R'_{eq} = \frac{GS}{G + S} + S'$.Setting $R'_{eq} = G$,we get:$G = \frac{GS}{G + S} + S'$$S' = G - \frac{GS}{G + S}$$S' = \frac{G(G + S) - GS}{G + S}$$S' = \frac{G^2 + GS - GS}{G + S}$$S' = \frac{G^2}{G + S}$

$A$ galvanometer of resistance $G$ is shunted by a resistance $S$. To keep the main current in the circuit unchanged,what value of resistance should be connected in series with the galvanometer?

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