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(A) Let $G$ be the resistance of the galvanometer and $I_g$ be the full-scale deflection current.The initial voltage range is $V = I_g G$.To increase

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$R = G(n-1)$

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(A) Let $G$ be the resistance of the galvanometer and $I_g$ be the full-scale deflection current.The initial voltage range is $V = I_g G$.To increase the range by a factor of $n$,the new voltage range becomes $V' = nV = n I_g G$.Let $R$ be the series resistance connected to the galvanometer.The total resistance of the voltmeter is $(G + R)$.According to Ohm's law,$V' = I_g(G + R)$.Substituting $V' = n I_g G$,we get $n I_g G = I_g(G + R)$.Dividing both sides by $I_g$,we get $nG = G + R$.Therefore,$R = nG - G = G(n - 1)$.

Write the equation for the series resistance required to increase the voltage range of a galvanometer by a factor of $n$.

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