To know the resistance G of a galvanometer by half deflection method, a battery of emf V_E, resistance R is used to deflect the galvanometer by angle $θ$ if a shunt of resistance s is needed to get half deflection then G, R and S are related by equation

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S ( R+G )= RG

2S (R+G)= RG

S G = S

2S = G

answer is A.

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Detailed Solution

$\begin{aligned} \frac{1}{2} \frac{V}{R + G} = \frac{V}{R + \frac{G S}{G + S}} \frac{S}{G + S} \\ \Rightarrow \frac{1}{2} \frac{V}{R + G} = \frac{V S}{G S + R G + R S} \end{aligned}$

$\Rightarrow S (R + G) = R G$

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