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

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S(R + G) = RG

2S(R + G) = RG

2S = G

2G = S

answer is A.

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Detailed Solution

$\frac{1}{2} (Current through galvano before shunting) = (Current through galvano after shunting)$

$\frac{1}{2} \frac{V}{R + G} = \frac{V}{R + \frac{GS}{G + S}} \frac{S}{G + S}$

$\Rightarrow \frac{1}{2} \frac{V}{R + G} = \frac{VS}{GS + RG + RS}$

After Solving we get,

S(R+G)=RG

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