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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 is needed to get half deflection then G, R and S are related by the equation

Asked in JEE Main Online 2016 · Galvanometer sensitivity and figure of merit

Answer: (1) S(R + G) = RG

Step-by-step solution

Without shunt: I₁ = (V_E)/(R + G).

With shunt: galvanometer current I₂ = (V_E S)/(R(G + S) + GS).

Half deflection: 2S(R + G) = R(G + S) + GS.

Simplify: SR + SG = RG, i.e. S(R + G) = RG.

Why the other options are wrong

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