Question

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 $\theta$. If a shunt of resistance $S$ is needed to get half deflection then $G,R$ and $S$ are related by the equation

• A. $2S=G$
• B. $S(R+G)=RG$
• C. $2S(R+G)=RG$
• D. $2G=S$

Answer 1

The correct option is B $S(R+G)=RG$

After applying shunt $S$, deflection gets halved, hence current gets halved. Hence,

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

Solving this gives $S(R+G)=RG$.