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 the $G,R$ and $S$ are related by the equation:

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

Answer 1

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

$\begin{array}{c}{i}_1=\frac{V_E}{R+G}\\ i=\frac{V_E}{R+\frac{GS}{G+S}}\\ \frac{i_1}{2}G=\left(i+\frac{I_1}{2}\right)S\\ i_1\left(G+S\right)=2iS\\ substituting{i}_{1}andiweget\\ S\left(R+G\right)=RG\end{array}$