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

Answer 1

Answer: (B)

$S (R+G)=RG$

Answer 2

$I_{g}=\frac{V}{R+G}$ $R_{c}=R+\frac{GS}{G+s}$ $I=\frac{V}{R+\frac{GS}{G+S}}$ $I '_{g}G=\left(I-I '_{g}\right)S$ $I '_{g}\left(G+S\right)=IS$ $\frac{I_{g}}{2}=\frac{IS}{G+S}$ $\frac{V}{2\left(R+G\right)}=\frac{V}{R+\frac{GS}{G+S}}\times\frac{S}{G+S}$ $\frac{1}{2\left(R+G\right)}=\frac{S}{R\left(G+S\right)+GS}$ $R\left(G+S\right)+GS=2S\left(R+G\right)$ $RG+RS+GS=2S\left(R+G\right)$ $RG=2S\left(R+G\right)-S\left(R+G\right)$ $RG=S\left(R+G\right)$