question_answer

If 2% of the main current is to be passed through the galvanometer of resistance G, the resistance of the shunt required is:

A) \[\frac{G}{49}\]                               

B)        \[\frac{G}{50}\]

C)         49 G                                     

D)         50 G

Correct Answer: A

Solution :

Key Idea: The potential difference across parallel combination should be equal. The shunt is a low resistance connected parallel with the galvanometer as shown. Potential difference across G = potential difference across S.                 i.e.,        \[{{i}_{g}}G=(i-{{i}_{g}})S\]                 or            \[{{i}_{g}}G+{{i}_{g}}S=iS\]                 or            \[{{i}_{g}}(G+S)=i\,S\]                 or            \[\frac{{{i}_{g}}}{i}=\frac{S}{S+G}\]                 Given,   \[\frac{{{i}_{g}}}{i}=\frac{2}{100}\]                 We have              \[\frac{2}{100}=\frac{S}{S+G}\]                 or            \[2S+2G=100\,S\]                 or            \[G=\frac{98S}{2}\]                 or            \[S=\frac{G}{49}\]