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 in parallel with the galvanometer as shown. Potential difference across G = potential difference across S. i.e., \[{{i}_{g}}G=(i-{{i}_{g}})S\] or \[{{i}_{g}}G={{i}_{g}}S=i\,\,S\] 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 \[S=\frac{G}{49}\]