Question

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. $50\, G$

Answer 1

Answer: (A)

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. $i_{g} G=\left(i-i_{g}\right) S$
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 $2 S+2 G=100\, S$
or $G=\frac{98 S}{2}$
or $S=\frac{G}{49}$