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What will be the resistance of the shunt when $5 \%$ of the main current is passed through a galvanometer of resistance G?
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Verified Answer
The correct answer is:
$\frac{G}{19}$
Let the total passing be $\mathrm{I}$.
Thus current passing through galvanometer $\mathrm{I}_{\mathrm{G}}=0.05 \mathrm{I}$
Also, current passing through shunt resistance $\mathrm{I}_{\mathrm{S}}=\mathrm{I}-0.05 \mathrm{I}=0.95 \mathrm{I}$
Using $I_{S} S=I_{G} G$
$\therefore \frac{S}{G}=\frac{0.05}{0.95}=\frac{1}{10}$
$\Longrightarrow S=\frac{G}{19}$
Thus current passing through galvanometer $\mathrm{I}_{\mathrm{G}}=0.05 \mathrm{I}$
Also, current passing through shunt resistance $\mathrm{I}_{\mathrm{S}}=\mathrm{I}-0.05 \mathrm{I}=0.95 \mathrm{I}$
Using $I_{S} S=I_{G} G$
$\therefore \frac{S}{G}=\frac{0.05}{0.95}=\frac{1}{10}$
$\Longrightarrow S=\frac{G}{19}$
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