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(B) The sensitivity of a galvanometer is proportional to the current $i_g$ flowing through it. When a shunt $S$ is connected in parallel,the new curre

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$9$

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(B) The sensitivity of a galvanometer is proportional to the current $i_g$ flowing through it. When a shunt $S$ is connected in parallel,the new current $i_g'$ becomes $i_g' = i \left( \frac{S}{G+S} ight)$,where $G = 171 \, \Omega$ is the galvanometer resistance.Given that the sensitivity becomes $1/20$ times,we have $\frac{i_g'}{i_g} = \frac{1}{20}$.Since $i_g = i \left( \frac{S}{G+S} ight) / 	ext{factor}$,we use the relation $S = \frac{G}{n-1}$,where $n$ is the factor by which the range increases (or sensitivity decreases).Here,$n = 20$ and $G = 171 \, \Omega$.$x = S = \frac{171}{20-1} = \frac{171}{19} = 9 \, \Omega$.Therefore,$x = 9 \, \Omega$.

The sensitivity of a galvanometer of resistance $171 \, \Omega$ becomes $1/20$ times when we use a shunt of $x \, \Omega$. Find $x$ ................. $\Omega$.

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