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(A) The sensitivity of a galvanometer is defined as the deflection per unit current,given by $S_g = \frac{	heta}{i_g}$. When a shunt $S$ is connected

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$4$

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(A) The sensitivity of a galvanometer is defined as the deflection per unit current,given by $S_g = \frac{	heta}{i_g}$. When a shunt $S$ is connected in parallel with a galvanometer of resistance $G$,the new sensitivity $S'$ is given by the ratio of the current through the galvanometer $i_g$ to the total current $i$.The current through the galvanometer is $i_g = i \left( \frac{S}{G+S} ight)$.Therefore,the new sensitivity is $S' = \frac{i_g}{i} = \frac{S}{G+S}$.Given,initial sensitivity $= 60 	ext{ div/A}$ and final sensitivity $= 10 	ext{ div/A}$.The ratio of sensitivities is $\frac{S'}{S_g} = \frac{10}{60} = \frac{1}{6}$.Substituting the formula: $\frac{1}{6} = \frac{S}{G+S}$.Cross-multiplying gives $G + S = 6S$,which simplifies to $G = 5S$.Given $G = 20 \ \Omega$,we have $20 = 5S$.Thus,$S = \frac{20}{5} = 4 \ \Omega$.

The sensitivity of a galvanometer is $60 \text{ division/A}$. When a shunt is used,its sensitivity becomes $10 \text{ division/A}$. If the galvanometer is of resistance $20 \ \Omega$,the value of shunt used is (in $\Omega$)

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