A galvanometer of resistance 30 Omega is conn | vedclass

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(C) The current for full-scale deflection ($20$ divisions) is given by $I_1 = \frac{V}{R_g + R_1} = \frac{2}{30 + 1970} = \frac{2}{2000} = 1 	imes 10

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$3970$

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(C) The current for full-scale deflection ($20$ divisions) is given by $I_1 = \frac{V}{R_g + R_1} = \frac{2}{30 + 1970} = \frac{2}{2000} = 1 	imes 10^{-3} 	ext{ A} = 1 	ext{ mA}$.Since the deflection $	heta$ is directly proportional to the current $I$ $(	heta \propto I)$,to reduce the deflection from $20$ divisions to $10$ divisions,the current must be halved.Thus,$I_2 = \frac{I_1}{2} = 0.5 	imes 10^{-3} 	ext{ A}$.Let the new total series resistance be $R_{total}$. Then $I_2 = \frac{V}{R_g + R_{total}}$.$0.5 	imes 10^{-3} = \frac{2}{30 + R_{total}}$.$30 + R_{total} = \frac{2}{0.5 	imes 10^{-3}} = 4000 \Omega$.$R_{total} = 4000 - 30 = 3970 \Omega$.

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