(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 \times 10

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

Class 12 Physics Moving Charges and Magnetism The Moving Coil Galvanometer (Sensitivity) and Ammeter and Voltmeter Conversion

Medium

$A$ galvanometer of resistance $30 \Omega$ is connected to a battery of emf $2 \text{ V}$ with $1970 \Omega$ resistance in series. $A$ full-scale deflection of $20$ divisions is obtained in the galvanometer. To reduce the deflection to $10$ divisions,the total resistance in series required is: (in $\Omega$)

MHT CET 2016 All MHT CET

A
$4030$
B
$4000$
C
$3970$
D
$2000$

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Class 12

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Moving Charges and Magnetism

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The Moving Coil Galvanometer (Sensitivity) and Ammeter and Voltmeter Conversion

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