A galvanorneter of resistance $G$ is converted into a voltmeter of range $0 - 1 V$ by connecting a resistance $R_{1}$ in series with it. The additional resistance $R_{1}$ in series with it. The additional resistance that should be connected in series with $R_{1}$ to increase the range of the voltmeter to $0 - 2 V$ wìll be:

G

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R_{1}

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R_{1} - G

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R_{1} + G

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Solution

The correct option is D $R_{1} + G$
Galvanometer of resistance $(G)$ converted into a voltmeter of range $0 - 1 V$ .
$V = 1 = i_{g} (G + R_{1})$ ... (i)
To increase the range of voltmeter $0 - 2 V$
$2 = i_{g} (R_{1} + R_{2} + G)$ ... (ii)
Dividing eq. (i) by (ii),
$\Rightarrow \frac{1}{2} = \frac{G + R_{1}}{G + R_{1} + R_{2}}$
$\Rightarrow G + R_{1} + R_{2} = 2 G + 2 R_{1}$
$∴ R_{2} = G + R_{1}$

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