A galvanometer of resistance $G$ is converted into a voltmeter of ragne $0-1 \mathrm{~V}$ by connecting a resistance $\mathrm{R}_{1}$ 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 $0-2 \mathrm{~V}$ will be:
Correct Option: 4
(4) Galvanometer of resistance (G) converted into a voltmeter of range $0-1 \mathrm{~V}$.
$V=1=i_{g}\left(G+R_{1}\right)$ ...(1)
To increase the range of voltmeter $0-2 \mathrm{~V}$
$2=i_{g}\left(R_{1}+R_{2}+G\right)$ ...(2)
Dividing eq. (i) by (ii),
$\Rightarrow \frac{1}{2}=\frac{G+R_{1}}{G+R_{1}+R_{2}}$
$\Rightarrow G+R_{1}+R_{2}=2 G+2 R_{1}$
$\therefore R_{2}=G+R_{1}$
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