Question:
A galvanometer of resistance $G$ is converted into a voltmeter of range $0-1 \mathrm{~V}$ by connecting a 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: , 2
Solution:
$\Rightarrow 1=\mathrm{i}_{\mathrm{g}}\left(\mathrm{G}+\mathrm{R}_{1}\right)$....(1)
$\Rightarrow 2=\mathrm{i}_{\mathrm{g}}\left(\mathrm{R}_{1}+\mathrm{R}_{2}+\mathrm{G}\right)$...(2)
(1) \% (2)
$\Rightarrow \frac{1}{2}=\frac{\mathrm{G}+\mathrm{R}_{1}}{\mathrm{G}+\mathrm{R}_{1}+\mathrm{R}_{2}}$
$\mathrm{G}+\mathrm{R}_{1}+\mathrm{R}_{2}=2 \mathrm{G}+2 \mathrm{~h}_{1}$
$\left(\mathrm{R}_{2}=\mathrm{G}+\mathrm{R}_{1}\right)$