A galvanometer of resistance


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 :

  1. $\mathrm{R}_{1}$

  2. $\mathrm{R}_{1}+\mathrm{G}$

  3. $\mathrm{R}_{1}-\mathrm{G}$

  4. $\mathrm{G}$

Correct Option: , 2


$\Rightarrow 1=\mathrm{i}_{\mathrm{g}}\left(\mathrm{G}+\mathrm{R}_{1}\right)$....(1)

$\Rightarrow 2=\mathrm{i}_{\mathrm{g}}\left(\mathrm{R}_{1}+\mathrm{R}_{2}+\mathrm{G}\right)$...(2)

(1) \% (2)

$\Rightarrow \frac{1}{2}=\frac{\mathrm{G}+\mathrm{R}_{1}}{\mathrm{G}+\mathrm{R}_{1}+\mathrm{R}_{2}}$

$\mathrm{G}+\mathrm{R}_{1}+\mathrm{R}_{2}=2 \mathrm{G}+2 \mathrm{~h}_{1}$


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