A galvanometer of resistance $G$ can be converted into a voltmeter of range $V$ by connecting a resistance…

A galvanometer of resistance $G$ can be converted into a voltmeter of range $V$ by connecting a resistance $R$ in series with it. The series resistance required to change its range to $\frac{V}{3}$ is
  1. $\frac{R-3 G}{4}$
  2. $\frac{R+G}{3}$
  3. $\frac{R-G}{2}$
  4. $\frac{R-2 G}{3}$

Solution

Case-1 $\begin{aligned} & R=\frac{V}{I_G}-G \\ & \Rightarrow I_G=\frac{V}{R+G} \end{aligned}$ Case-2: $R^{\prime}=\frac{\left(\frac{V}{3}\right)}{I_G}-G=\frac{\left(\frac{V}{3}\right)}{\left(\frac{V}{R+G}\right)}-G=\left(\frac{R-2 G}{3}\right)$

Asked in: MHT CET 2022 (11 Aug Shift 1)

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