A galvanometer of resistance $G$ has voltage range $V_g$. Resistance requirec to convert it to read voltage…

A galvanometer of resistance $G$ has voltage range $V_g$. Resistance requirec to convert it to read voltage up to $V$ is
  1. $\frac{G \cdot V_g}{V}-G$
  2. $\left(\frac{G+V_g}{V}\right) \cdot G$
  3. $\left(\frac{V-V_g}{V}\right) \cdot G$
  4. $G \cdot\left[\frac{V}{V_g}-1\right]$

Solution

The correct option is (D). To convert a galvanometer into a voltmeter we need to connect a large resistor in series. Consider the following diagrams with usual labels. Consider the following, net potential drop across the voltmeter: $I_g R+l_g G=V$ On re-writing, $R=\frac{V}{I_g}-G$, and we know, $V_g=I_g G$. Therefore, $R=G\left(\frac{V}{V_g}-1\right)$

Asked in: MHT CET 2022 (05 Aug Shift 1)

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