Question

A voltmeter has a resistance of $G$ $\Omega$ and range $V\text{volt}$. The value of resistance used in series to convert it into voltmeter of range $nV\text{volt}$ is

• A. $nG$
• B. $(n-1)$$G$
• C. $\frac{G}{n}$
• D. $\frac{G}{n-1}$

Answer 1

The correct option is B $(n-1)$$G$

Given, the voltmeter of resistance $G$ gives the full scale deflection for potential difference $V$.
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$\therefore I_g=\frac{V}{G}$

Voltage across voltmeter and resistance is given by

$V^{\prime }=I_g(R+G)$

Here, $V^{\prime }=nV;I_g=V/G$

$nV=\frac{V}{G}(R+G)$

$\therefore R=nG-G=(n-1)G$

Hence, option $\left(b\right)$ is correct.
$$\begin{array}{c}\text{Why this question ?}\\ \text{We can change the range of a voltmeter}\\ \text{by attaching some resistance in series with it.}\end{array}$$