Question

A voltmeter has resistance of $G$ ohm and range of $V$ volt. The value of resistance used in series to convert it into a voltmeter of range $nV$ volt is:

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

Answer 1

Answer: (B)

Let $G$ is resistance of galvanometer and $ i_{g}$ the current through it.
From Ohms law
$i_{g}=\frac{V}{G+R} $
$\Rightarrow G+R=\frac{V}{i_{g}} $
$\Rightarrow R=\frac{V}{i_{g}}-G$
Given, $ V=n V, $
$i_{g}=\frac{V}{G} $
$\therefore R=\frac{n V}{V / G}-G $
$=n G-G=(n-1) G$