The range of voltmeter of resistance ' G ' $\Omega$ is ' V ' volt. The resistance required to be connected…
The range of voltmeter of resistance ' G ' $\Omega$ is ' V ' volt. The resistance required to be connected in series with it in order to convert it into a voltmeter of range ' $n V$ ' volt, will be
$(\mathrm{n}-1) \mathrm{G}$
$\mathrm{G} / \mathrm{n}$
nG
$\frac{\mathrm{G}}{\mathrm{n}}-1$
Solution
Here, The range of a voltmeter of resistance G is V volt. Let, I be the current thruogh it then
\(\mathrm{G}=\frac{\mathrm{V}}{\mathrm{I}} \ldots\) (1)
Now to convert it into voltmeter of range nV , the required resistance will be,
\(\mathrm{R}=\frac{\mathrm{nV}}{\mathrm{I}}=\mathrm{nG}\) (from (1))
Hence, the resistance to be added in series is
\(\mathrm{R}-\mathrm{G}=\mathrm{nG}-\mathrm{G}=(\mathrm{n}-1) \mathrm{G}\)
The resistance \((\mathrm{n}-1) \mathrm{G}\) is to be connected in series with voltmeter of range V in order to convert it into a voltmeter of range nV volt,