When an additional resistance $1980 \Omega$ is connected in series with a voltmeter, each scale division has…
When an additional resistance $1980 \Omega$ is connected in series with a voltmeter, each scale division has 100 times larger value. The resistance of the voltmeter is
$60 \Omega$
$20 \Omega$
$30 \Omega$
$40 \Omega$
Solution
Let $R$ be the resistance of voltmeter. Let $n$ be the number of divisions in the voltmeter. Then the voltage $V$ recorded by each division of voltmeter when current $i_g$ flow through it is
\(i_g \frac{R}{n}=V\) ...(1) When resistance is connected in series with voltmeter, then \(i_g \frac{(R+1980 \Omega)}{n}=100 \mathrm{~V}\) ...(2)
Dividing (2) by (1), we get
$\begin{aligned} & R+1980 \Omega=100 R \\ & \Rightarrow R=\frac{1980}{99} \Omega=20 \Omega\end{aligned}$