A galvanometer having a coil resistance $100 \Omega$ gives a full scale deflection when a current of $1 \mathrm{~mA}$ is passed through it. What is the value of the resistance which can convert this galvanometer into a voltmeter giving full scale deflection for a potential difference of $10 \mathrm{~V}$ ?
Correct Option: 4,
(4)
Given,
Resistance of galvanometer, $G=100 \Omega$
Current, $i_{\mathrm{g}}=1 \mathrm{~mA}$
A galvanometer can be converted into voltmeter by connecting a large resistance $R$ in series with it.
Total resistance of the combination $=G+R$
According to Ohm's law, $V=i_{\mathrm{g}}(G+R)$
$\therefore 10=1 \times 10^{-3}\left(100+R_{0}\right)$
$\Rightarrow 10000-100=9900 \Omega=\mathrm{R}_{0}$
$\Rightarrow \mathrm{R}_{0}=9.9 \mathrm{k} \Omega$