Question:
A moving coil galvanometer, having a resistance $\mathrm{G}$, produces full scale deflection when a current $I_{g}$ flows through it. This galvanometer can be converted into (i) an ammeter of range 0 to $\mathrm{I}_{0}\left(\mathrm{I}_{0}>\mathrm{I}_{g}\right)$ by connecting a shunt resistance $R_{A}$ to it and (ii) into a voltmeter of range 0 to $V$ $\left(\mathrm{V}=\mathrm{GI}_{0}\right)$ by connecting a series resistance $\mathrm{R}_{\mathrm{v}}$ to it. Then,
Correct Option: , 2
Solution:
(2) In an ammeter,
$i_{g}=i_{0} \frac{R_{\mathrm{A}}}{R_{\mathrm{A}}+G}$
and for voltmeter,
$V=i_{g}\left(G+R_{V}\right)=G i_{0}$
On solving above equations, we get
$R_{A} R_{V}=G^{2}$
and $\frac{R_{A}}{R_{V}}=\left(\frac{i_{g}}{i_{0}-i_{g}}\right)^{2}$