Question

A moving coil galvanometer, having a resistance $G$ produces full scales deflection when a current $I_{g}$ flows through it. It can be converted into an ammeter of range $0$ to $I_{0}\left(> I_{g}\right)$ by connecting a shunt of resistance $R_{A}$ to it. If it can also be converted into a voltmeter of range $0$ to $V=I_{0}G$ by connecting a resistance $R_{V}$ to it in series, then which among the following is correct?

• A. $R_{A}R_{V}=G^{2}\left(\frac{I_{0} - I_{g}}{I_{g}}\right)$ and $\frac{R_{A}}{R_{V}}=\left(\frac{I_{g}}{I_{0} - I_{g}}\right)^{2}$
• B. $R_{A}R_{V}=G^{2}$ and $\frac{R_{A}}{R_{v}}=\frac{I_{g}}{\left(I_{0} - I_{g}\right)}$
• C. $R_{A}R_{v}=G^{2}$ and $\frac{R_{A}}{R_{v}}=\left(\frac{I_{g}}{I_{0} - I_{g}}\right)^{2}$
• D. $R_{A}R_{V}=G^{2}\left(\frac{I_{g}}{I_{0} - I_{g}}\right)$ and $\frac{R_{A}}{R_{V}}=\left(\frac{I_{0} - I_{g}}{I_{g}}\right)^{2}$

Answer 1

Answer: (C)

$\left(I_{0}-I_{g}\right)R_{A}=I_{g}G$ and $V_{0}=I_{0}\left(G + R_{V}\right)$
$I_{0}=\frac{I_{g} \left(G + R_{A}\right)}{R_{A}}$ and $V_{0}=I_{0}\left(G + R_{V}\right)$
$V_{0}=I_{0}G\left(\right.\text{ given }\left.\right)\Rightarrow I_{0}\left(G + R_{V}\right)=I_{g}\frac{\left(G + R_{A}\right) G}{R_{A}}$
$R_{A}G+R_{V}R_{A}=G^{2}+R_{A}G$
$R_{V}R_{A}=G^{2}$
$R_{A}=\frac{I_{g} G}{I_{0} - I_{g}};R_{V}=\frac{\left(I_{0} - I_{g}\right) G}{I_{g}}$
$\frac{R_{A}}{R_{V}}=\frac{I_{g}^{2}}{\left(I_{0} - I_{g}\right)^{2}}$