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 $V_0=I_0\left(G+R_V\right)$
$V_0=I_{0}G(\text{ given })\Rightarrow I_0\left(G+R_V\right)=I_g\frac{\left(G+R_A\right)G}{R_A}$
$R_{A}G+R_V{R}_A=G^2+R_{A}G$
$R_V{R}_A=G^2$
$R_A=\frac{I_{g}G}{I_0-I_g};R_V=\frac{\left(I_0-I_g\right)G}{I_g}$
$\frac{R_A}{R_V}=\frac{I_g^2}{{\left(I_0-I_g\right)}^2}$