$A$ moving coil galvanometer,having a resistance $G$,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 $I_0$ $(I_0 > I_g)$ by connecting a shunt resistance $R_A$ to it and $(ii)$ into a voltmeter of range $0$ to $V$ $(V = GI_0)$ by connecting a series resistance $R_V$ to it. Then,

• A
  $R_A R_V = G^2$ and $\frac{R_A}{R_V} = \frac{I_g}{(I_0 - I_g)}$
• B
  $R_A R_V = G^2$ and $\frac{R_A}{R_V} = \left( \frac{I_g}{I_0 - I_g} \right)^2$
• C
  $R_A R_V = G^2 \left( \frac{I_g}{I_0 - I_g} \right)$ and $\frac{R_A}{R_V} = \left( \frac{I_0 - I_g}{I_g} \right)^2$
• D
  $R_A - R_V = G^2 \left( \frac{I_0 - I_g}{I_g} \right)$ and $\frac{R_A}{R_V} = \left( \frac{I_g}{I_0 - I_g} \right)^2$