A moving coil of galvanometer when shunted with 2 $$\Omega$$ resistance gives a full scale deflection for a current of 500 mA. When a resistance of 470 $$\Omega$$ is connected in series it gives a full scale deflection for 10 V potential applied on it. The value of resistance of galvanometer coil is __________ $$\Omega$$.

$$I_g \cdot G = (I - I_g) \cdot S$$

$$I_g \cdot G = (0.5 - I_g) \cdot 2$$

$$I_g \cdot G = 1 - 2I_g \implies I_g(G + 2) = 1 \implies I_g = \frac{1}{G + 2} \quad \text{--- (Equation 1)}$$

$$V = I_g \cdot (G + R)$$

$$10 = I_g \cdot (G + 470) \implies I_g = \frac{10}{G + 470} \quad \text{--- (Equation 2)}$$

$$\frac{1}{G + 2} = \frac{10}{G + 470}$$

$$1 \cdot (G + 470) = 10 \cdot (G + 2)$$

$$G + 470 = 10G + 20$$

$$G = \frac{450}{9} = 50\ \Omega$$