When a coil is connected across a $$20$$ V dc supply, it draws a current of $$5$$ A. When it is connected across $$20$$ V, $$50$$ Hz ac supply, it draws a current of $$4$$ A. The self inductance of the coil is ______ mH. (Take $$\pi = 3$$)

From DC supply: $$V = 20$$ V, $$I = 5$$ A. Resistance of coil: $$R = V/I = 4\Omega$$.

From AC supply: $$V = 20$$ V, $$I = 4$$ A. Impedance: $$Z = V/I = 5\Omega$$.

For a coil (R-L circuit): $$Z = \sqrt{R^2 + (\omega L)^2}$$

$$25 = 16 + \omega^2 L^2$$

$$\omega^2 L^2 = 9$$

$$\omega L = 3$$

$$\omega = 2\pi f = 2\pi \times 50 = 2 \times 3 \times 50 = 300$$ rad/s (using $$\pi = 3$$).

$$L = \frac{3}{300} = 0.01 \text{ H} = 10 \text{ mH}$$

The answer is $$\boxed{10}$$ mH.