A coil when given supply of 20 V D.C. draws a current of 4 A. When the same coil is given supply of 20 V A.C. with 80 Hz, draw a current of 2 A. The self Inductance of the coil is :

1.7 × 10^-2 H

For DC Circuit $ R = \frac{V}{I} = \frac{20}{4} = 5\Omega$

For AC Circuit $ I = \frac{V}{Z} \Rightarrow Z = \frac{V}{I} = \frac{20}{2} = 10\Omega$

$ Z = \sqrt{R^2 + \omega^2L^2} = 10$

$ \omega^2L^2 = 100 - 25 = 75\Omega$

$ L = \frac{\sqrt{75}}{\omega} = \frac{5\sqrt{5}}{2\pi \times 80}$

$ L = 1.7\times 10^{-2}H$