A coil is connected to a 20 V DC supply and draws a steady current of 5 A . When the same coil is connected to a 20 V , 50 Hz AC supply, it draws an rms current of 4 A . The resistance and the inductance of the coil are respectively:

Step-by-step solution

For a DC supply, the frequency is zero, so the inductive reactance is zero. The steady current is limited only by the resistance of the coil. R = V_ DC I_ DC = 20 5 = 4 For an AC supply, the impedance Z of the coil limits the current. Z = V_ rms I_ rms = 20 4 = 5 The impedance of the coil is given by Z = R^2 + X_L^2 , where X_L is the inductive reactance. 5 = 4^2 + X_L^2 25 = 16 + X_L^2 X_L = 3 The inductive reactance is X_L = L = 2 f L . 3 = 2 ( 50 ) L 3 = 100 L L = 3 100 H = 0.03 H = 30 mH The resistance is 4 and