A coil draws a steady current of 2 A when connected to a 100 V d.c. source. When the same coil is connected to a 100 V , 50 Hz a.c. source, it draws an rms current of 1 A . The inductance of the coil is:

Step-by-step solution

For the DC source, the frequency is zero, so the inductive reactance X_L = 0 . The coil acts as a pure resistor. R = V_ dc I_ dc = 100 2 = 50 , For the AC source, the coil offers both resistance and inductive reactance. The total impedance Z is: Z = V_ ac I_ ac = 100 1 = 100 , The impedance of an RL circuit is given by Z = R^2 + X_L^2 . 100 = 50^2 + X_L^2 10000 = 2500 + X_L^2 X_L^2 = 7500 X_L = 50 3 , The inductive reactance is X_L = 2 f L . 50 3 = 2 50 L 50 3 = 100 L L = 50 3 100 = 3 2 H Answer: 3 2 H