A coil offers a resistance of 20 ~ohm for a direct current. If we send an alternating current through the same coil, the resistance offered by the coil to the alternating current will be :

Step-by-step solution

A coil is characterized by its resistance R and its self-inductance L . When a direct current (DC) flows through the coil, the frequency f is 0 , so the inductive reactance X_L = 2 f L = 0 . Thus, the total impedance Z for DC is equal to the resistance R = 20 . When an alternating current (AC) flows through the coil, the frequency f > 0 , which results in an inductive reactance X_L = 2 f L > 0 . The impedance Z for AC is given by Z = R^2 + X_L^2 . Since X_L > 0 , it follows that Z = 20^2 + X_L^2 > 20^2 = 20 . There