An inductor stores 16 J of magnetic field energy and dissipates 32 W of thermal energy due to its resistance when an a.c. current of 2 A (rms) and frequency 50 Hz flows through it. The ratio of inductive reactance to its resistance is _ _ _ _ . ( =3.14)

Step-by-step solution

Given: Magnetic field energy = 16 J, Thermal power dissipated = 32 W, I_ rms = 2 A, f = 50 Hz. From energy stored in inductor: 1 2 L I_ rms ^2 = 16 1 2 L 4 = 16 L = 8 H From thermal power dissipated: I_ rms ^2 R = 32 4R = 32 R = 8 ; Inductive reactance: X_L = L = 2 f L = 2 3.14 50 8 = 2512 ; X_L R = 2512 8 = 314