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 i $s ________.$
(π = 3.14)

Question

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 i $s ________.$

(π = 3.14)

G1 Physics · Accepted Answer

Using the relation employed in the supplied source, magnetic energy = ½L I(rms)². Given, 16 = ½L(2)². Therefore, L = 8 H. The thermal power dissipated is P = I(rms)²R. Hence, 32 = (2)²R, so R = 8 Ω. Inductive reactance is X(L) = ωL = 2πfL. Therefore, X(L) = 2×3.14×50×8 = 2512 Ω. Thus, X(L)/R = 2512/8 = 314. Hence the answer is 314.

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 i s ________. (π = 3.14)