A 100 V (rms), 50 Hz AC supply is connected to a series circuit containing resistance 10 Ω and inductance 1/(10π) H. Its average power is 100x watt. Find x.
Physics · Mixed Chapter
JEE Mains

Question

A 100 V (rms), 50 Hz AC supply is connected to a series circuit containing resistance 10 Ω and inductance 1/(10π) H. Its average power is 100x watt. Find x.

G1 Physics · Accepted Answer

Step 1 — Inductive reactance: Xₗ = 2πfL = 2π×50/(10π) = 10 Ω. Step 2 — Impedance: Z² = R² + Xₗ² = 10² + 10² = 200 Ω². Step 3 — Average dissipated power (rms voltage): P = V² R/Z² = 100²×10/200 = 500 W. Step 4 — Compare with 100x W: 100x = 500 ⇒ x = 5. Answer: 5.