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\( X_L = 2\pi fL = 2\pi\times50\times0.04 = 12.566\ \Omega \).

Impedance: \( Z = \sqrt{10^2 + 12.566^2} = \sqrt{257.91} = \) 16.06 Ω (= 10 + j12.566 = 16.06∠51.49° Ω).

Current: \( I = \dfrac{200}{16.06} = \) 12.45 A (lagging the voltage by 51.49°).

Power factor: \( \cos\phi = R/Z = 10/16.06 = \) 0.623 lagging.

Power consumed: \( P = I^2R = 12.45^2\times10 = \) 1550.9 W ≈ 1.55 kW (check: VI cos φ = 200 × 12.454 × 0.6227 = 1551 W ✓).

Doubtly AI · 25 Oct 2026 AI-verified · Oct 2026 Report
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