Three similar coils each having a resistance of 5 Ω and an inductance of 0.02 H are connected in star to a 440 V, 50 Hz, 3-phase supply. Calculate (i) line current and (ii) active and reactive power

Given: R = 5 Ω, L = 0.02 H, star connection, V_L = 440 V, f = 50 Hz.

\( X_L = 2\pi fL = 2\pi\times50\times0.02 = 6.283\ \Omega \); \( Z_{ph} = \sqrt{5^2+6.283^2} = \sqrt{64.48} = 8.030\ \Omega \).

Phase voltage (star): \( V_{ph} = \dfrac{V_L}{\sqrt3} = \dfrac{440}{\sqrt3} = 254.03 \) V.

(i) \( I_{ph} = \dfrac{V_{ph}}{Z_{ph}} = \dfrac{254.03}{8.030} = 31.64 \) A. In star I_L = I_ph ⇒ I_L = 31.64 A.

Power factor \( \cos\phi = R/Z = 5/8.030 = 0.6227 \) lagging; \( \sin\phi = X_L/Z = 6.283/8.030 = 0.7825 \).

(ii) Active power: \( P = \sqrt3V_LI_L\cos\phi = \sqrt3\times440\times31.64\times0.6227 = 15013 \) W ≈ 15.01 kW (check: 3I_ph²R = 3 × 31.64² × 5 = 15.01 kW ✓).

Reactive power: \( Q = \sqrt3V_LI_L\sin\phi = 3I_{ph}^2X_L = 3\times31.64^2\times6.283 = 18866 \) VAR ≈ 18.87 kVAR (lagging). Apparent power S = √3 × 440 × 31.64 = 24.11 kVA.