Phase angle of current = 2π/3 = 2 180°/3 = 120° and phase angle of voltage = 5π/6 = 5 × 180°/6 = 150°.
Also, Z = Vm/Im = 3Ω.
Hence, current lags behind voltage by 30°. It means that it is an R-L circuit.
Also 314 = 2π f or f = 50 Hz.
Now, R/Z = cos 30° = 0.866; R = 2.6 Ω ; XL/Z = sin 30° = 0.5
∴ XL = 1.5 Ω 314 L = 1.5, L = 4.78 mH
(a) Z = 3 Ω (b) R = 2.6 Ω (c) L = 4.78 mH
(d) P = I2R = (5/√2)2 x 2.6 × = 32.5 W
(e) p.f. = cos 30° = 0.866 (lag).