Question

An a.c. voltage (80 + j 60) volts is applied to a circuit and the current flowing is (− 4 + j 10) amperes. Find (i) impedance of the circuit (ii) power consumed and (iii) phase angle. 

Answer 1

V = (80 + j 60) = 100 ∠ 36.9°;

I = − 4 + j 10 = 10.77 ∠ tan⁻¹ (− 2.5)

= 10.77 ∠ (180° − 68.2°)

= 10.77 ∠ 111.8°

(i) Z = V/I = 100 ∠36.9°/10.77∠ 111.8°

= 9.28 ∠ − 74.9° = 9.28 (cos 74.9° − j sin 74.9°)

= 2.42 − j 8.96 Ω

Hence R = 2.42 Ω and X_C = 8.96 Ω capacitive

(ii) P = I² R = 10.772 × 2.42 = 2.81 W

(iii) Phase angle between voltage and current = 74.9° with current leading as shown in Fig..