(a) What is the impedance of the circuit ? (b) What is the value of the resistance?

Question

In a series circuit containing pure resistance and a pure inductance, the current and the voltage are expressed as : 

i(t) = 5 sin (314t + 2 π/3) and v(t) = 15 sin(314 t + 5π/6) 

(a) What is the impedance of the circuit ? 

(b) What is the value of the resistance? 

(c) What is the inductance in henrys ? 

(d) What is the average power drawn by the circuit ? 

(e) What is the power factor ?

Answer 1

Phase angle of current = 2π/3 = 2 180°/3 = 120° and phase angle of voltage = 5π/6 = 5 × 180°/6 = 150°. 

Also, Z = V_m/I_m = 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 ; X_L/Z = sin 30° = 0.5

∴ X_L = 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).