Question

A resistance of 20 ohm, inductance of 0.2 H and capacitance of 150 μF are connected in series and are fed by a 230 V, 50 Hz supply. Find X_L, X_C, Z, Y, p.f., active power and reactive power.

Answer 1

X_L = 2 π fL = 2π × 50 × 0.2 = 62.8Ω ; X_C = 1/2π fC 

= 10⁻⁶ 2π × 50 × 150 = 21.2 Ω ; X = (X_L − X_C) = 41.6 Ω ;

Z = √(R² + X²) = √(20² + 41.6²)

= 46.2Ω; I = V/Z = 230/46.2 = 4.98A

Also, Z = R + jX = 20 + j 41.6 = 46.2 ∠ 64.3° ohm 

∴ Y = 1/Z = 1/46.2 ∠ 64.3° = 0.0216 ∠ − 64.3° siemens 

p.f. = cos 64.3° = 0.4336 (lag) 

Active power = VI cos φ = 230 × 4.98 × 0.4336 = 497 W 

Reactive power = VI sin φ = 230 × 4.98 × sin 64.3° = 1031 VAR