A resistance of 20 ohm, inductance of 0.2 H and capacitance of 150 μF

1.	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 XL, XC, Z, Y, p.f., active power and reactive power.
Answer» 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

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 XL, XC, Z, Y, p.f., active power and reactive power.

Answer»

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

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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 XL, XC, Z, Y, p.f., active power and reactive power.

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