An LCR series circuit with R = 20 Ω, L = 0.15 H, and C = 50 μF is connected to a 100 V, 50 Hz supply. The power factor is.
Correct answer: C. 0.75
- A. 0.55
- B. 0.65
- C. 0.75
- D. 0.85
Explanation
XL = 2π × 50 × 0.15 ≈ 47.12 Ω, XC = 1/(2π × 50 × 50 × 10⁻⁶) ≈ 63.66 Ω. Net reactance |XL - XC | = 63.66 - 47.12 = 16.54 Ω. Impedance Z = √(20² + 16.54²) ≈ 26.0 Ω. Power factor cosφ = R/Z = 20/26.0 ≈ 0.77, closest to 0.75.
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Alternating current varies periodically, so phase relationships become essential when current passes through a resistor, capacitor or inductor. The chapter distinguishes resistance from capacitive and inductive reactance, explains phase lead and lag, and connects changing electric and magnetic fields with the production and properties of electromagnetic waves.
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