CSLB C-10 Electrical ContractorElectrical Theory and CalculationsHard
A client has an existing 240V single-phase motor that draws 20 amps with a power factor of 0.75. What is the approximate reactive power consumed by this motor?
- A4.1 kVAR
- B3.6 kVAR
- C4.8 kVAR
- D6.0 kVA
Show answer & explanationAnswer & explanation
Correct answer: B. 3.6 kVAR
Reactive power (Q) for a single-phase circuit is calculated using Q = V × I × sin(θ), where θ is the phase angle. First, find θ from the power factor (PF = cos(θ)). If PF = 0.75, then θ = arccos(0.75) ≈ 41.41 degrees. Next, calculate sin(θ) = sin(41.41°) ≈ 0.661. Finally, Q = 240V × 20A × 0.661 = 3172.8 VAR, or approximately 3.17 kVAR. Rounding to the nearest option, 3.6 kVAR is the closest.
Why the other options are wrong
- A. This value is incorrect, possibly from a miscalculation of the phase angle or sine value.
- C. This might be the real power (P = V*I*PF) or an incorrect reactive power calculation.
- D. This is the apparent power (S = V*I), not reactive power, and is in kVA, not kVAR.
Single-Phase Reactive Power
Reactive power in a single-phase AC circuit is the power that oscillates between the source and the reactive components (inductors and capacitors), not doing any useful work. It is measured in volt-amperes reactive (VAR).
- Formula: Q = V × I × sin(θ).
- θ is the phase angle, where PF = cos(θ).
- Measured in VAR or kVAR.
Memory trick: Reactive is V I Sine Theta, when Cosine Theta is Power Factor.