gen-define-power-factor-and-give-one-short-worked-example-bddd

Define power factor and give one short worked example.

# Power Factor ## Definition **Power factor (PF)** is the ratio of real power (P) to apparent power (S) in an AC electrical circuit. It measures how effectively electrical power is being converted into useful work output. $$\text{Power Factor} = \cos(\phi) = \frac{P}{S} = \frac{\text{Real Power (W)}}{\text{Apparent Power (VA)}}$$ where φ is the phase angle between voltage and current. **Range:** 0 to 1 (or 0% to 100%) - PF = 1: Ideal (purely resistive load) - PF < 1: Current and voltage are out of phase (reactive components present) --- ## Worked Example **Problem:** A factory has the following electrical loads: - Real Power (P) = 75 kW - Reactive Power (Q) = 100 kVAR Calculate the power factor. **Solution:** Step 1: Find apparent power using the power triangle: $$S = \sqrt{P^2 + Q^2} = \sqrt{75^2 + 100^2} = \sqrt{5625 + 10000} = \sqrt{15625} = 125 \text{ kVA}$$ Step 2: Calculate power factor: $$\text{PF} = \frac{P}{S} = \frac{75}{125} = 0.6 \text{ or } 60\%$$ **Answer:** The power factor is **0.6 lagging** (or 60%), indicating poor power efficiency. This factory would benefit from power factor correction.