Power factor can be mathematically expressed as:

Question

Examoogle · Accepted Answer

$P/S$

Explanation: Power factor is defined as the ratio of real power (active power) to apparent power in an AC electrical circuit. It represents the efficiency with which the current is being converted into useful work output.

Working Principle: In an AC circuit containing inductance or capacitance, the voltage and current waveforms are out of phase. The power factor is the cosine of the phase angle ($\cos \phi$) between the voltage and current, which mathematically equals the ratio of real power $P$ (in Watts) to the apparent power $S$ (in Volt-Amperes).

Key Formulas: $PF = \frac{P}{S}$ — Power factor as the ratio of Real Power (Watts) to Apparent Power (VA); $S = \sqrt{P^2 + Q^2}$ — Apparent power calculated from active and reactive components

Key Points: Unity power factor ($\cos \phi = 1$) indicates a purely resistive load.; Lagging power factor occurs in inductive loads (e.g., motors).; Leading power factor occurs in capacitive loads (e.g., capacitor banks).; Low power factor increases current flow for the same power delivery, leading to higher $I^2R$ losses.

Advantages: Reduced $I^2R$ line losses; Improved voltage regulation; Increased system capacity; Reduction in electricity utility penalties

Disadvantages: Requires additional investment for capacitors; Over-correction leads to leading power factor issues

Applications: Industrial motor installations; Electrical distribution networks; Power electronic converters

Additional Info: Real Power $P$ is measured in Watts (W).. Reactive Power $Q$ is measured in Volt-Ampere Reactive (VAR).. Apparent Power $S$ is measured in Volt-Amperes (VA).. Option A ($P/Q$) represents the cotangent of the phase angle.. Option B ($Q/P$) represents the tangent of the phase angle.

Answer: C is correct — Power factor is defined as the real power $P$ divided by the apparent power $S$.

Exam Tip: Always remember the mnemonic 'ELI the ICE man': in Inductive circuits, current lags voltage (ELI), and in Capacitive circuits, current leads voltage (ICE).

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