Power factor of an electrical circuit is equal to

Question

Examoogle · Accepted Answer

all of the above

Explanation: The power factor of an electrical circuit is defined as the cosine of the phase angle between the voltage and current waveforms. It represents the ratio of real power (kW) to apparent power (kVA) and, in a series R-L-C circuit, is equivalent to the ratio of resistance (R) to impedance (Z).

Working Principle: In AC circuits, the phase difference between voltage and current is caused by reactive elements (inductors and capacitors). The power factor indicates how much of the total power supplied (apparent power) is actually converted into useful work (real power). A power factor of 1 (unity) signifies a purely resistive circuit, while values less than 1 indicate the presence of reactive loads.

Key Formulas: $pf = \cos(\phi)$ — cosine of the phase angle; $pf = \frac{P}{S} = \frac{kW}{kVA}$ — ratio of real power to apparent power; $pf = \frac{R}{Z}$ — ratio of resistance to impedance

Key Points: Power factor ranges from 0 to 1.; A lagging power factor occurs in inductive circuits (current lags voltage).; A leading power factor occurs in capacitive circuits (current leads voltage).; Unity power factor (1.0) is ideal for electrical efficiency.

Advantages: Minimizes current for the same amount of real power transfer.; Reduces I^2R losses in transmission lines.

Disadvantages: Low power factor increases the required kVA rating of electrical equipment.; Increases billing costs for industrial consumers.

Applications: Electrical load management; Power factor correction using capacitor banks

Additional Info: For purely resistive circuits, the phase angle is 0, so cos(0) = 1.. Option A is valid for series impedance triangles, Option B is the fundamental definition, and Option C is the practical measurement ratio.

Answer: D is correct — all the given expressions represent valid definitions or representations of the power factor in an AC electrical circuit.

Exam Tip: Always remember that in an impedance triangle, cos(θ) = Base/Hypotenuse = R/Z, which perfectly aligns with the Power Triangle where cos(θ) = kW/kVA.

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