What is the formula of power factor ?

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Explanation: The power factor of an AC circuit is defined as the cosine of the phase angle between voltage and current. It represents the ratio of real power (active power) to the apparent power, reflecting the efficiency with which electrical power is converted into useful work.

Working Principle: In an AC circuit with a load, the total power is represented by the power triangle. The base is real power (P in kW), the height is reactive power (Q in kVAR), and the hypotenuse is apparent power (S in kVA). The cosine of the angle between P and S gives the power factor, which is also equivalent to the ratio of resistance to impedance in a series R-L-C circuit.

Key Formulas: $PF = \cos(\phi) = \frac{P}{S} = \frac{kW}{kVA}$ — Basic power factor relation; $PF = \frac{R}{Z}$ — Impedance triangle relationship

Key Points: Power factor is a dimensionless quantity ranging from 0 to 1.; A lagging power factor indicates an inductive load, while a leading power factor indicates a capacitive load.; Unity power factor (PF=1) occurs in purely resistive circuits where voltage and current are in phase.

Advantages: Improves system efficiency by reducing I^2R losses.; Increases the active power carrying capacity of existing lines and transformers.

Disadvantages: Low power factor increases line currents, requiring larger conductor cross-sections.; Leads to higher voltage drops, resulting in poor voltage regulation at the load end.

Applications: Industrial motor installations to improve system efficiency.; Power system grids using capacitor banks to compensate for inductive reactive power.

Additional Info: All options provided describe the same physical quantity from different perspectives (circuit parameters, power units, and vector representation).. Option A relates to the impedance triangle, Option B to units of power, and Option C to the definition of power.

Answer: D is correct — All the given options represent mathematically valid ways to define or express the power factor in an AC circuit.

Exam Tip: Always remember that while PF=1 is ideal, most practical industrial loads are inductive (lagging) and require capacitor banks for correction.

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