Power factor of an electrical circuit is equal to _____

Question

Examoogle · Accepted Answer

All of the above

Explanation: The power factor of an AC circuit is defined as the cosine of the phase angle difference between the circuit voltage and current. It represents the ratio of real power to apparent power, and in an RLC circuit, it is also equivalent to the ratio of resistance to impedance.

Working Principle: In an AC system, the load impedance $Z$ forms a triangle with resistance $R$ and reactance $X$. The power factor $\cos(\phi)$ is defined by the geometry of this impedance triangle as the ratio of the adjacent side (resistance) to the hypotenuse (impedance). Simultaneously, the power triangle relates real power $P$ (kW) to apparent power $S$ (kVA), where the ratio $P/S$ yields the same cosine value.

Key Formulas: $PF = \cos(\phi) = \frac{R}{Z}$ — Impedance triangle definition; $PF = \frac{P}{S} = \frac{kW}{kVA}$ — Power triangle definition

Key Points: A unity power factor indicates a purely resistive circuit where voltage and current are in phase.; Lagging power factor is associated with inductive loads (motors, transformers).; Leading power factor is associated with capacitive loads (capacitor banks, synchronous condensers).; Power factor correction is essential to reduce line losses and improve system efficiency.

Advantages: Reduces current for a given load, minimizing $I^2R$ losses.; Increases the active power capacity of the source.

Disadvantages: Low power factor increases the required kVA rating of electrical equipment.; Leads to increased voltage drops in transmission and distribution lines.

Applications: Industrial power system optimization.; Synchronous motor control for grid stability.

Additional Info: The range of power factor is always between 0 and 1.. Option B refers to the mathematical definition based on the phase angle between waveforms, while options A and C refer to circuit properties and power metrics, respectively.

Answer: D is correct — Power factor is defined equivalently by the ratio of resistance to impedance, the ratio of real power to apparent power, and the cosine of the phase angle between voltage and current.

Exam Tip: Always verify if the power factor is lagging or leading by checking the nature of the load (Inductive/Capacitive), as this determines the reactive power flow direction.

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