The power factor of ac circuit lies between

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Examoogle · Accepted Answer

0 and 1

Explanation: The power factor (p.f.) of an AC circuit is defined as the cosine of the phase angle between the voltage and current phasors. Since the phase difference $\phi$ in a passive circuit varies from $-90^\circ$ to $+90^\circ$, the value of $\cos(\phi)$ remains bounded within the interval $[0, 1]$.

Working Principle: In an AC circuit, the power factor is given by the ratio of real power to apparent power. Because real power $P = VI \cos(\phi)$ can never exceed the apparent power $S = VI$ in passive components, the ratio $\frac{P}{S} = \cos(\phi)$ must fall between 0 (purely reactive) and 1 (purely resistive).

Key Formulas: $p.f. = \cos(\phi) = \frac{P}{S}$ — Basic definition of power factor as a ratio of real power to apparent power; $\phi = \angle V - \angle I$ — Phase angle between voltage and current phasors

Key Points: A power factor of 1 is termed 'unity', representing a purely resistive circuit.; A power factor of 0 occurs in purely inductive or capacitive circuits where the phase shift is $90^\circ$.; Lagging power factor is associated with inductive loads, while leading is associated with capacitive loads.; The power factor is dimensionless.

Advantages: High power factor reduces $I^2R$ losses in transmission lines.; Higher power factor improves voltage regulation and system efficiency.

Disadvantages: Low power factor increases the current required to deliver the same real power, leading to larger cable sizing.; Utilities impose penalties for low power factor as it increases the kVA demand on the system.

Applications: Industrial motor drives and transformer loading optimization.; Power factor correction capacitor banks in distribution networks.

Additional Info: Values outside the range 0 to 1 would imply the generation of real power by a passive component, which violates the law of conservation of energy.. Option B (-1 to 1) is mathematically incorrect because the cosine function for phase angles between $-\pi/2$ and $\pi/2$ is always non-negative.

Answer: A is correct — The power factor is defined as the cosine of the phase angle difference between voltage and current, which mathematically ranges from 0 to 1.

Exam Tip: Always remember that in power systems, we prioritize maintaining a 'lagging' p.f. close to unity, as active power consumption is required for most industrial inductive loads like induction motors.

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