The power factor of an ac circuit lies between

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Examoogle · Accepted Answer

0 and 1

Explanation: The power factor of an AC circuit is defined as the cosine of the phase angle between the voltage and current waveforms. Since the phase angle $\phi$ varies from $-90^{\circ}$ to $+90^{\circ}$, the cosine value ranges between 0 and 1, representing the ratio of real power to apparent power.

Working Principle: In an AC circuit, the instantaneous power is a function of voltage and current vectors. Power factor ($pf = \cos \phi$) quantifies the efficiency of energy conversion. A purely resistive circuit has $\phi = 0^{\circ}$ (pf=1), while purely reactive circuits have $\phi = \pm 90^{\circ}$ (pf=0). Thus, for all passive linear circuits, the power factor is confined to the non-negative interval $[0, 1]$.

Key Formulas: $P = VI \cos \phi$ — Real Power formula; $pf = \frac{P}{S} = \cos \phi$ — Power Factor definition

Key Points: Power factor is the cosine of the phase difference between voltage and current.; A power factor of 1 indicates a purely resistive load (Unity Power Factor).; A power factor of 0 indicates a purely reactive load (inductor or capacitor).; Lagging pf occurs in inductive loads, while leading pf occurs in capacitive loads.

Advantages: High power factor reduces line losses ($I^2R$).; Improved voltage regulation at the load end.

Disadvantages: Low power factor requires higher current for the same real power transfer.; Increased burden on power system equipment (transformers, generators).

Applications: Industrial motor drives; Power system grid stability and capacitor bank deployment

Additional Info: The range is mathematically $[0, 1]$. While sometimes referred to as 'leading' or 'lagging', the numerical value is always between 0 and 1 inclusive.. Option B is incorrect because, while the phase angle $\phi$ can be negative (for capacitive circuits), the cosine function $\cos(\phi)$ is an even function, making the result non-negative.

Answer: A is correct — The power factor is defined as the cosine of the phase angle difference, which restricted to the interval $[0, 1]$ for all passive loads.

Exam Tip: Always remember that while the phase angle $\phi$ can range from $-90^{\circ}$ to $+90^{\circ}$, the cosine function $\cos(\phi)$ eliminates the negative sign, keeping the power factor positive in standard AC passive systems.

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