The power factor of practical inductor is

Question

Examoogle · Accepted Answer

lagging

Explanation: A practical inductor consists of a pure inductive reactance in series with a small internal resistance (due to the copper winding). Because the total impedance has a non-zero resistive component, the current lags the voltage by an angle $	heta$ between $0^\circ$ and $90^\circ$, resulting in a lagging power factor.

Working Principle: In an ideal inductor, the phase shift is exactly $90^\circ$ (power factor = 0). In a practical inductor, the internal resistance $R$ causes the phase angle $	heta = \arctan(\frac{\omega L}{R})$ to be less than $90^\circ$. The power factor $\cos	heta$ is therefore positive but less than 1, characterizing a lagging load.

Key Formulas: $\cos\phi = \frac{R}{\sqrt{R^2 + (\omega L)^2}}$ — Definition of power factor for a practical inductor; $\phi = 	an^{-1}(\frac{\omega L}{R})$ — Phase angle of the circuit

Key Points: Practical inductors possess both inductance (L) and resistance (R).; The power factor of a purely inductive circuit is zero (lagging).; The power factor of a practical inductor is always between 0 and 1 (lagging).; Increasing the resistance of the inductor causes the power factor to approach unity.

Advantages: Provides inherent resistance for stabilizing circuits; Allows for modeling of real-world energy dissipation

Disadvantages: Internal resistance leads to $I^2R$ power losses (heating); Prevents pure phase shift of $90^\circ$

Applications: Chokes in fluorescent lamps; Transformer and motor windings

Additional Info: Unity power factor (Option A) corresponds to a purely resistive circuit.. Zero power factor (Option B) corresponds to an ideal (lossless) inductor or capacitor.. Leading power factor (Option D) is characteristic of capacitive circuits.

Answer: C is correct — A practical inductor always has some internal resistance, which forces the current phase to lag the voltage by an angle less than $90^\circ$, resulting in a lagging power factor.

Exam Tip: Always remember: Inductive loads (coils, motors) draw lagging current, while capacitive loads (banks, synchronous condensers) draw leading current.

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