Correct Answer

Concept & PrincipleElectricalBasic Electrical

Option A

Quick Summary: In a pure inductive circuit, the average power dissipated over one complete cycle is zero. This occurs because the inductor stores energy in its magnetic field during one quarter of a cycle and returns that exact same energy to the source in the next quarter cycle.

💡 Explanation

In a pure inductive circuit, the average power dissipated over one complete cycle is zero. This occurs because the inductor stores energy in its magnetic field during one quarter of a cycle and returns that exact same energy to the source in the next quarter cycle.

🔢 Key Formulas

$P_{avg} = V_{rms} I_{rms} \cos(\phi)$ — General average power formula

$\phi = 90°$ — Phase angle for a pure inductor

⚙️ Working Principle

In an AC circuit with a pure inductor, the voltage $V$ leads the current $I$ by a phase angle of $90°$ ( ${\pi/2}$ radians). The average power is calculated using the formula $P_{avg} = V_{rms} I_{rms} \cos(\phi)$ , where $\phi$ is the phase difference. Since $\phi = 90°$ , $\cos(90°) = 0$ , leading to zero net power consumption.

📌 Key Points

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A pure inductor is a lossless component.
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Power factor ( $cos \phi$ ) for a pure inductor is 0 (lagging).
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Energy is only stored in the magnetic field, not dissipated as heat.
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The net work done over a full cycle is zero.

✅ Advantages

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Does not consume real power (no energy wastage).
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Used effectively in reactive power compensation.

❌ Disadvantages / Limitations

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Cannot be used for heating or lighting purposes.
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Causes voltage drops in transmission lines due to inductive reactance.

🛠️ Applications / Uses

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Induction motors (for magnetic field creation).
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Tuned circuits and filters.
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Smoothing reactors in power supplies.

📄 Additional Information

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Option B (1) represents a purely resistive circuit where phase angle is 0.
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Option C (infinity) is physically impossible for passive components.
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Option D (1.414) represents the peak factor for a sinusoidal waveform ( $\\sqrt{2}$ ).

📊 Diagram / Illustration

✅

A is correct — The average power in a pure inductor is zero because it does not dissipate energy as heat, acting only as an energy storage element.

Core Concepts Used

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Inductive Reactance ($X_L$) Phase Angle ($phi$) Power Factor ($cos \phi$) Reactive Power

💡 EXAM TIP

Remember: Resistors dissipate real power ( $P = I^2R$ ), whereas Inductors and Capacitors only exchange reactive power with the source.

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