Correct Answer

Concept & PrincipleElectricalBasic Electrical

Option D

VIcos∅

Quick Summary: In an AC series circuit, the average power (or active power) consumed is defined as the product of the RMS voltage, RMS current, and the power factor (cosine of the phase angle). This represents the real power that performs useful work, as opposed to reactive power which oscillates between source and load.

💡 Explanation

In an AC series circuit, the average power (or active power) consumed is defined as the product of the RMS voltage, RMS current, and the power factor (cosine of the phase angle). This represents the real power that performs useful work, as opposed to reactive power which oscillates between source and load.

🔢 Key Formulas

$P = VI\cos\phi$ — Average real power consumed in Watts

$P = I^2R$ — Power dissipated by the resistive part of the circuit

⚙️ Working Principle

The instantaneous power in an AC circuit is $p(t) = v(t)i(t)$ . When integrating this over a complete cycle $T$ to find average power $P = \frac{1}{T}\int_{0}^{T} v(t)i(t)dt$ , the term simplifies to $VI\cos\phi$ . While the capacitor does not consume real power, the entire series circuit impedance $Z = R + jX_C$ creates a phase difference $\phi$ between voltage and current, where $\cos\phi$ accounts for the resistive component's share of the energy.

📌 Key Points

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The term $\cos\phi$ is known as the Power Factor.
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In an RC circuit, the current leads the voltage, but the real power formula remains $VI\cos\phi$ .
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Capacitors only exchange reactive power ( $Q = VI\sin\phi$ ), they do not dissipate real energy as heat.

✅ Advantages

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Allows calculation of energy consumption efficiency.
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Helps in determining system load requirements.

❌ Disadvantages / Limitations

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Does not account for harmonic distortions in non-linear loads.
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Requires knowledge of phase angle $\phi$ which varies with frequency.

🛠️ Applications / Uses

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Electrical power system design.
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AC motor and induction load analysis.

📄 Additional Information

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Option A (0) is the average power for a pure capacitor or pure inductor.
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The phase angle $\phi$ for an RC circuit is given by $\phi = -\tan^{-1}(\frac{X_C}{R})$ .
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Standard unit for average power is Watt (W).

📊 Diagram / Illustration

✅

D is correct — The average power in an AC circuit is defined by the formula $P = VI\cos\phi$ , where $\phi$ is the phase difference between voltage and current.

Core Concepts Used

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AC Circuit Theory Power Factor Real vs Reactive Power

💡 EXAM TIP

Always remember that in AC circuits, the real power is ONLY consumed by resistive elements, while inductors and capacitors only store and release energy.

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