Correct Answer

Concept & PrincipleElectricalBasic Electrical

Option D

VIcos∅

Quick Summary: In an AC circuit containing resistance and inductance (RL series circuit), the average power consumed is the product of the RMS voltage, RMS current, and the power factor of the circuit. Since the power factor is defined as $\cos\phi$, where $\phi$ is the phase angle between voltage and current, the average power is given by $P = VI\cos\phi$.

💡 Explanation

In an AC circuit containing resistance and inductance (RL series circuit), the average power consumed is the product of the RMS voltage, RMS current, and the power factor of the circuit. Since the power factor is defined as $\cos\phi$ , where $\phi$ is the phase angle between voltage and current, the average power is given by $P = VI\cos\phi$ .

🔢 Key Formulas

$P = VI \cos\phi$ — Formula for real average power in an AC circuit

$\phi = \tan^{-1}(\frac{X_L}{R})$ — Phase angle calculation for an RL circuit

⚙️ Working Principle

In an RL series circuit, the resistor dissipates real power as heat, while the inductor stores energy in its magnetic field during one part of the cycle and returns it to the source in the next, resulting in zero average power consumption for the ideal inductor component. Therefore, the total average power is entirely attributed to the resistive component, which is expressed as $I^2R$ , equivalent to the total power formula $VI\cos\phi$ .

📌 Key Points

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The resistor is the only element in an RL circuit that consumes real power.
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The power factor $\cos\phi$ in an RL circuit is always lagging.
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The inductor and capacitor do not consume average power, only reactive power.
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The total apparent power is $S = VI$ measured in Volt-Amperes (VA).

✅ Advantages

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Simple calculation using RMS values.
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Readily measurable using a wattmeter.

❌ Disadvantages / Limitations

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Does not account for reactive power (VARs) which affects circuit size.
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Assumes sinusoidal steady-state conditions.

🛠️ Applications / Uses

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AC power distribution analysis
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Design of motor starters and chokes
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Electrical machine efficiency calculations

📄 Additional Information

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Option A is 0, which would be true only for an ideal inductor or capacitor.
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Option C, $VI\sin\phi$ , represents the Reactive Power ( $Q$ ) measured in VAR.
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The term $\cos\phi$ is the power factor, ranging from 0 to 1 for inductive loads.

📊 Diagram / Illustration

✅

D is correct — The average power in an RL series circuit is given by the product of voltage, current, and the cosine of the phase angle between them, denoted as $VI\cos\phi$ .

Core Concepts Used

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Real Power Power Factor Phase Angle RL Circuit Dynamics

💡 EXAM TIP

Always remember that in AC circuits, the power consumed is only the 'Real Power' ( $P = VI\cos\phi$ ); reactive components only cause power factor shifts without permanent energy loss.

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