Correct Answer

Concept & PrincipleElectricalBasic Electrical

Option A

Quick Summary: When voltage and current are in phase, they reach their peak and zero values at the same time, resulting in a phase difference of 0 radians or 0 degrees. This condition typically occurs in purely resistive circuits where the impedance is purely real.

💡 Explanation

When voltage and current are in phase, they reach their peak and zero values at the same time, resulting in a phase difference of 0 radians or 0 degrees. This condition typically occurs in purely resistive circuits where the impedance is purely real.

🔢 Key Formulas

$P = VI \cos(\phi)$ — Power in an AC circuit where $\phi = 0$ results in $P = VI$

$Z = R + j(X_L - X_C)$ — General impedance formula; for $\phi = 0$ , $(X_L - X_C) = 0$

⚙️ Working Principle

In an A.C. circuit, the phase angle $\phi$ represents the time displacement between the voltage waveform $v(t) = V_m \sin(\omega t)$ and the current waveform $i(t) = I_m \sin(\omega t - \phi)$ . When $\phi = 0$ , the impedance $Z$ of the circuit consists only of resistance $R$ , as there are no inductive or capacitive components to cause a phase shift. Consequently, the power factor, defined as $\cos(\phi)$ , reaches its maximum value of unity (1).

📌 Key Points

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Phase difference ( $\phi$ ) is the angular difference between voltage and current phasors.
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A phase angle of $0°$ indicates a unity power factor.
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This occurs in pure resistive loads like incandescent bulbs or heaters.

✅ Advantages

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Maximum active power transfer for a given voltage and current
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No reactive power consumption ( $Q = 0$ )

❌ Disadvantages / Limitations

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Limited to purely resistive components
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Rarely achieved in industrial power systems containing motors or transformers

🛠️ Applications / Uses

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Electrical heating elements
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Incandescent lighting circuits
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Reference standard for phase measurement

📄 Additional Information

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The phase difference is measured in degrees ( $°$ ) or radians.
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Options B, C, and D represent lagging or leading phase angles which occur in reactive circuits.

📊 Diagram / Illustration

✅

A is correct — The phase difference between voltage and current in a purely resistive circuit is $0°$ .

Core Concepts Used

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AC Fundamentals Phase Angle Unity Power Factor

💡 EXAM TIP

Always remember that inductive circuits cause current to lag ( $90°$ ) while capacitive circuits cause current to lead ( $90°$ ); resistive circuits are the only ones keeping them in phase.

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