Correct Answer

Concept & PrincipleElectricalBasic Electrical

Option A

Quick Summary: In a pure resistive circuit, the voltage and current are in phase, meaning the phase difference (\Phi) between them is $0^\circ$. The power factor is defined as the cosine of the phase angle ($\\cos \Phi$), and since $\\cos(0^\circ) = 1$, the power factor is unity.

💡 Explanation

In a pure resistive circuit, the voltage and current are in phase, meaning the phase difference ( $\Phi)$ between them is $0°$ . The power factor is defined as the cosine of the phase angle ( $\\cos \Phi$ ), and since $\\cos(0°) = 1$ , the power factor is unity.

🔢 Key Formulas

$PF = \cos(\Phi)$ — Definition of Power Factor

$\Phi = 0$ — Phase angle in a pure resistive circuit

⚙️ Working Principle

In a purely resistive circuit, the resistance does not store energy in magnetic or electric fields, preventing any phase lag or lead. Consequently, the instantaneous voltage and current waveforms cross the horizontal axis at the same time, leading to a phase displacement of zero degrees.

📌 Key Points

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Pure resistive circuits exhibit unity power factor.
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Active power (P) is equal to apparent power (S) in a resistive circuit.
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Reactive power (Q) is zero because there are no inductors or capacitors.
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Current is always in phase with the applied voltage.

✅ Advantages

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Maximum efficiency in power transfer as no reactive power is drawn.
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No phase shift, simplifying power calculations.

❌ Disadvantages / Limitations

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Real-world components are rarely 'pure' and include parasitic inductance or capacitance.
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Limited utility in circuits requiring phase manipulation.

🛠️ Applications / Uses

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Heaters and incandescent lamps.
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Calibration of AC electrical instruments.

📄 Additional Information

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Option A (0) corresponds to a purely reactive circuit (inductor or capacitor).
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Option C ( $\infty)$ is physically impossible for a linear passive circuit.
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Option D (VI) represents the Apparent Power (S) in Volt-Amperes.

📊 Diagram / Illustration

✅

B is correct — In a pure resistive circuit, the voltage and current are in phase, resulting in a power factor of $\\cos(0°) = 1$ .

Core Concepts Used

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Phase difference Resistive impedance Power Factor

💡 EXAM TIP

Always remember: 'ELI the ICE man'. In a resistive circuit (the 'R'), there is no ELI or ICE, so phase angle is always 0.

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