Correct Answer

Concept & PrincipleElectricalBasic Electrical

Option A

$R/Z$

Quick Summary: The power factor of an A.C. circuit is defined as the cosine of the phase angle between the voltage and current vectors, mathematically represented as the ratio of resistance to impedance. It signifies the fraction of apparent power that is converted into real work.

💡 Explanation

The power factor of an A.C. circuit is defined as the cosine of the phase angle between the voltage and current vectors, mathematically represented as the ratio of resistance to impedance. It signifies the fraction of apparent power that is converted into real work.

🔢 Key Formulas

$PF = \cos(\phi) = \frac{R}{Z}$ — Fundamental Power Factor definition

$Z = \sqrt{R^2 + (X_L - X_C)^2}$ — Impedance triangle relationship

⚙️ Working Principle

In an RLC series circuit, the total opposition to current flow is the impedance ( $Z$ ), which is the vector sum of resistance ( $R$ ) and net reactance ( $X$ ). The voltage across the resistor is in phase with the current, while the total circuit voltage leads or lags by the phase angle $\phi$ . Therefore, $\cos(\phi) = \frac{V_R}{V_Z} = \frac{I \times R}{I \times Z} = \frac{R}{Z}$ .

📌 Key Points

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Power factor is dimensionless, ranging from 0 to 1.
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A lagging power factor indicates an inductive load, while a leading power factor indicates a capacitive load.
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Unity power factor (1.0) occurs in purely resistive circuits where voltage and current are in phase.

✅ Advantages

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Helps in determining the efficiency of electrical equipment.
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Essential for calculating the required rating of power factor correction capacitors.

❌ Disadvantages / Limitations

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Low power factor increases $I^2R$ copper losses in the distribution system.
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High reactive power demand reduces the available capacity of transformers and alternators.

🛠️ Applications / Uses

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Electrical Power Systems efficiency monitoring.
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Industrial motor and transformer sizing.

📄 Additional Information

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The power factor is often expressed as a percentage, though the ratio is between 0 and 1.
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Option B ( $Z/R$ ) is the reciprocal of the power factor and does not represent a standard circuit parameter.
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Option C ( $V/I$ ) represents the magnitude of the impedance ( $|Z|$ ).

📊 Diagram / Illustration

✅

A is correct — Power factor is defined by the ratio of the resistive component to the total impedance in an A.C. circuit, expressed as $PF = \frac{R}{Z}$ .

Core Concepts Used

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Impedance Triangle Phase Angle Real vs Apparent Power

💡 EXAM TIP

Always remember the mnemonic 'ELI the ICE man': In an Inductor (L), Voltage (E) leads Current (I); in a Capacitor (C), Current (I) leads Voltage (E).

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