Correct Answer

Concept & PrincipleElectricalBasic Electrical

Option C

$\cos\phi$

Quick Summary: The power factor of an A.C. circuit is defined as the cosine of the phase angle difference between the voltage and current waveforms. It represents the ratio of real power (active power) to apparent power in an electrical system.

💡 Explanation

The power factor of an A.C. circuit is defined as the cosine of the phase angle difference between the voltage and current waveforms. It represents the ratio of real power (active power) to apparent power in an electrical system.

🔢 Key Formulas

$P = VI \cos\phi$ — Formula for active power

$\cos\phi = \frac{R}{Z}$ — Power factor in terms of impedance triangle

⚙️ Working Principle

In an A.C. circuit containing resistance, inductance, or capacitance, the voltage and current are generally out of phase by an angle $\phi$ . The real power is given by $P = VI \cos\phi$ . Thus, the ratio $\frac{P}{VI}$ , which is the power factor, is equal to $\cos\phi$ .

📌 Key Points

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Power factor is a dimensionless quantity 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.
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Low power factor increases system losses and reduces the capacity of transmission equipment.

✅ Advantages

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Helps in calculating system efficiency.
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Essential for assessing the sizing of generators and transformers.

❌ Disadvantages / Limitations

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Does not inherently indicate the direction of power flow without specifying phase angle.
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Values near zero result in high reactive current circulation.

🛠️ Applications / Uses

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Electrical power system management.
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Industrial motor drive optimization.
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Energy auditing.

📄 Additional Information

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Option A ( $Z$ ) represents Impedance in Ohms.
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Option B ( $\sin\phi$ ) relates to reactive power factor.
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Option D ( $VI$ ) represents Apparent Power in Volt-Amperes.

📊 Diagram / Illustration

✅

C is correct — Power factor is defined mathematically as the cosine of the phase angle ( $\phi$ ) between the voltage and current, expressed as $\cos\phi$ .

Core Concepts Used

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Phase difference Active vs Apparent power Impedance triangle

💡 EXAM TIP

Always remember that the power factor triangle is derived from the impedance triangle; thus, $\cos\phi$ is equivalent to $\frac{R}{Z}$ for series R-L-C circuits.

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