Correct Answer

Concept & PrincipleElectricalPower System

Option B

Unity

Quick Summary: In a circuit breaker, the arc is essentially an ionized plasma path through which the current flows. Because the arc resistance is primarily ohmic in nature during the moment of current interruption, the arc voltage and arc current are in phase, resulting in a unity power factor.

💡 Explanation

In a circuit breaker, the arc is essentially an ionized plasma path through which the current flows. Because the arc resistance is primarily ohmic in nature during the moment of current interruption, the arc voltage and arc current are in phase, resulting in a unity power factor.

🔢 Key Formulas

$P_{arc} = V_{arc} \times I_{arc} \times \cos(\phi)$

$\phi = 0°\implies \cos(\phi) = 1$

⚙️ Working Principle

As the circuit breaker contacts separate, the current flows through the ionized gas (plasma) created between them. This plasma behaves as a non-linear resistance. Since the arc voltage drop $V_{arc}$ is nearly in phase with the arc current $I_{arc}$ at the instant of zero crossing, the instantaneous power factor of the arc is considered to be unity.

📌 Key Points

▸
The arc path in a circuit breaker acts as a resistive load at the moment of extinction.
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The arc voltage is roughly in phase with the current passing through the ionized path.
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A unity power factor implies the arc is purely resistive at the contact gap interface.

✅ Advantages

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Simplifies analysis of arc energy dissipation ( $W = \int V I dt$ ).
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Facilitates calculation of the arc resistance $R_{arc} = \frac{V_{arc}}{I_{arc}}$ .

❌ Disadvantages / Limitations

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Does not account for the non-linear dynamic behavior of the arc plasma over the full cycle.
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Real-world arcs exhibit minor reactive components due to magnetic effects near the contact.

🛠️ Applications / Uses

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Switchgear design for HV and LV circuit breakers.
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Calculation of transient recovery voltage (TRV) characteristics.

📄 Additional Information

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The arc duration is the time interval between the separation of the contacts and the final extinction of the arc.
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Options like 'Lagging' or 'Leading' refer to the external circuit impedance, whereas the arc itself is considered unity.

📊 Diagram / Illustration

✅

B is correct — The arc behaves as a resistive element in the circuit breaker, meaning the arc voltage and current are in phase, resulting in a unity power factor.

Core Concepts Used

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Arc Extinction Switchgear Protection Ohmic Nature of Arc

💡 EXAM TIP

Always remember that while the entire transmission system is typically inductive (lagging), the arc itself during the breaking process is modeled as purely resistive.

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