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What will be the value of the Maximum power factor if the value of the dispersion coefficient is 0.25?

Correct Answer

⚙️ TE • Technical Concept & PrincipleElectricalMachine

Option A

Quick Summary:

The maximum power factor ( $\\cos \\phi_{max}$ ) of an induction motor is related to the dispersion coefficient ( $\sigma$ ) by the relation $\\cos \\phi_{max} = \frac{1 - \sigma}{1 + \sigma}$ . Given $\sigma = 0.25$ , substituting this value into the formula yields $\frac{1 - 0.25}{1 + 0.25} = \frac{0.75}{1.25} = 0.6$ . Note: The provided option A (6) appears to be a transcription error in the source material for 0.6.

⚙️TETechnical SolutionConcept & Principle

💡 Explanation

🔢 Key Formulas

$\\cos \\phi_{max} = \frac{1 - \sigma}{1 + \sigma}$ — Relationship between Max Power Factor and Dispersion Coefficient

$\sigma = 1 - \frac{M^2}{L_1 L_2}$ — Definition of Dispersion Coefficient

⚙️ Working Principle

The dispersion coefficient, also known as the leakage coefficient, is defined as $\sigma = 1 - \frac{M^2}{L_1 L_2}$ , where $M$ is mutual inductance and $L_1, L_2$ are self-inductances. A lower dispersion coefficient indicates better magnetic coupling between stator and rotor, which effectively reduces leakage flux and improves the power factor.

📌 Key Points

▸
The dispersion coefficient $\sigma$ is always less than 1.
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A smaller $\sigma$ signifies superior electromagnetic coupling.
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Maximum power factor in induction motors is limited by leakage reactance.
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The value 0.6 represents the theoretical peak efficiency at the specified leakage.

✅ Advantages

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Improved motor efficiency
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Reduced reactive power demand
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Better voltage regulation

❌ Disadvantages / Limitations

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High cost of high-permeability materials
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Manufacturing tolerances affect $\sigma$

🛠️ Applications / Uses

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Industrial induction motor design
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Transformer leakage analysis

📄 Additional Information

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The value 0.25 for a dispersion coefficient is typical for medium-sized induction motors.
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Option A is likely a typographical error for 0.6, as power factor cannot exceed 1.

📊 Diagram / Illustration

✅

A is correct — The calculated value of the maximum power factor is 0.6 based on the provided dispersion coefficient.

Core Concepts Used

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Dispersion Coefficient Induction Motor Power Factor Leakage Flux

💡 EXAM TIP

Always verify if the result of a power factor calculation is $\leq 1$ ; if you get a value $>1$ , re-check the formula inversion or the given parameters.

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