The dispersion coefficient of an induction motor is the ratio of

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The correct answer is Option C: magnetizing current to ideal short circuit current. The dispersion coefficient ($\sigma$) of an induction motor represents the degree of magnetic coupling between the stator and rotor windings. It is defined as the ratio of the magnetizing current ($I_m$) to the ideal short-circuit current ($I_{sc}$), which is the current that would flow if the leakage reactance were zero.

Step-by-Step Solution & Concepts:
The dispersion coefficient ($\sigma$) of an induction motor represents the degree of magnetic coupling between the stator and rotor windings. It is defined as the ratio of the magnetizing current ($I_m$) to the ideal short-circuit current ($I_{sc}$), which is the current that would flow if the leakage reactance were zero.

Working Principle: In an ideal induction motor with zero leakage flux, the magnetizing current would be the only current required to establish the air-gap flux. However, due to slot leakage and end-turn leakage, an additional component of current is required. The dispersion coefficient acts as an inverse measure of the coupling coefficient; a smaller $\sigma$ indicates better magnetic coupling and superior performance.

Key Formulas: $\sigma = \frac{I_m}{I_{sc}}$ — Definition of dispersion coefficient; $\sigma \approx 1 - k_1 k_2$ — Relation with coupling coefficients $k_1$ and $k_2$

Key Points: The dispersion coefficient is always less than 1.; A lower value of $\sigma$ indicates higher power factor and better torque characteristics.; It is primarily influenced by the leakage flux paths in the stator and rotor slots.

Advantages: Useful for calculating the circle diagram of an induction motor.; Provides a dimensionless index to evaluate motor design quality.

Disadvantages: Cannot be measured directly in a simple laboratory test.; Assumes linear magnetic circuits which may not hold under deep saturation.

Applications: Induction motor design optimization.; Performance analysis using circle diagrams.

Additional Info: The ideal short-circuit current $I_{sc}$ is defined as $V_1 / X_l$, where $X_l$ is the total leakage reactance referred to the stator.. Option B is incorrect as it describes a ratio involving voltage and reactance rather than current components.

Answer: C is correct — The dispersion coefficient $\sigma$ is defined as the ratio of magnetizing current to the ideal short-circuit current.

Exam Tip: Always remember that a low dispersion coefficient is desirable for high-performance motors, just as a low leakage factor is preferred in transformers.

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Option A: ideal short circuit current to magnetizing current

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Option B: Starot voltage per phase to leakage reactance

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Option D: None of these

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