In an induction motor when the air gap field between rotor and stator increases power factor of the

Question

In an induction motor when the air gap field between rotor and stator increases power factor of the machine:

Examoogle · Accepted Answer

Decreases

Explanation: Increasing the air gap in an induction motor significantly increases the magnetizing current required to produce the same rotating magnetic field. Since this magnetizing current is purely inductive and reactive, its increase leads to a higher reactive power demand, thereby causing a decrease in the overall power factor of the machine.

Working Principle: The stator of an induction motor must establish a flux in the air gap to induce rotor currents. The air gap reluctance is directly proportional to the gap length; therefore, a wider gap increases the reluctance. To overcome this higher reluctance and maintain the necessary flux density, the magnetizing current $I_m$ must increase. Because the total stator current is the phasor sum of the load current and the magnetizing current ($I_s = I_L + I_m$), an increase in the lagging reactive component $I_m$ reduces the power factor angle $\cos \phi$.

Key Formulas: $I_m = \frac{V}{\omega L_m}$ — magnetizing current where $L_m$ decreases as air gap increases; $\cos \phi = \frac{P}{\sqrt{P^2 + Q^2}}$ — power factor definition showing dependence on reactive power $Q$

Key Points: The air gap of an induction motor acts as a high-reluctance path in the magnetic circuit.; Magnetizing current ($I_m$) is inversely proportional to the magnetizing reactance ($X_m$), which decreases with a larger air gap.; A lower power factor leads to higher line currents and increased $I^2R$ losses in the supply system.

Advantages: Larger air gap provides better mechanical clearance for high-speed rotors.; Improved cooling and reduced noise levels in certain machine designs.

Disadvantages: Poor power factor results in higher reactive power consumption from the grid.; Increased stator copper losses due to higher current magnitude for the same mechanical output.

Applications: Design of induction motors where mechanical robustness is prioritized over electrical efficiency.; Industrial systems requiring compensation capacitors to correct low power factor caused by wide air gaps.

Additional Info: Standard industrial practice is to keep the air gap as small as possible (limited by mechanical tolerances) to maximize magnetizing reactance.. Option A is incorrect because increasing the air gap increases the inductive nature of the input impedance, which forces the power factor to decrease, not increase.

Answer: B is correct — increasing the air gap increases the magnetizing current (reactive component), which inherently reduces the power factor of the induction motor.

Exam Tip: Always remember that any factor increasing the reactive power demand of an inductive load (like larger air gaps or lower frequencies) will decrease the power factor.

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