The power factor of the induction motor will decrease with

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The correct answer is Option D: All of these. The power factor of an induction motor is defined by the ratio of active power to apparent power. Since the motor is an inductive load, the power factor decreases as the reactive power demand increases relative to the active power output.

Step-by-Step Solution & Concepts:
The power factor of an induction motor is defined by the ratio of active power to apparent power. Since the motor is an inductive load, the power factor decreases as the reactive power demand increases relative to the active power output.

Working Principle: The induction motor requires magnetizing current ($I_m$) to establish the air-gap flux and leakage reactance current to account for flux leakage. An increase in $I_m$ or leakage reactance increases the lagging reactive component ($I_q$), causing the total current vector to shift, thereby reducing the cosine of the phase angle (power factor).

Key Formulas: $\cos \phi = \frac{P}{V_1 I_1}$ — General definition of power factor; $Q \approx I_m^2 X_L + I_2^2 X_{leak}$ — Reactive power dependency on magnetizing current and leakage reactance

Key Points: Induction motors always operate at a lagging power factor.; Magnetizing current is relatively constant but high, which is why induction motors have poor power factor at light loads.; Leakage reactance increases with motor size and air-gap dimensions, directly impeding power factor improvement.

Advantages: Provides simple mechanism for speed control; High starting torque with wound rotor

Disadvantages: Low power factor at light load; Requires reactive power compensation (capacitors)

Applications: Industrial pumps and compressors; Conveyor belts and fans

Additional Info: The magnetizing current is determined by the air-gap reluctance; a larger air gap requires higher magnetizing current, reducing PF.. Short circuit current refers to the locked-rotor current; if this decreases due to high leakage, the magnetizing component becomes more dominant, lowering PF.

Answer: D is correct — All listed factors increase the reactive power component required by the motor, which shifts the current phase angle and reduces the power factor.

Exam Tip: In exams, remember that any factor that increases the ratio of reactive power to active power will necessarily lead to a lower power factor.

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Option A: With increase in Magnetizing current

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Option B: With an increase in the value of leakage reactance

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Option C: With a decrease in Ideal short circuit current

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