The torque developed by a single-phase motor at starting is

Question

Examoogle · Accepted Answer

Option D: zero

Explanation & Concepts:
A single-phase induction motor has no inherent starting torque, meaning its torque at zero speed is zero. This occurs because the single-phase alternating winding current produces a pulsating magnetic field rather than a rotating magnetic field. Consequently, the motor cannot start by itself unless an auxiliary starting mechanism is provided.

Working Principle: According to Double Field Revolving Theory, a pulsating single-phase magnetic field can be decomposed into two equal magnetic fields rotating in opposite directions at synchronous speed. At standstill (slip $s = 1$), both forward and backward rotating fields induce equal and opposite electromagnetic torques ($T_f = T_b$). The net starting torque developed by the rotor is the vector sum of these two opposing torques, which evaluates to zero.

Key Formulas: $T_f = \frac{I_2^2 R_2/s}{\omega_s}$ — Forward torque developed by the forward rotating field; $T_b = \frac{I_2^2 R_2/(2-s)}{\omega_s}$ — Backward torque developed by the backward rotating field; $T_{net} = T_f - T_b$ — Resultant torque developed by the rotor ($T_{net} = 0$ at starting where $s = 1$)

Key Points: A single-phase stator winding carrying alternating current produces a stationary pulsating magnetic flux.; At standstill ($s=1$), the forward slip and backward slip are equal ($s_f = s_b = 1$), generating equal and opposite torque components.; To make a single-phase motor self-starting, an auxiliary winding with a phase-shifting element (capacitor or resistor) is added to create a rotating magnetic field.

Advantages: Simple, robust construction and low manufacturing cost.; Operates efficiently on standard single-phase residential AC power supplies.

Disadvantages: Inherently non-self-starting without auxiliary starting devices.; Lower power factor and lower efficiency compared to polyphase induction motors.

Applications: Ceiling fans and blowers (using permanent split capacitor motors).; Domestic refrigerators and air conditioners (using capacitor-start capacitor-run motors).; Small power tools and washing machines.

Additional Info: Option A is incorrect because equal to rated torque is only possible when auxiliary starting mechanisms (like starting capacitors) are engaged.. Option B is incorrect because starting torque cannot exceed rated torque natively without phase-splitting methods.. Option C is incorrect because the torque is strictly zero rather than merely reduced.

Answer: D is correct — The torque developed by a single-phase induction motor at starting is zero because the single-phase pulsating field produces two equal and opposite torque components at standstill.

Exam Tip: For competitive exams like GATE and ESE, remember that at standstill ($s=1$), $s_f = 1$ and $s_b = 2-s = 1$, leading to $T_f = T_b$ and $T_{start} = 0$. Once rotated in either direction, $T_net > 0$ in that direction.

Examoogle · Answer

Option A: equal to the rated torque

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Option B: greater than the rated torque

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Option C: less than the rated torque

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