Double-Revolving-Field Theory
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At standstill a single-phase stator field can be resolved into equal forward and backward rotating fields. Their starting torques are equal and opposite, giving zero net starting torque; hence the motor is not self-starting. Both assertion and reason are true and the reason correctly explains the assertion: option A.

Single-phase induction motor needs an auxiliary starting means because forward/backward torques cancel at rest.
After the rotor starts, the two slips differ and the torques no longer cancel.
Single-phase induction motor needs an auxiliary starting means because forward/backward torques cancel at rest.