Why is a single-phase induction motor not self-starting, according to double revolving field theory?

In one line

A single-phase winding produces a pulsating (not rotating) flux, which can be split into two equal fields rotating in opposite directions; at standstill their torques cancel, so the motor has no starting torque.

Explained simply

Imagine two equally strong people pulling a cart from opposite sides. The cart does not move. But give it a push in one direction and the balance breaks: one side wins and the cart keeps going. A single-phase motor is like that: it hums but does not start until something gives it a direction, after which it runs happily.

Technically, a single-phase stator current produces flux \( \phi = \phi_m\cos\omega t \) along a fixed axis. By double revolving field theory, this equals two fields of magnitude \( \phi_m/2 \) rotating at synchronous speed in opposite directions (forward and backward).

How it works

1. Each rotating component induces rotor currents and produces torque in its own direction.
2. At standstill (slip = 1 for both), the two torques are equal and opposite, so net starting torque is zero.
3. If the rotor is pushed forward, the forward field's slip becomes small and the backward field's slip becomes nearly 2. The forward torque now exceeds the backward torque, so the rotor accelerates in the pushed direction.
4. So a single-phase induction motor will run in either direction once started, but needs a starting method.
5. Practical solution: add an auxiliary (starting) winding displaced 90° in space from the main winding, and make its current out of phase with the main current (using resistance, capacitor, or shading). Two out-of-phase fluxes at an angle produce a rotating field, giving starting torque.

Key formula

\( \phi_m\cos\omega t = \dfrac{\phi_m}{2}\angle\omega t + \dfrac{\phi_m}{2}\angle(-\omega t) \); forward slip \( s \), backward slip \( 2 - s \).

\( \phi_m \) = maximum flux of the pulsating field (Wb), \( \omega \) = supply angular frequency (rad/s), \( s \) = slip with respect to the forward field.

Quick example

If the starting capacitor of a ceiling fan fails, the fan hums but does not start. Give the blades a gentle push and it runs in that direction, a direct demonstration of double revolving field theory.

Common mistakes

• Saying a single-phase motor has a rotating field from the main winding alone.
• Saying the motor cannot run on single phase at all; it runs once started.
• Saying the auxiliary winding must stay in circuit in all types (in split-phase and capacitor-start types it is disconnected by a centrifugal switch).

How MU asks it

Numericals are not expected in this module (as per the MU syllabus), so questions are theory. Typical: "Explain why a single-phase induction motor is not self-starting" (5 marks) or "Explain double revolving field theory". For full marks draw the pulsating flux resolved into two opposite rotating fluxes, sketch forward, backward and net torque against speed (net torque zero at standstill), and explain how an auxiliary winding solves the problem.