Single phase induction motor is not the self starting so, to make it self start we can use capacitor.

The main restriction with single phase induction motors is that there is only one phase on the stator winding. Hence the magnetic field in a single phase induction motor does not rotate. Instead, it pulses, getting first larger and then smaller but always remaining in the same direction. Because there is no rotating stator magnetic field, a single phase induction motor has no starting torque.

The idea behind capacitor start single phase motors is an extension of the split phase winding technique used to produce the starting torque in single phase induction motor. In capacitor start induction motor a capacitor is placed in series with the auxiliary winding of the motor. By propoer selection of capacitor size, the magnetomotive force of the starting current in the auxiliary winding can be adjusted to be equal to the magnetomotive force of the current in the main winding.  The current leads the voltage by90 degrees when capacitor is introduced.

Now with the proper selection of capacitor, the current in the auxiliary windings can be made to lead the current in the main windings by90 degrees.

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