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# What is a Single-phase Induction Motor?￼

A single-phase induction motor has a cage winding on its rotor and single phase winding on the stator. The size of these motors is very small; barely fractional kilowatt ratings. These motors find their application in daily household equipment like mixers, fans, and  other kitchen equipment. These motors are also in A.C, blowers, small farming equipment etc.

When a single-phase supply is connected to the stator winding a pulsating magnetic field is produced. Due to inertia there is no rotation in the rotor. Since, the single-phase induction motor requires means for getting started and is not self starting.

When an auxiliary means is used to start the rotor and stator windings are excited. After removing the starting device the motor rotates continuously in the direction in which it initially started.

The two windings a, b which are displaced below produce magnetic fields 90° in space.

Since magnetic field produced by these windings is equal and and 90° apart in the time then

The resultant of these fields is the rotating magnetic field of constant magnitude . This rotating magnetic field may be represented by a phasor constant magnitude .

## Double Revolving theory of Single-Phase Induction Motor

According to the double revolving theory the stationary pulsating magnetic field of a single phase induction motor can have two rotating magnetic fields of equal magnitude but in opposite directions. The net torque in the motor is equal to the sum of torque due to each magnetic field. Since, the induction motor gives a separate response to each magnetic field.

The alternating magnetic field with fixed axis in space is

Where:

is the maximum value of the sinusoidal distribut air-gap flux density. This production of this flux density is due to proper distribution of stator winding carrying an alternating current of frequency ⍵. Also, α being the space displacement angle from the axis of the stator winding.

The first term on the RHS represents the equation of a revolving field. This field is moving in the positive ɑ direction. It has a maximum value equal to

The first term on the RHS represents the equation of a revolving field. This field is moving in the negative ɑ direction. It has a maximum value equal to

The field moving in the positive  direction is the forward rotating field. The field moving in the negative direction is a backward rotating field.

The direction in which the single-phase motor initially started is positive.

The value of induced voltage will be equal when the rotor is stationary. Hence, the value of two torques will be equal and opposite. Therefore, the value of net torque is zero at standstill. A single phase induction motor with stator winding has no starting torque.