# Frequency of stator current in induction motors

I am learning about induction motors.

I have a question about the stator current, especially the rotor induced current.

If the rotor rotates at 1-s of sync frequency, then the emf and current induced in the rotor with respect to rotating magnetic field would be less than sync frequency.

I understand that the same rotor current is induced at stator.

Does that mean stator would have current of sync frequency and another frequency of s times sync frequency?

Another query on rotor emf.

If the rotor is perfectly conducting with copper rods, I understand that the resistance would be low.

Since induced emf is proportional to rate of change of stator flux, then I believe that same stator voltage (which causes the rate of change of flux in first place) is induced in the rotor rods (ignoring small resistive drop at stator.)

If, for example, the motor is supplied with 400 volts line to line voltage, does it mean than same 400 volts will appear on the rotor? What does it say about the rotor currents?

Would it be ginormous given small resistances?

Does that mean stator would have current of sync frequency and another frequency of s times sync frequency?

No. The rotor frequency is s x stator frequency. That results in a magnetic field in the rotor that rotates at the slip frequency. However that speed of rotation is the speed with respect to the rotor. The speed of the rotor magnetic field with respect to the stator is the speed of the rotor plus the speed of the rotor magnetic field or [(1 - s) + s] x stator frequency. So the rotor magnetic field rotates synchronously with the stator magnetic field. The net effect is that the motor behaves like a rotating transformer that operates at the power frequency.

When the equivalent circuit is determined, the actual rotor resistance and reactance are referred to the rotor and the circuit is drawn as a transformer with a 1:1 turns ratio.

What does it say about the rotor currents? Would it be ginormous given small resistances?

Yes, the rotor currents are large and the rotor voltage is small. However, the mechanical load, in effect, adds resistance to the rotor circuit once the load begins to turn and the slip falls from 1 to the normal operating slip.

1. The rotor frequency is f_rotor = s*f_stator. You can see, that when rotor is in sync it has 0 Hz, no current is induced therefore no torque is produced.

2. The equivalent circuit of induction motor is similar to the equivalent circuit of the transformer. There is a transformation ratio in between stator and rotor, like the ratio of number of turns of primary and secondary windings in the transformer. A hint: the squirrel cage can be seen as single turn.