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Book says rotor mostly runs at speed near to synchronous due to which the relative velocity between rotor and stator magnetic field is very less. Correspondingly making rotor core losses tiny and stator big. I also know that voltage induced in rotor depends on the relative velocity. I dont get it what does relative velocity have to do with core losses and how does it make stator core loss big and rotor tiny?

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The rotor is rotating at near the frequency of the rotating field produced by the stator, so it only actually sees an alternating field at a frequency proportional to the slip (In the absence of harmonic distortion), maybe a few percent of line frequency.

The stator has a field at the line frequency and that is very much higher then the slip angular frequency, since the losses are proportional to frequency (to a first order) you would expect the rotor losses to be much smaller then the stator losses all else being equal.

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