Torque output problem on three phase induction motor

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If the torque output per phase is proportional to the power input per phase ignoring losses it can be shown that:

Torque is proportional to: sR2/R2^2+(sX2)^2

Then show by differentiating with respect to the slip, s, that maximum torque occurs when: R2=sX2

Please show full workings.

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Solution Summary

This solution discusses torque output.

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