Torque Equation of Three Phase Induction Motor

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Firstly the magnitude of rotor current, secondly the fluxwhich interact with the rotor of three phase induction motor and is responsible for producing emf in the rotor part of the induction motor lastly the power factor of rotor of the three phase induction motor.

Combining all these factors, we get the equation of torque as-


Where, T is the torque produced by the induction motor,

φ is flux responsible for producing induced emf,

I2 is rotor current,

cosθ2 is the power factor of rotor circuit.

The flux φ produced by the stator is proportional to stator emf E1.

i.e φ ∝ E1

We know that transformation ratio K is defined  as the ratio of secondary voltage (rotor voltage) to that of primary voltage (stator voltage).


Rotor current I2 is defined as the ratio of rotor-induced emf under running condition , sE2 to total impedance, Z2 of rotor side,

and total impedance Z2 on the rotor side is given by ,

Putting this value in above equation we get,

s = slip of induction motor

We know that power factoris defined as ratio of resistance to that of impedance. The power factor of the rotor circuit is

Putting the value of flux φ, rotor current I2, power factor cosθ2 in the equation of torque we get,

Combining similar term we get,

Removing proportionality constant we get,

Where, ns is synchronous speed in r. p. s, ns = Ns / 60. So, finally the equation of torque becomes,


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