Derivation the value of K in induction motor torque equation

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 Derivation the value of K in induction motor  torque equation 


In case of 3-phase induction motor, there occur copper losses in rotor. These rotor copper losses are expressed as

Pc = 3I22R2
We know that rotor current,

Substitute this value of I2 in the equation of rotor copper losses, Pc. So, we get

The ratio of P2 : Pc : Pm = 1 : s : (1 – s)
Where, P2 is the rotor input,
Pc is the rotor copper losses,
Pm is the mechanical power developed.

Substitute the value of Pc in above equation we get,

On simplifying we get,

The mechanical power developed Pm = Tω,

Substituting the value of Pm

We know that the rotor speed N = Ns(1 – s)
Substituting this value of rotor speed in above equation we get,

Ns is speed in revolution per minute (rpm) and ns is speed in revolution per sec (rps) and the relation between the two is

Substitute this value of Ns in above equation and simplifying it we get

Comparing both the equations, we get, constant

                                                     K = 3 / 2πns


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