**Torque of a three phase induction motor**is proportional to flux per stator pole, rotor current and the power factor of the rotor.

T

**∝**ɸ I

_{2}cosɸ

_{2}OR T

**= k**ɸ I

_{2}cosɸ

_{2}.

where, ɸ = flux per stator pole,

I

_{2}= rotor current at standstill,

ɸ

_{2 }= angle between rotor emf and rotor current,

k = a constant.

Now, let E

_{2}= rotor emf at standstill

we know, rotor emf is directly proportional to flux per stator pole, i.e. E

_{2}

**∝**ɸ.

therefore, T

**∝**E

_{2}I

_{2}cosɸ

_{2 }OR T =k

_{1}E

_{2}I

_{2}cosɸ

_{2}.

### Starting torque

The torque developed at the instant of starting of a motor is called as starting torque. Starting torque may be greater than running torque in some cases, or it may be lesser.

We know, T =k

_{1}E_{2}I_{2}cosɸ_{2}.
let, R2 = rotor resistance per phase

X2 = standstill rotor reactance

then,

Therefore, starting torque can be given as,

The constant k1 = 3 / 2πNs

#### Condition for maximum starting torque

If supply voltage V is kept constant, then flux ɸ and E

_{2}both remains constant. Hence,
Hence, it can be proved that

**maximum starting torque**is obtained when rotor resistance is equal to standstill rotor reactance. i.e. R_{2}^{2}+ X_{2}^{2}=2R_{2}^{2 }.#### Torque under running condition

T

**∝**ɸ I_{r}cosɸ_{2 }.
where, E

_{r}= rotor emf per phase under running condition = sE_{2}. (s=slip)
I

_{r}= rotor current per phase under running condition
reactance per phase under running condition will be = sX

_{2}
therefore,

as, ɸ

**∝ E**_{2}.####
**Maximum torque under running condition**

Torque under running condition is maximum at the value of slip (s) which makes rotor reactance per phase equal to rotor resistance per phase.

This answer are write and easy to understand.

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