Torque slip characteristics ,effect of change of supply voltage on torque and speed.

As we know the torque equation of induction motor is

T = K1 * φ * sE2 * R2/( R2² + (sX2)²)

So , if s=0 then T=0

Let start the curve from point 0.

Let's say, motor is running near to synchronous speed. The term  sX2 = 0 negligible

Therefore T =  K1 * φ * sE2 /R2

T > s [ other is let say constant]

So for low value of slip, torque slip curve is straight line.

as a load increases sleep increases. As the load further increases it the touches Tmax point when s= R2/ X2 called pull out torque.

Any further increases in load i.e slip increases R2 becomes negligible

 Therefore T > (1/s)

Hence after pull out aur breakdown torque the curve will be rectangular hyperbola. Hance we can see that any further increases in load motor slow down and eventually stop. If we provide some electrical protection for overload it will trip circuit. From figure it is also clear that by increasing the value of rotor resistance we can get maximum torque at the s = 1 or zero speed

Effect of change in supply voltage is on torque and speed.

T = K1 * φ * sE2 * R2/( R2² + (sX2)²)

Since ,φ >   E2

And     E2   > V

Therefore    T > V²

if there is any change in supply voltage then it is not only changes the starting torque but also running torque. So if there is any decrease in voltage to maintain same torque increases slip.