To draw the **torque slip characteristics of induction motor** (three phase) following points are considered:

- At synchronous speed (N
_{s}); slip, s = 0 and torque, T = 0. - When rotor speed is very near to synchronous speed i.e. when the slip is very low the value of the term (sX
_{2})^{2}is very small in comparison to R_{2}^{2}and is neglected. Therefore, torque is given by the expression: - As the slip increases torque increases and attains its maximum value when s = R
_{2}/X_{2}. This maximum value of torque is also known as break down or pull out torque. - When a further increase in slip occurs due to increase in load beyond the point maximum torque

i.e. when slip is high, the value of term (sX_{2})^{2}is very large in comparison to R_{2}^{2}.

Therefore, R_{2}^{2}is neglected as compare to (sX_{2})^{2}and torque is given by the expression:

T = ksE_{2}^{2}R_{2} / R_{2}^{2}

In the above expression, all quantities are constant except slip s.

Therefore, T α s

# Torque Slip Characteristics of Induction Motor

Thus, **at low values of slip, torque is approximately proportional to slip s and the torque slip characteristics of induction motor is a straight line as shown in the figure.
The region (from s = 0 to s = s_{m}) is called the stable region of operation and operating point of the motor should be in this region.**

In the stable region, the value of slip is small. Hence this region is also called as the low slip region.

T = ksE_{2}^{2}R_{2} / (sX_{2})^{2}

or T = kE_{2}^{2}R_{2} / (sX_{2}^{2})

In the above expression, all quantities are constant except s.

Therefore, T α 1/s

**Thus at higher values of slip (i.e. the slip beyond that corresponding to maximum torque) torque is approximately inversely proportional to slip, s and the torque slip characteristics of induction motor is rectangular hyperbola as shown in the figure.**

**The region (extending from s = s _{m} to s = 1) is called unstable region. In this region with the increase in load, slip increases but torque decreases.
The result is that the motor could not pick up the load and slows down and eventually stops.** In the unstable region, the value of slip is large so this region is also called as the high-slip region.

## Effect of Rotor Resistance on Torque Slip Characteristics

To see the effect of rotor resistance on *torque slip characteristics of induction motor*, consider a slip ring induction motor in which additional resistance in the rotor circuit can be introduced through slip rings. The rotor reactance at stand still X_{2} remains constant.

**The maximum value of the torque developed by an induction motor is independent of rotor resistance R _{2}.
Therefore, the effect of change in rotor resistance is the change in slip at which this maximum torque takes place**; greater the rotor resistance, greater the value of slip at which the maximum torque occurs since

s = R

_{2}/X

_{2}

The torque

*slip characteristics of induction motor*(three phase) are shown in the figure for various values or rotor resistance R

_{2}keeping rotor reactance X

_{2}constant. The maximum value of the torque can be obtained even at the start by adding that much resistance in the rotor circuit so that R

_{2}becomes equal to X

_{2}.

When R

_{2}= X

_{2}; s = R

_{2}/X

_{2}= 1 i.e. at start torque will be maximum.

Thanks for reading about torque slip characteristics of induction motor.

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