####
The curve obtained by plotting torque against slip is called torque-slip characteristics of the induction motor.

The expression for the torque is,

####
We can evaluate value of torque at different values of slip in the range from 0 to 1.

(i) When slip s = 0, N = Ns and hence torque, T = 0. Motor can not run at synchronous speed.

(ii) When slip ' s ' is very low i.e., the speed is very near to synchronous speed, then the term ( sX_{2}
)^{2} is very small and can be neglected in comparison with R_{2}^{2}.

(i) When slip s = 0, N = Ns and hence torque, T = 0. Motor can not run at synchronous speed.

(ii) When slip ' s ' is very low i.e., the speed is very near to synchronous speed, then the term ( sX

_{2})^{2}is very small and can be neglected in comparison with R_{2}^{2}.#### Therefore,

####
T α s
/ R_{s}

####
T α s if R_{2} is constant

####
Hence for low values of slip, the torque-slip curve is a straight line.

(iii) When slip increases i.e., the speed decreases ( with increase load ), the torque increases and becomes maximum when

s = s_{m} = R_{2}
/ X_{2}

####
i.e., T = T_{m } when s = s_{m}

The maximum torque is called as pull-out or breakdown torque

(iv) When slip is further increases beyond s = s_{m}, then the term R_{2}^{2} is very small as compared to ( sX_{2} )^{2} and may be neglected.

(iii) When slip increases i.e., the speed decreases ( with increase load ), the torque increases and becomes maximum when

s = s

_{m}= R_{2}/ X_{2}####
i.e., T = T_{m } when s = s_{m}

(iv) When slip is further increases beyond s = s

_{m}, then the term R_{2}^{2}is very small as compared to ( sX_{2})^{2}and may be neglected.####
T α sR_{2}
/ (sX_{2})^{2}

####
T α 1
/ s if R_{2} & X_{2} are constants

#### Hence the torque values of slip, the torque-slip curve is a rectangular hyperbola.

####

(v) If slip s = 1, then motor is stationary hence corresponding torque is nothing but starting torque.

i.e., T = T_{st} when s = 1

Figure below shows the Torque-slip Characteristics.

(v) If slip s = 1, then motor is stationary hence corresponding torque is nothing but starting torque.

_{st}when s = 1

####
The region from s = 0 to s = s_{m} is called as operating region for the induction motor because if load is increased beyond s = s_{m}, them torque decreases and motor will stop. The Torque-speed Characteristic is shown below.

## Effect of Rotor Resistance on Torque-slip Curve :

####

In slip ring induction motor it is possible to add external resistance in series with the rotor through slip rings. This is used to control starting torque developed by the motor.

In slip ring induction motor it is possible to add external resistance in series with the rotor through slip rings. This is used to control starting torque developed by the motor.

####
Let R_{2} = rotor resistance / phase, then torque

####
The stand still rotor reactance phase, X_{2} will remain constant, since it is fixed by the design of the rotor.

_{2}will remain constant, since it is fixed by the design of the rotor.

### Let us Consider

#### (i) When no external resistance is inserted in the rotor circuit. Maximum torque is developed at

####
s_{m} = R_{2}
/ X_{2}

_{m}= R

_{2}/ X

_{2}

####

(ii) Now if rotor resistance is increased ( inserting external resistance in the rotor circuit) from

R_{2} to R'_{2}.

####
The magnitude of the maximum torque, T_{max} remains unchanged but the slip for maximum torque is

s'_{m} = R'_{2} /
X_{2}

(iii) As rotor resistance is increased from R'_{2} to R''_{2}, and so on, as shown in figure that T_{max} remains same but starting torque increases.

_{max}remains unchanged but the slip for maximum torque is

_{m}= R'

_{2}/ X

_{2}

_{2}to R''

_{2}, and so on, as shown in figure that T

_{max}remains same but starting torque increases.

####
(iv) At s_{m} = 1 i.e., when R_{2} = X_{2}, motor will develop maximum torque at the instant of starting. This is represented by point ' A ' in the figure.

_{m}= 1 i.e., when R

_{2}= X

_{2}, motor will develop maximum torque at the instant of starting. This is represented by point ' A ' in the figure.

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