The shape of the torque/slip curve of an induction motor is a rectangular-hyperbola. This curve represents the relationship between the torque produced by the motor and its slip. The slip of an induction motor is defined as the difference between the synchronous speed and the actual speed of the rotor divided by the synchronous speed.

The torque/slip curve is obtained by plotting the torque developed by the motor against the slip. It provides valuable information about the motor's performance characteristics and helps in understanding its behavior under different operating conditions.

1. Rectangular-Hyperbola Shape:
The torque/slip curve of an induction motor is characterized by a rectangular-hyperbola shape. It consists of two distinct regions: the "pull-up" region and the "pull-out" region.

2. Pull-Up Region:
In the pull-up region, the torque/slip curve is almost linear and almost parallel to the slip axis. This region represents the starting and low-speed operation of the motor. As the slip increases, the torque also increases linearly until it reaches a maximum value known as the breakdown torque.

3. Pull-Out Region:
In the pull-out region, the torque/slip curve starts to deviate from the linear behavior and curves downward. This region represents the high-speed operation of the motor. As the slip continues to increase beyond the breakdown torque, the torque decreases and eventually approaches zero at the synchronous speed.

4. Maximum Torque:
The maximum torque that can be developed by the motor is obtained at the breakdown torque point. This point is located at the intersection of the pull-up and pull-out regions of the torque/slip curve.

5. Base Speed:
The base speed of the motor is the speed at which the motor develops its rated torque. It is located at the intersection of the torque/slip curve and the rated torque line.

6. Importance of Torque/Slip Curve:
The torque/slip curve is essential for determining the motor's starting capability, maximum torque, and operating range. It helps in selecting the right motor for a specific application and optimizing its performance.

In conclusion, the torque/slip curve of an induction motor exhibits a rectangular-hyperbola shape. It provides valuable information about the motor's performance characteristics and helps in understanding its behavior under different operating conditions.