To draw the **torque slip characteristics of induction motor** 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

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 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.

#### 1. In a squirrel cage induction motor, torque with autostarter is ....... times the torque with direct-switching. Where K is the transformation ratio of the autotransformer.

#### 2. If stator voltage of a squirrel cage induction motor is reduced to 50 per cent of its rated value, torque developed is reduced by ....... per cent of its full-load value.

#### 3. For the purpose of starting an induction motor, a Y-Δ switch is equivalent to an auto-starter of ratio.......per cent.

#### 4. A double squirrel-cage motor (DSCM) scores over SCIM in the matter of

#### 5. In a DSCM, outer cage is made of high resistance metal bars primarily for the purpose of increasing its

#### 6. A SCIM with 36-slot stator has two separate windings : one with 3 coil groups/ phase/pole and the other with 2 coil groups/phase/pole. The obtainable two motor speeds would be in the ratio of

#### 7. A 6-pole 3-φ induction motor taking 25 kW from a 50-Hz supply is cumulatively-cascaded to a 4-pole motor. Neglecting all losses, speed of the 4-pole motor would be ....... r.p.m.

#### 8. Two separate induction motors, having 6 poles and 5 poles respectively and their cascade combination from 60 Hz, 3-phase supply can give the following synchronous speeds in rpm

#### 9. When a stationary 3-phase induction motor is switched on with one phase disconnected

#### 10. If single-phasing of a 3-phase induction motor occurs under running conditions, it

#### 11. One of the characteristics of a single- phase motor is that it

#### 12. After the starting winding of a single- phase induction motor is disconnected from supply, it continues to run only on ............winding.

#### 13. The direction of rotation of a single-phase motor can be reversed by

#### 14. If a single-phase induction motor runs slower than normal, the more likely defect is

#### 15. The capacitor in a capacitor-start induction- run ac motor is connected in series with ...... winding.

#### 16. The starting torque of a capacitor-start induction-run motor is directly related to the angle α between its two winding currents by the relation

#### 17. In a two-value capacitor motor, the capacitor used for running purposes is a/an

#### 18. If the centrifugal switch of a two-value capacitor motor using two capacitors fails to open, then

#### 19. Each of the following statements regarding a shaded-pole motor is true except

#### 20. Compensating winding is employed in an ac series motor in order to

#### 21. A universal motor is one which

#### 22. In a single-phase series motor the main purpose of inductively-wound compensating winding is to reduce the

#### 23. A repulsion motor is equipped with

#### 24. A repulsion-start induction-run single- phase motor runs as an induction motor only when

#### 25. If a dc series motor is operated on ac supply, it will

#### 26. An outstanding feature of a universal motor is its

#### 27. The direction of rotation of a hysteresis motor is determined by the

#### 28. Speed of the universal motor is

#### 29. In the shaded pole squirrel cage induction motor the flux in the shaded part always

#### 30 . Which of the following motor is an interesting example of beneficially utilizing a phenomenon that is often considered undesirable ?

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- Starting Methods of Induction Motor
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- What is a variable frequency drive?
- Autotransformer Starter Working Principle
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- Induction Motor Equivalent Circuit
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