The document discusses the relationship between torque and slip in a three-phase induction motor. It explains that torque is proportional to slip at low slip values, so the torque-slip curve is a straight line in this stable region. At higher slip values, torque is inversely proportional to slip, so the curve is a rectangular hyperbola in the unstable region. The maximum torque occurs at the slip value where the motor transitions between these two regions.

1. RELATION BETWEEN TORQUE
AND SLIP OF THREE PHASE
INDUCTION MOTOR Name: Subhadip Ghosh
University Roll Number: 11701620012
Year & Semester: 3rd year (5th Sem)
Paper Name: ELECTRIC MACHINE II
Paper Code: PE-EE 501
CO Number : CO1,CO2
Module Number: 1
Bloom's Level of Taxonomy : Understanding
RCC Institute of Information Technology
Subject: B.Tech in Electrical Engineering
Continuous Assessment -1(CA1)
Academic Session: 2022-23 (Odd Sem)

2. TORQUE-SLIP
CHARACTERISTICS
• The torque slip curve for an induction motor gives us the information about the
variation of torque with the slip. The slip is defined as the ratio of difference of
synchronous speed and actual rotor speed to the synchronous speed of the
machine. The variation of slip can be obtained with the variation of speed that is
when speed varies the slip will also vary and the torque corresponding to that
speed will also vary.
• The curve drawn between torque and slip from start (s=1) to Synchronous speed
(s=0) is called the Torque-Slip characteristics of the induction motor.
• Torque Equation :-
Torque,𝑇 ∝
𝑠𝐸2
2𝑅2
𝑅2
2+(𝑠𝑋2)2

3. TORQUE-SLIP
CHARACTERISTICS
• To draw the torque slip
characteristics of induction
motor (three phase) following points
are considered :
1. At synchronous speed (𝑁𝑠); slip, s
= 0 and torque, T = 0.
2. When rotor speed is very near to
synchronous speed i.e. when the
slip is very low the value of the
term (𝑠𝑋2)2
is very small in
comparison to 𝑅2
2
and is
neglected.

4. TORQUE SLIP
CHARACTERISTICS
• Stable Region :-
1. In the stable region, the value of slip is small. Hence this region is
also called as the low slip region. As the slip increases torque increases
and attains its maximum value when s = R2/X2. This maximum value of
torque is also known as break down or pull out torque.
2.‘s’ is very small (then (𝑠𝑋2)2 << 𝑅2
2
), Hence, 𝑠2𝑋2
2
is neglected.
𝑇 ∝
𝑠𝑅2
𝑅2
2 ∝ s [ as 𝑅2 =constant ]
3. In this region as Load , T , s
4. Characteristics is approximately straight line

5. TORQUE SLIP
CHARACTERISTICS
• Unstable Region :-
1.The region (extending from s = sm 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.
2. When s increases further from 𝑠𝑚 the region is unstable region , s is high (between
𝑠𝑚 and 1), 𝑅2
2
can be neglected as compare to 𝑠2𝑋2
2
𝑇 ∝
𝑠
(𝑠𝑋2)2 ∝
1
𝑠
[ as 𝑋2 = constant]
3.In this region as load , s , T
4. Characteristics is approximately rectangular hyperbola.
5. When the load further increases , N , s , leads motor to standstill condition, hence the
motor should not be operated at any point in this region.

6. TORQUE SLIP
CHARACTERISTICS
Low Slip Region:-
1. At synchronous speed, the slip s = 0, thus, the torque is 0. When the speed is
very near to the synchronous speed, the slip is very low and the term (𝑠𝑋2)2 is
negligible in comparison with R2. Therefore,
Tr ∝ S/R2...........(1)
If R2 is constant, then
Tr ∝ S..............(2)
Eqn. (2) shows that the torque is proportional to the slip. Hence, when the slip is
small, the torque-slip curve is straight line.
2. Low slip region, the motor continuously operated in this region.

7. CONCLUSION
1. When s is high, 𝑇∝
1
𝑠
(At starting), torque-slip characteristics
will be rectangular hyperbola.
2. When s is low, 𝑇∝ s , torque-slip curve is straight line.