---
title: "Define slip; linear portion of T-S curve"
subject: "Electrical Machines"
chapter: 5
key: "semester_4/electrical_machines:slip-define-linear-portion"
source: https://www.bctengineer.com/q/semester_4/electrical_machines/slip-define-linear-portion
site: BCT Engineering
---

# Define slip; linear portion of T-S curve

Electrical Machines · Chapter 5: Three Phase Induction Machines

- Asked in: 2078 Chaitra, 4 marks
- Video: [Torque slip characteristics of three phase induction motor | Easy explanation- hindi | With notes](https://www.youtube.com/watch?v=EKuDko6d3iA) — Electrical Yaar 
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machines/slip-define-linear-portion
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-5

## Question

Define slip. Why does the induction motor operate only in the linear portion of torque-slip characteristics?

## Short answer

Slip is s = (Ns - Nr)/Ns, equal to 1 at standstill and 0 at synchronous speed; rated slip is 2-5%. The motor operates in the linear region because T is proportional to s when sX2 is negligible, giving stable speed, high efficiency and low rotor copper loss; beyond maximum torque operation is unstable.

## Answer

#### Slip
Slip is the fractional difference between synchronous speed and rotor speed, expressed as a fraction or percentage of synchronous speed:
$$
s = \frac{N_s - N_r}{N_s}
$$
Here $N_s = \frac{120f}{P}$ is the speed of the rotating magnetic field and $N_r$ is the rotor speed. At standstill $s = 1$; at synchronous speed $s = 0$. At rated load it is about 2 to 5 %. The rotor frequency is $f_r = sf$.

#### Why only the linear portion is used
The torque-slip curve is nearly a straight line for small slip (from $s=0$ to the slip at about full load) because $sX_2 \ll R_2$, so
$$
T \approx \frac{3E_2^2}{\omega_s R_2}\,s \;\propto\; s
$$
- This region lies on the **stable** side of the maximum torque ($s < s_m$). An increase in load slows the rotor a little, slip and torque increase, and the motor settles at a new steady speed.
- Beyond the maximum torque ($s > s_m$) the torque falls as slip increases, so any extra load makes the motor stall.
- In the linear region the rotor copper loss ($sP_g$) is small, so efficiency is high, and the speed is nearly constant.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Slip is defined as:
   A. (N_s - N_r)/N_s
   B. (N_r - N_s)/N_r
   C. N_r/N_s
   D. (N_s + N_r)/N_s
   Answer: A. s = (N_s - N_r)/N_s. (Key point: Slip definition)

2. Typical full-load slip of an induction motor is:
   A. 50 %
   B. 2 to 5 %
   C. 20 to 30 %
   D. 100 %
   Answer: B. Rated load slip is about 2 to 5 %. (Key point: Typical slip)

3. Why does the motor run in the linear part?
   A. It is stable (s < s_m), efficient and nearly constant speed
   B. It gives maximum torque
   C. It has the highest slip
   D. It has zero current
   Answer: A. Low slip gives stability, low copper loss and nearly constant speed. (Key point: Why linear portion)

## Related in Electrical Machines

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- [Induction motor torque equation and torque-slip characteristic](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aim-torque-equation-ts-characteristic) — Electrical Machines I, chapter 5
- [Torque-slip characteristic and linear operating region](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Aim-torque-slip-linear-region) — Electrical Machines I, chapter 5
- [Draw and explain torque-slip characteristics](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Ats-characteristics-regions) — Electrical Machines, chapter 5
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## Related in other subjects

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- [Torque-slip curve and max torque condition](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Atorque-slip-max-torque-condition) — Electrical Machine, chapter 5, asked 4×
- [Torque-slip curve and rotor resistance](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Atorque-slip-rotor-resistance-effect) — Electrical Machine, chapter 5, asked 3×
- [Max torque condition and torque-slip curve](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_and_electronics_engineering%3Amax-torque-induction-motor) — Basic Electrical and Electronics Engineering, chapter 2