---
title: "No torque at synchronous speed"
subject: "Electrical Machines"
chapter: 5
key: "semester_4/electrical_machines:im-no-torque-at-synchronous-speed"
source: https://www.bctengineer.com/q/semester_4/electrical_machines/im-no-torque-at-synchronous-speed
site: BCT Engineering
---

# No torque at synchronous speed

Electrical Machines · Chapter 5: Three Phase Induction Machines

- Asked in: 2067 Mangsir (old course), 4 marks
- Video: [Slip Speed and Slip in a Motor](https://www.youtube.com/watch?v=xxvFTC-ybbk) — Zack Hartle
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machines/im-no-torque-at-synchronous-speed
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-5

## Question

Justify the statement: Induction motor cannot develop torque when rotor runs at synchronous speed.

## Short answer

At synchronous speed, slip s=0, so rotor EMF and current are zero, giving zero torque. Without torque, friction and load slow the rotor, creating slip to induce current and restore torque; thus the motor cannot remain at synchronous speed.

## Answer

The statement is true because an induction motor works by **induction**, and induction needs relative motion between the rotating magnetic field and the rotor conductors.

1. At synchronous speed $N_s = \frac{120f}{P}$, the rotor and the field rotate together. The slip is zero:
$$
s = \frac{N_s - N_r}{N_s} = 0
$$
2. The rotor conductors do not cut any flux, so the rotor emf is $E_{2s} = sE_2 = 0$.
3. With no emf, the rotor current is $I_2 = 0$, so there is no rotor mmf and no force on rotor conductors.
4. Torque is $T = \frac{3}{\omega_s}\cdot\frac{sE_2^2R_2}{R_2^2+(sX_2)^2}$, which is zero at $s = 0$.
5. Without torque, friction and windage slow the rotor. Slip then appears, an emf is induced, and torque is produced again.

So the motor can only run at a speed slightly below synchronous speed, where the rotor current produces just enough torque to supply the load and the mechanical losses. At no load, the slip is very small (about 0.5 %) but not zero.

This also shows on the T-S curve, where the torque curve passes through zero at $s = 0$.

## Check yourself

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

1. Induction needs:
   A. Relative motion between field and rotor conductors
   B. DC excitation
   C. Zero slip
   D. A permanent magnet rotor
   Answer: A. Without relative motion no emf is induced. (Key point: Need for relative motion)

2. At synchronous speed the slip and rotor emf are:
   A. 1 and E_2
   B. 0 and 0
   C. 0 and E_2
   D. 1 and 0
   Answer: B. s = 0 so sE_2 = 0. (Key point: Slip at N_s)

3. If the rotor reached N_s, it would:
   A. Keep speed
   B. Speed up
   C. Slow down due to friction, then slip appears and torque returns
   D. Reverse
   Answer: C. Slip reappears and torque is regenerated. (Key point: What follows)

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