---
title: "Unequal stator/rotor slots and output equation"
subject: "Electric Machine Design"
chapter: 4
key: "semester_5/electric_machine_design:slots-unequal-output-equation"
source: https://www.bctengineer.com/q/semester_5/electric_machine_design/slots-unequal-output-equation
site: BCT Engineering
---

# Unequal stator/rotor slots and output equation

Electric Machine Design · Chapter 4: Three phase induction motor design

- Asked in: 2070 Chaitra, 2+8 marks
- Video: [Output equation of three phase Induction Motor | Design of Electrical Machines by S. D.Yelgatte](https://www.youtube.com/watch?v=m8vAfFiVWzQ) — S D Yelgatte 📖 ⚡
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/electric_machine_design/slots-unequal-output-equation
- Whole chapter: https://www.bctengineer.com/md/semester_5/electric_machine_design/chapter-4

## Question

Why should the number of stator slots never be equal to number of rotor slots? Prove that the output of a three phase induction machine can be expressed in terms of its main dimension, specific loading and speed.

## Short answer

If stator and rotor slots are equal, all teeth face simultaneously, causing magnetic locking (cogging) that prevents starting and creates noise. The output equation is Q = 11 B_av ac K_w 10^-3 D^2 L n_s kVA, showing output depends on main dimensions D^2 L, specific loadings B_av and ac, and speed n_s.

## Answer

#### Why stator slots should never equal rotor slots
If $S_s = S_r$, all rotor teeth face stator teeth at the same time. At these positions the reluctance is minimum, and a strong alignment force holds the rotor there. This **cogging** (magnetic locking) can stop the motor from starting, and it also produces noise and vibration. So $S_r \ne S_s$ is always used.

#### Output equation in terms of main dimensions
Let $D$ = stator bore, $L$ = core length, $P$ = poles, $n_s$ = synchronous speed (rps).

1. kVA input: $Q = 3E_{ph}I_{ph}\times10^{-3}$
2. Emf: $E_{ph} = 4.44f\Phi T_{ph}K_w$, with $f = Pn_s/2$
3. Specific magnetic loading:
$$
B_{av} = \frac{P\Phi}{\pi DL} \Rightarrow \Phi = \frac{\pi DL B_{av}}{P}
$$
4. Specific electric loading (total conductors $6T_{ph}$):
$$
ac = \frac{6I_{ph}T_{ph}}{\pi D} \Rightarrow I_{ph}T_{ph} = \frac{\pi D\,ac}{6}
$$
5. Substitute into $Q$:
$$
\begin{aligned}
Q &= 3 \times 4.44 \times \frac{Pn_s}{2} \times \frac{\pi DLB_{av}}{P} \times K_w \times \frac{\pi D\,ac}{6} \times 10^{-3} \\
&= 1.11\pi^2 B_{av}\,ac\,K_w\times10^{-3}\, D^2Ln_s \\
&= 11B_{av}\,ac\,K_w\times10^{-3}\, D^2Ln_s
\end{aligned}
$$
Hence
$$
Q = C_0D^2Ln_s, \qquad C_0 = 11B_{av}\,ac\,K_w\times10^{-3}
$$

This shows the output (kVA) is proportional to:
- the **main dimensions** through $D^2L$ (active volume),
- the **specific loadings** $B_{av}$ and $ac$ through $C_0$,
- the **speed** $n_s$.

The kW rating is related by $Q = \text{kW}/(\eta\cos\phi)$. For example, with $B_{av} = 0.44$, $ac = 21000$, $K_w = 0.955$: $C_0 = 97.07$, so a 3.235 kVA, 4-pole motor needs $D^2L = 3.235/(97.07 \times 25) = 1.33 \times 10^{-3}$ m³.

## Check yourself

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

1. Why must stator and rotor slots never be equal?
   A. All teeth would align at once, giving minimum reluctance, cogging and possible failure to start
   B. The winding factor would become zero
   C. The rotor would overheat due to eddy currents
   D. The flux would be zero in the air gap
   Answer: A. Equal slots make a strong magnetic locking force and noise; unequal slots avoid simultaneous alignment. (Key point: Why slots unequal)

2. Which relation is used with f = P ns/2 for the induced emf per phase?
   A. Eph = 2.22 f Phi Tph
   B. Eph = 4.44 f Phi Tph Kw
   C. Eph = 4.44 f Phi Kw/Tph
   D. Eph = 11 f Phi Tph Kw
   Answer: B. The standard rms emf equation with winding factor is used in the derivation. (Key point: Emf expression)

3. How is flux per pole written from specific magnetic loading?
   A. Phi = Bav D L/P
   B. Phi = Bav pi D L x P
   C. Phi = Bav pi D L/P
   D. Phi = Bav pi D/L
   Answer: C. Bav = P Phi/(pi D L), as total flux P Phi crosses the gap area pi D L. (Key point: Flux per pole)

4. On what does the kVA output depend?
   A. Only on the diameter D
   B. Only on the specific loadings
   C. Only on the number of poles
   D. D^2L (volume), loadings Bav and ac through C0, and speed ns
   Answer: D. Q = C0 D^2 L ns where C0 contains both loadings. (Key point: Meaning of the output equation)

## Related in Electric Machine Design

- [Output equation of three phase induction motor](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Ainduction-motor-output-equation) — Electric Machine Design, chapter 4, asked 6×
- [Choice of specific electric loading in induction machine](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Ainduction-specific-electric-loading) — Electric Machine Design, chapter 4, asked 3×
- [Selection of number of stator slots](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Astator-slot-number-selection) — Electric Machine Design, chapter 4, asked 4×
- [Rotor slots and turns, 90 kW motor](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Arotor-design-90kw-slip-ring) — Electric Machine Design, chapter 4
- [Output equation of three phase transformer](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Aoutput-equation-three-phase-transformer) — Electric Machine Design, chapter 3, asked 2×
- [Three phase output equation and circular windings](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Aoutput-equation-circular-windings) — Electric Machine Design, chapter 3

## Related in other subjects

- [Synchronous speed and why rotor lags stator field](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Asynchronous-speed-rotor-direction-slip) — Electrical Machines I, chapter 5
- [3-phase induction machine at slip 0.05](https://www.bctengineer.com/question.md?key=semester_1%2Fbasic_electrical_and_electronics_engineering%3Ainduction-machine-3phase-numerical) — Basic Electrical and Electronics Engineering, chapter 2
- [Synchronous speed; rotor follows rotating field](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Asynchronous-speed-rotor-direction) — Electrical Machines, chapter 5
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