---
title: "Minimum number of commutator segments"
subject: "Electric Machine Design"
chapter: 5
key: "semester_5/electric_machine_design:dc-minimum-commutator-segments"
source: https://www.bctengineer.com/q/semester_5/electric_machine_design/dc-minimum-commutator-segments
site: BCT Engineering
---

# Minimum number of commutator segments

Electric Machine Design · Chapter 5: DC Machine Design

- Asked in: 2074 Chaitra, 8 marks; 2070 Chaitra, 8 marks (asked 2 times)
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/electric_machine_design/dc-minimum-commutator-segments
- Whole chapter: https://www.bctengineer.com/md/semester_5/electric_machine_design/chapter-5

## Question

For a dc machine, derive the expression for calculating the minimum number of commutator segments (show that the minimum number of coils or commutator segments required is EP/15). Note the number of commutator segments = number of coils in armature.

## Short answer

The minimum number of commutator segments C_min = EP/15 is obtained by limiting the maximum voltage between adjacent segments to 30 V. With average voltage per coil E_avg = EP/C and peak about twice the average, the condition 2EP/C ≤ 30 yields C ≥ EP/15.

## Answer

The number of commutator segments $C$ (= number of armature coils) is limited by the **voltage between adjacent segments**. If this voltage is too high, arcing between segments can lead to flashover.

#### Derivation
Let $E$ = terminal (induced) voltage, $P$ = poles. For a lap winding there are $a = P$ parallel paths, so the number of coils in series per path is:
$$
\text{Coils per path} = \frac{C}{P}
$$
Average voltage per coil, which is the average voltage between adjacent segments:
$$
E_{c(av)} = \frac{E}{C/P} = \frac{EP}{C}
$$
The flux density under the pole is not uniform: armature reaction distorts it, and the peak density is about twice the average. So the **maximum** voltage between adjacent segments is about:
$$
E_{c(max)} \approx 2E_{c(av)} = \frac{2EP}{C}
$$
For safe operation, the maximum voltage between segments is limited to about **30 V**:
$$
\frac{2EP}{C} \le 30
$$
Hence
$$
C_{min} = \frac{2EP}{30} = \frac{EP}{15}
$$

Since each coil ends on two segments and each segment joins two coil ends, the number of commutator segments equals the number of coils.

#### Example
A 220 V, 4-pole machine:
$$
C_{min} = \frac{220 \times 4}{15} = 58.7 \approx 59\ \text{segments}
$$
A practical value is chosen above this, also matching the number of slots (coils per slot $\times$ slots).

#### Other limits on $C$
- Segment pitch (about 4 mm minimum) for mechanical strength.
- Commutator peripheral speed (not more than about 30 m/s).
- Reactance voltage: fewer turns per coil (more coils) gives better commutation.

## Check yourself

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

1. For a lap winding with C coils, what is the average voltage between adjacent segments?
   A. E/(PC)
   B. EC/P
   C. E/C
   D. EP/C
   Answer: D. Coils per path are C/P, so each coil carries E/(C/P) = EP/C. (Key point: Average segment voltage)

2. Why is the maximum voltage taken as twice the average?
   A. Two brushes are in series
   B. Because of commutation
   C. Armature reaction distorts flux so peak density is about twice average
   D. Because lap winding has two paths
   Answer: C. Emax = 2EP/C. (Key point: Maximum voltage)

3. What limit on the maximum voltage between segments is used?
   A. About 3 V
   B. About 300 V
   C. About 15 V
   D. About 30 V
   Answer: D. 2EP/C <= 30 gives Cmin = EP/15. (Key point: Voltage limit)

4. What is Cmin for a 220 V, 4-pole machine?
   A. About 59 segments
   B. About 29 segments
   C. About 117 segments
   D. About 15 segments
   Answer: A. 220 x 4/15 = 58.7 which is about 59. (Key point: Example)

## Related in Electric Machine Design

- [Choice of number of poles in DC machine](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Adc-number-of-poles) — Electric Machine Design, chapter 5, asked 8×
- [Choice of number of armature slots](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Adc-armature-slots-selection) — Electric Machine Design, chapter 5
- [Output equation of DC machine](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Adc-output-equation) — Electric Machine Design, chapter 5, asked 3×
- [Choice of ampere conductors per meter in DC machine](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Adc-ampere-conductors-selection) — Electric Machine Design, chapter 5, asked 4×
- [Choice of specific loadings in DC machine](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Adc-specific-loadings-selection) — Electric Machine Design, chapter 5, asked 2×
- [Disadvantages of high specific loadings in DC machine](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Adc-high-specific-loading-disadvantages) — Electric Machine Design, chapter 5, asked 2×

## Related in other subjects

- [Commutator function and DC generator emf equation](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Acommutator-function-emf-equation) — Electrical Machines I, chapter 3
- [Short note: Armature reaction in DC machine](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Aarmature-reaction-dc-machine-note) — Electrical Machine, chapter 3
- [Short note: Armature reaction in dc machine](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Anote-armature-reaction-dc) — Electrical Machines, chapter 3
- [Function of commutator in DC generator](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Acommutator-function-dc-generator) — Electrical Machines I, chapter 3