---
title: "Field form factor and choice of poles"
subject: "Electric Machine Design"
chapter: 5
key: "semester_5/electric_machine_design:field-form-factor-poles"
source: https://www.bctengineer.com/q/semester_5/electric_machine_design/field-form-factor-poles
site: BCT Engineering
---

# Field form factor and choice of poles

Electric Machine Design · Chapter 5: DC Machine Design

- Asked in: 2071 Shrawan, 1+7 marks
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/electric_machine_design/field-form-factor-poles
- Whole chapter: https://www.bctengineer.com/md/semester_5/electric_machine_design/chapter-5

## Question

What is field form factor of a dc machine? What are the factors to be considered while selecting the number of poles in a dc machine? Explain.

## Short answer

Field form factor ψ = Bav/Bg ≈ pole arc/pole pitch, typically 0.64–0.72. Number of poles depends on frequency (25–50 Hz), iron and copper weight, armature reaction, current per brush arm, commutator length, flashover limits, and labour cost.

## Answer

#### Field form factor
The **field form factor** $\psi$ (or $K_f$) is the ratio of average gap flux density over a pole pitch to the maximum gap flux density:
$$
\psi = \frac{B_{av}}{B_g} \approx \frac{\text{pole arc}}{\text{pole pitch}}
$$
Its usual value is 0.64–0.72.

#### Factors in selecting the number of poles
1. **Frequency**: $f = Pn/2$ should usually be 25–50 Hz. More poles raise frequency and iron loss in the armature.
2. **Weight of iron**: flux per pole falls as $P$ increases, so the yoke and armature core become thinner; iron weight falls.
3. **Weight of copper**: armature end connections are shorter with smaller pole pitch, so armature copper falls; field copper changes little.
4. **Armature reaction**: armature AT per pole $= ac\,\pi D/2P$ falls with more poles, reducing distortion and the extra field mmf needed.
5. **Current per brush arm**: for a lap winding the current per path ($I_a/P$) should not exceed about 200 A; large-current machines need more poles.
6. **Commutator length**: more poles give more brush arms with less current each, so a shorter commutator.
7. **Labour and cost**: more poles mean more field coils and parts, so more labour.
8. **Flashover**: voltage between brush arms and the voltage between segments must stay within safe limits.

So the number of poles is chosen as a compromise. Usual choices: 2 poles up to about 5 kW, 4 poles for about 5–100 kW, and 6 or more for larger machines.

## Check yourself

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

1. What is the field form factor?
   A. Ratio of maximum to average gap density
   B. Ratio of average gap density over a pole pitch to maximum gap density
   C. Ratio of pole pitch to pole arc
   D. Ratio of armature flux to field flux
   Answer: B. psi = Bav/Bg, approximately pole arc/pole pitch, typically 0.64-0.72. (Key point: Field form factor)

2. What frequency limit applies in choosing poles?
   A. f = Pn/2 within 25-50 Hz
   B. f = Pn within 5-10 Hz
   C. f = Pn/2 above 100 Hz
   D. No limit
   Answer: A. More poles raise iron loss. (Key point: Frequency)

3. How does increasing poles affect armature AT per pole?
   A. It rises
   B. It is unchanged
   C. It becomes zero
   D. It falls
   Answer: D. AT = ac pi D/2P. (Key point: Armature reaction)

## Close variants set in other exams

- [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×

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