---
title: "DC generator working and emf equation"
subject: "Electrical Machine"
chapter: 3
key: "semester_4/electrical_machine:dc-generator-principle-emf-equation"
source: https://www.bctengineer.com/q/semester_4/electrical_machine/dc-generator-principle-emf-equation
site: BCT Engineering
---

# DC generator working and emf equation

Electrical Machine · Chapter 3: DC Generator

- Asked in: 2068 Bhadra, 8 marks
- Video: [EMF Equation of DC Generator - DC Machines - Basic Electrical Engineering](https://www.youtube.com/watch?v=S8VIewhwqZs) — Ekeeda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machine/dc-generator-principle-emf-equation
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machine/chapter-3

## Question

Explain working principle of DC generator in detail and hence derive the expression of emf equation also.

## Short answer

A DC generator converts mechanical energy to DC electrical energy by rotating conductors through a magnetic field (Faraday's law). The commutator mechanically rectifies the alternating emf. The average generated emf is E = PΦZN/(60A) volts, derived from flux cut per revolution ΦP, time per revolution 60/N, and series conductors per path Z/A.

## Answer

A DC generator is a machine that turns mechanical power into DC electrical power. Its action is based on Faraday's laws of electromagnetic induction.

#### Working principle
1. When a conductor is moved in a magnetic field so that it cuts the lines of flux, an emf is induced in it: e = B l v (V). The direction is given by Fleming's right-hand rule.
2. The armature conductors, rotated by a prime mover, cut the flux of the N and S poles. The emf induced in a coil is alternating, because each conductor passes alternately under N and S poles.
3. The commutator is a mechanical rectifier. As the coil emf reverses, the commutator segment connection to the brush also reverses, so the brush polarity does not change.
4. The brushes deliver unidirectional current to the load. The magnitude depends on speed and flux.
5. Field excitation is supplied either by a separate source (separately excited) or by the machine itself (self-excited: shunt, series, compound).

```text
 prime mover -> rotating armature -> commutator -> brushes -> load
   (N rpm)      (cuts flux Φ)       (AC to DC)
```
Energy flow: mechanical input − (friction, windage, iron, copper losses) = electrical output.

#### Derivation of EMF equation
Let P = number of poles, Φ = flux per pole (Wb), Z = total armature conductors, A = parallel paths, N = speed (rpm).

- Flux cut by a conductor in one revolution: dΦ = ΦP
- Time for one revolution: dt = 60/N s
- Average emf generated per conductor: e = dΦ/dt = ΦPN/60 volts
- Number of conductors in series in each parallel path = Z/A
- Emf of the generator = emf per path

**E_g = (ΦPN/60) × (Z/A) = PΦZN / (60A) volts**

| Winding | A | E_g |
|---|---|---|
| Lap | P | ΦZN/60 |
| Wave | 2 | PΦZN/120 |

For a given machine, E_g = KΦN with K = PZ/(60A), which shows that emf depends on the flux per pole and the speed.

## Check yourself

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

1. How does the commutator act in a DC generator?
   A. As a mechanical rectifier: connection to the brush reverses as the coil emf reverses
   B. As an amplifier of voltage
   C. As a source of field excitation
   D. As a flux regulator
   Answer: A. The reversal of segment-to-brush connection keeps the brush polarity unchanged. (Key point: Commutator action)

2. In the derivation, what is the time for one revolution at N rpm?
   A. N/60 seconds
   B. 60/N seconds
   C. 60N seconds
   D. 1/(60N) seconds
   Answer: B. N rpm means N/60 revolutions per second, so one takes 60/N s. (Key point: Time for one revolution)

3. How many conductors are in series in each parallel path?
   A. Z x A
   B. A/Z
   C. Z/A
   D. Z/P always
   Answer: C. Z conductors split into A parallel paths, so Z/A in each path. (Key point: Series conductors)

4. From E_g = KΦN, what does the emf depend on for a given machine?
   A. Only the load current
   B. Only the number of brushes
   C. Only the armature resistance
   D. Flux per pole and speed
   Answer: D. K = PZ/(60A) is constant for a machine, so E_g is proportional to Φ and N. (Key point: Emf dependence)

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