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

# DC generator principle and emf equation

Electrical Machines · Chapter 3: DC Generator

- Asked in: 2078 Baisakh, 8 marks; 2076 Baisakh, 8 marks; 2068 Bhadra, 8 marks; 2066 Magh (old course), 8 marks (asked 4 times)
- Video: [Lect 1. DC Generators - Principle of Operation and EMF Equation](https://www.youtube.com/watch?v=gbQ9rldgPpM) — BeTECH SIVA
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machines/dc-generator-principle-emf
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-3

## Question

Explain the operating principle of a DC generator. Derive the emf equation for the DC generator.

## Short answer

A DC generator uses Faraday's law: when armature conductors cut flux, an AC emf is induced, rectified to DC by commutator and brushes. Emf equation: E_g = (Φ Z N P)/(60 A) volts, where Φ is flux per pole, Z total conductors, N speed in rpm, P poles, A parallel paths.

## Answer

A DC generator converts mechanical energy into electrical energy using **Faraday's law of electromagnetic induction**: when a conductor cuts magnetic flux, an emf is induced in it, $e = Blv$ volts (direction by Fleming's right-hand rule).

**Working:**
1. The field poles produce a flux $\Phi$ across the air gap.
2. The prime mover rotates the armature, so the armature conductors cut this flux and an emf is induced in each conductor.
3. In a single coil the induced emf is alternating, because each coil side passes under a north pole and then a south pole.
4. The **commutator** and **brushes** act as a mechanical rectifier. Each time the coil emf reverses, the segments reverse their connection to the brushes, so the brush terminals give a **unidirectional** (DC) voltage.
5. With a load connected, current flows out through the positive brush.

```text
        N pole            S pole
      +---------+       +---------+
      |    ^    |       |         |
      |  B -->  |       |         |
      |  ______ |_______|______   |
      | / loop (armature coil) \  |
      +-+-----------------------+-+
        | split-ring commutator |
     brush A ----[ load ]---- brush B
```

The figure shows a simple loop generator: one coil rotating between the N and S poles, with a split-ring commutator (two segments) and two brushes.

#### Derivation of the emf equation

Let
- $\Phi$ = flux per pole (Wb), $P$ = number of poles
- $Z$ = total armature conductors, $A$ = number of parallel paths
- $N$ = speed in rpm

In one revolution a conductor cuts the flux of all poles, $P\Phi$ weber, in time $60/N$ second.

$$
\text{average emf per conductor} = \frac{d\phi}{dt} = \frac{P\Phi}{60/N} = \frac{P\Phi N}{60}\ \text{V}
$$

The $Z$ conductors form $A$ parallel paths, so each path has $Z/A$ conductors in series. The generated emf equals the emf of one path:

$$
E_g = \frac{P\Phi N}{60}\times\frac{Z}{A} = \frac{\Phi Z N P}{60A}\ \text{V}
$$

- Lap winding: $A = P$, so $E_g = \dfrac{\Phi Z N}{60}$
- Wave winding: $A = 2$, so $E_g = \dfrac{\Phi Z N P}{120}$

In terms of angular speed, $E_g = \dfrac{ZP}{2\pi A}\Phi\omega = K_a\Phi\omega$.

## Check yourself

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

1. The operating principle of a DC generator is
   A. Lenz's law of repulsion between two magnets
   B. Faraday's law: an emf is induced when a conductor cuts magnetic flux
   C. Ohm's law applied to the armature
   D. Fleming's left-hand rule giving motion
   Answer: B. Armature conductors cut the flux, inducing e = Blv; the direction is given by Fleming's right-hand rule. (Key point: Principle)

2. What does the commutator do in a DC generator?
   A. Increases the flux
   B. Acts as a mechanical rectifier, reversing connections when the coil emf reverses
   C. Stores energy
   D. Changes DC to AC
   Answer: B. The emf in a coil is alternating; the commutator and brushes give a unidirectional voltage at the terminals. (Key point: Role of commutator)

3. In the emf derivation, in one revolution a conductor cuts a flux of
   A. Phi weber
   B. P x Phi weber, in time 60/N seconds
   C. Phi / P weber
   D. Z x Phi weber
   Answer: B. A conductor passes all P poles, so it cuts P Phi weber in 60/N s, giving P Phi N/60 volts per conductor. (Key point: Flux cut per revolution)

4. The emf equation Eg = Phi Z N P/(60A), for wave winding becomes
   A. Phi Z N/60
   B. Phi Z N P/120
   C. Phi Z N P/60
   D. Phi Z N/120
   Answer: B. Wave winding has A = 2 parallel paths, so Eg = Phi Z N P/120. For lap, A = P gives Phi Z N/60. (Key point: EMF equation and winding types)

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