# Principle of DC Generator

DOI: 10.4018/978-1-4666-8441-6.ch002

## Abstract

In this chapter, the authors discuss about principles of DC generator, variation of voltage induced in the conductor with the position of conductor. After that the authors discuss frequency of induced voltage, magnitude of induced voltage. This chapter ends with discussion of the main parts and construction of a DC machine.
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## 2.1 Principle Of D.C. Generator

Faraday’s 2nd law of electro-magnetic induction states that whenever, there is a relative motion between a conductor and a magnetic field, a voltage is induced in the conductor. Now there are two possibilities:

• Field is stationary and conductor is moving.

• Field is revolving and conductor is stationary.

The first is the principle of D.C. generator and the second is the principle of a transformer.

As is obvious from the principle of DC generator that two things are needed

### Magenetic Field

This is produced by a permanent magnet or electromagnet. The electromagnet consists of silicon steel core and copper windings.

### Rotating Armature

It consists of armature made of silicon steel having slots and teeth. Copper windings are placed in the slots of rotating armature

The voltage induced is given by

where B is flux density

1 is length of conductor

θ is the angle between direction of magnetic field and direction of motion

of conductor.

See Figure 1.

Figure 1.

­

The angles between field and direction of motion of conductor at various points is

180˚ at point 1

90˚ at point 2

0˚ at point 3

-90˚ at point 4

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## 2.2 Variation Of Voltage Induced In The Conductor With The Position Of Conductor

Let us consider an elementary two pole generator as shown in Figure 1. A conductor starts moving in the direction shown from position 1. It is under the influence of North Pole up to position 3 and generates a positive half cycle. Similarly under the influence of South Pole a negative half cycle is generated. So we see that for a two pole machine corresponding to 360˚ mechanical, a complete full cycle is generated. One electrical cycle corresponds to 360˚ electrical. Similarly for a four pole machine corresponding to 360˚ mechanical rotation, two complete electrical cycles i.e. 7200 are generated, so we can write down following relation:

(2.1) where Өe are the electrical degrees and Өm are the mechanical degrees, P is the number of poles.

Differentiating equation

(2.2)
(2.2) where ωe is the electrical angular velocity and ωm is the angular mechanical velocity. From the above discussion it is obvious that alternating voltage is being generated in this elementary generator. This alternating voltage is converted to direction voltage by the use of commutator.

### 2.2.1 Frequency of Induced Voltage

From equation 2.2

where f is the frequency and n is the speed in revolutions per second
(2.3) where N is speed in revolutions per minute

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