Electric Generator-Diagram, Types, Practice problems, FAQs

Everyone feels the discomfort when power goes off. In order to have a constant source of power once electricity goes off, one needs to install generators in their houses. They were invented by Charles F Brush who used an electric lamp which supplies a constant voltage and thereby, a constant load current for running appliances. Generators are of two types, AC and DC. The latter supplies a constant current, also known as direct current – by which we mean a current which does not change polarity with time. On the other hand, AC generators use a time varying current with ever changing polarity called the alternating current. Depending upon the need, generators have different ratings. For instance, small business can run on AC generators which are rated 50 Volt Amperes. For larger power requirements like school buildings or malls, generators rated at 20 kiloVolt are required. The simplest form of generator one can imagine is the dynamo attached to bicycle tyres. It generates small electricity which can be used to run small appliances like bulbs attached to the bicycle. In this article, we will explore electric generators in detail.

Table of contents

What is an electric generator?
Principle of AC generator
Construction and working of AC generator
DC generator
Practice problems
FAQs

What is an electric generator?

A generator is a device that is used for converting mechanical energy into electrical energy. The input mechanical energy is supplied by turbines or engines–that are usually run by natural gas or diesel fed into the combustion chamber.

Principle of AC generator

An AC generator works on the principle of Faraday’s laws of electromagnetic induction. When a coil is rotated in a magnetic field, the magnetic flux linked to the coil changes with rotation (that cuts the coil at different angles). This in turn produces an emf in the coil causing a current to flow. The induced current is transferred onto the windings which supplies current to the rest of the external circuit.

Construction and working of AC generator

An AC generator produces a changing magnetic flux linked with the coil by rotating the coil in a static magnetic field or rotating magnetic field in a stationary conductor. We use AC generators in our everyday life. They are capable of supplying current at 220 V, 50 Hz. A typical AC generator consists of the following parts:

1) Magnetic field

The necessary magnetic field is provided by horseshoe magnets. It consists of two horse-shoe magnets which supply a strong magnetic field which starts radially from the North pole and ends in the South Pole.

2) Armature

Armature is a rectangular coil with many turns wound over a soft-iron core. The soft iron core provides the necessary support for the armature. The axis of rotation of the coil is perpendicular to the magnetic field.

3) Rotor

The rotating component of a generator is called its rotor.

4) Stator

The stationary part of a generator is called its stator. It does not move. It is laminated to protect against eddy currents losses.

5) Slip rings

Slip rings are used to transmit electrical energy from the armature coil to the brushes.

6) Brushes

Carbon brushes are made of graphite. They are permanently in contact with the slip rings and they are connected to the external circuit.

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Let us consider an armature coil having N turns placed in a magnetic field B.. The area of cross section of the coil is A. Upon rotation, the coil makes an angle $θ = ω t$ with the area vector of the coil. Here w is the angular velocity of the coil.

When the armature coil rotates, the flux lined with it can be written as $ϕ = N B A c o s ω t$

Now according to Faraday’s law, the induced emf can be written as,

$ε = - \frac{d ϕ}{d t} = - \frac{d (N B A c o s ω t)}{d t} = N B A ω s i n ω t$

$ε = ε_{0} s i n ω t - - (i)$

$ε_{0} = N B A ω$ indicates the maximum value of emf.

Equation (i) shows that the induced emf varies sinusoidally with time.

The maximum value of induced current $I_{o} = \frac{N B A ω}{R}$

Where R indicates the resistance of the armature coil.

$ω = \frac{2 π}{T} = 2 π ν$ where T indicates the time period of the coil rotation in seconds. It is the time taken for one full rotation. is the frequency of rotation (in Hz).

The induced emf can be written as

$ε = ε_{0} \sin (\frac{2 π}{T}) t$

When $t = 0, \frac{T}{2}, T, \frac{3 T}{2}$ , $ε = 0 \Rightarrow$ emf is minimum, hence there will be no induced current.

When $t = \frac{T}{4}, \frac{3 T}{4}, \frac{5 T}{4}$ …. $ε = ε_{0} \Rightarrow$ emf will be maximum. So, there will be maximum induced current.

DC generator

The DC generator is also used to convert mechanical energy into electrical energy. They produce a unidirectional current called direct current. Unlike an AC current, it does not change polarity with time. In other words, it is not bidirectional. DC generators do not contain slip rings like AC generators have. Instead they use commutators to convert a bidirectional current into a unidirectional current. Additionally, the brushes used in DC generators wear out much quicker unlike AC generators.

1) Stator

It is the stationary part consisting of many windings. It supplies the necessary magnetic fields for the coil.

2) Rotor

It is the rotating part which consists of an armature, commutator and a shaft. It is moveable – and rotates in the magnetic field produced by the stator.

3) Bearings

It is used for minimising the friction between the stationary and the rotating parts of the machine. It is usually made up of carbon steel. This also provides support to the system.

Practice problems

Q1. In a region where the magnetic field has a value of 10^-3 T, a circular coil of radius 60 cm and resistance $π^{2} Ω$ is rotated about an axis which is perpendicular to the magnetic field. If the speed of rotation of the coil is 250 rpm, the amplitude of the alternating current induced in the coil is,

(a) 1 A (b) 2 A (c) 3 A (d) None of these

Answer. c

Given $B = 10^{- 3} T$

r=0.6 m

R= $π^{2} Ω$

N=1

=250 rpm= $\frac{250}{60} r p s$

$ω = 2 π ν = 2 π \times \frac{250}{60} = \frac{25 π}{3}$

Area of the coil $A = π r^{2} = π {(0.6)}^{2} = 0.36 π m^{2}$

Max. emf $ε_{0} = N B A ω =$ $1 \times 10^{- 3} \times 0.36 π \times \frac{25 π}{3} = {3 π}^{2} \times 10^{- 3} V$

Induced current, $i = \frac{ε}{R} = \frac{{3 π}^{2} \times 10^{- 3}}{π^{2}} = 3 m A$

Q2. The magnetic flux between the poles of a horse magnet varies with time t as $ϕ = 3 t^{2} + 2 t^{} - 2$ . Calculate the induced emf at time t=2 s.

(a) 14 V
(b) 12 V
(c) 10 V
(d) None of these

Answer. $ϕ = 3 t^{2} + 2 t^{} - 2$

$ε =$ | $\frac{d ϕ}{d t} | = \frac{d}{d t} (3 t^{2} + 2 t^{} - 2) = 6 t + 2$

At $t = 2, ε = 14 V .$

Q3. A rectangular loop having area 600 cm² and resistance 10 is used in an AC generator. A magnetic field of 0.20 T exists between the poles. The angular velocity with which it is rotated is $25 \frac{r a d}{s}$ The number of turns in the coil is 100. What is the maximum current produced in the coil during this interval?

(a) 3 A
(b) 4 A
(c) 1 A
(d) None of these

Answer. a

Area $A = 600 \times 10^{- 4} = 0.06 m^{2} .$

N=100

$ω = 25 \frac{r a d}{s}$

$R = 10 Ω$

B=0.2 T

Maximum induced current i₀= $\frac{N B A ω}{R} = \frac{100 \times 0.2 \times 0.06 \times 25}{10} = 3 A .$

Q4. The magnetic field in the armature coil of a AC generator varies with time according to the relation $B = B_{0} t^{3}, B_{0}$ 0 is a positive constant. If r denote the radius of the coil, then calculate the induced emf as a function of time. Consider the coil as stationery.

(a) $3 B_{0} t^{2} (π r^{2})$
(b) $4 B_{0} t^{3} (π r^{2})$
(c) $2 B_{0} t^{2} (π r^{2})$
(d)None of these

Answer. a

Area of the coil, $A = π r^{2}$

Since the magnetic field varies with time,

$\frac{d B}{d t} = 3 B_{0} t^{2}$

Induced emf

$ε =$ $\frac{d ϕ}{d t} = \frac{d (B A)}{d t} = \frac{d B}{d t} (A)$

$= 3 B_{0} t^{2} (π r^{2})$

FAQs

Q1. Write three advantages of AC over DC.
Answer. AC can be transmitted over long distances compared to DC. AC undergoes lesser power losses in comparison to DC.

Q2. Which rule is used to find induced emf in a generator?
Answer. Fleming’s Right hand rule is used to find direction of induced current in a generator. Stretch the three fingers of your right hand mutually perpendicular to each other, the forefinger indicates the direction of magnetic field, the middle finger indicates the direction of induced current, and the thumb indicates the direction of force on the conductor.

Q3. Why is DC not used in homes?
Answer. For the same value of voltage, DC is more dangerous than AC, since it never reaches a zero value at any instant of time. Having an unidirectional nature, it is prone to cause more damage than DC.

Q4. Mention 3 mistakes one should never make with a DC generator.
Answer. The three mistakes could be,

1) For a liquid fuel power generator for home use, we should not fuel up the generator while operating.

2) Improper powering on and off can damage the armature coil.

3) Using poor quality fuel can reduce the life of the generator as the carbon content of the fuel can even create a short circuit in the spark plug.