##### Document Text Contents

Page 220

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Chapter 14

Alternating voltages

and currents

At the end of this chapter you should be able to:

• appreciate why a.c. is used in preference to d.c.

• describe the principle of operation of an a.c. generator

• distinguish between unidirectional and alternating waveforms

• define cycle, period or periodic time T and frequency f of a waveform

• perform calculations involving T =1/ f

• define instantaneous, peak, mean and r.m.s. values, and form and peak factors for a sine wave

• calculate mean and r.m.s. values and form and peak factors for given waveforms

• understand and perform calculations on the general sinusoidal equation v= Vm sin (ωt ±φ)

• understand lagging and leading angles

• combine two sinusoidal waveforms (a) by plotting graphically, (b) by drawing phasors to scale and (c) by

calculation

• understand rectification, and describe methods of obtaining half-wave and full-wave rectification

• appreciate methods of smoothing a rectified output waveform

14.1 Introduction

Electricity is produced by generators at power stations

and then distributed by a vast network of transmission

lines (called the National Grid system) to industry and

for domestic use. It is easier and cheaper to gener-

ate alternating current (a.c.) than direct current (d.c.)

and a.c. is more conveniently distributed than d.c.

since its voltage can be readily altered using trans-

formers. Whenever d.c. is needed in preference to a.c.,

devices called rectifiers are used for conversion (see

Section 14.7).

14.2 The a.c. generator

Let a single turn coil be free to rotate at constant angular

velocity symmetrically between the poles of a magnet

system as shown in Fig. 14.1.

An e.m.f. is generated in the coil (from Faraday’s

laws) which varies in magnitude and reverses its direc-

tion at regular intervals. The reason for this is shown

in Fig. 14.2. In positions (a), (e) and (i) the conductors

of the loop are effectively moving along the magnetic

field, no flux is cut and hence no e.m.f. is induced. In

position (c) maximum flux is cut and hence maximum

e.m.f. is induced. In position (g), maximum flux is cut

DOI: 10.1016/B978-0-08-089056-2.00014-0

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210 Electrical and Electronic Principles and Technology

Figure 14.1

Figure 14.2

and hence maximum e.m.f. is again induced. However,

using Fleming’s right-hand rule, the induced e.m.f. is in

the opposite direction to that in position (c) and is thus

shown as −E . In positions (b), (d), (f) and (h) some

flux is cut and hence some e.m.f. is induced. If all such

Figure 14.3

positions of the coil are considered, in one revolution

of the coil, one cycle of alternating e.m.f. is produced

as shown. This is the principle of operation of the a.c.

generator (i.e. the alternator).

14.3 Waveforms

If values of quantities which vary with time t are plotted

to a base of time, the resulting graph is called a wave-

form. Some typical waveforms are shown in Fig. 14.3.

Waveforms (a) and (b) are unidirectional waveforms,

for, although they vary considerably with time, they flow

in one direction only (i.e. they do not cross the time axis

and become negative). Waveforms (c) to (g) are called

alternating waveforms since their quantities are con-

tinually changing in direction (i.e. alternately positive

and negative).

A waveform of the type shown in Fig. 14.3(g) is called

a sine wave. It is the shape of the waveform of e.m.f.

produced by an alternator and thus the mains electricity

supply is of ‘sinusoidal’ form.

One complete series of values is called a cycle (i.e. from

O to P in Fig. 14.3(g)).

The time taken for an alternating quantity to complete

one cycle is called the period or the periodic time, T,

of the waveform.

The number of cycles completed in one second is called

the frequency, f, of the supply and is measured in hertz,

Hz. The standard frequency of the electricity supply in

Great Britain is 50 Hz

T = 1

f

or f = 1

T

cyan-background.eps

Chapter 14

Alternating voltages

and currents

At the end of this chapter you should be able to:

• appreciate why a.c. is used in preference to d.c.

• describe the principle of operation of an a.c. generator

• distinguish between unidirectional and alternating waveforms

• define cycle, period or periodic time T and frequency f of a waveform

• perform calculations involving T =1/ f

• define instantaneous, peak, mean and r.m.s. values, and form and peak factors for a sine wave

• calculate mean and r.m.s. values and form and peak factors for given waveforms

• understand and perform calculations on the general sinusoidal equation v= Vm sin (ωt ±φ)

• understand lagging and leading angles

• combine two sinusoidal waveforms (a) by plotting graphically, (b) by drawing phasors to scale and (c) by

calculation

• understand rectification, and describe methods of obtaining half-wave and full-wave rectification

• appreciate methods of smoothing a rectified output waveform

14.1 Introduction

Electricity is produced by generators at power stations

and then distributed by a vast network of transmission

lines (called the National Grid system) to industry and

for domestic use. It is easier and cheaper to gener-

ate alternating current (a.c.) than direct current (d.c.)

and a.c. is more conveniently distributed than d.c.

since its voltage can be readily altered using trans-

formers. Whenever d.c. is needed in preference to a.c.,

devices called rectifiers are used for conversion (see

Section 14.7).

14.2 The a.c. generator

Let a single turn coil be free to rotate at constant angular

velocity symmetrically between the poles of a magnet

system as shown in Fig. 14.1.

An e.m.f. is generated in the coil (from Faraday’s

laws) which varies in magnitude and reverses its direc-

tion at regular intervals. The reason for this is shown

in Fig. 14.2. In positions (a), (e) and (i) the conductors

of the loop are effectively moving along the magnetic

field, no flux is cut and hence no e.m.f. is induced. In

position (c) maximum flux is cut and hence maximum

e.m.f. is induced. In position (g), maximum flux is cut

DOI: 10.1016/B978-0-08-089056-2.00014-0

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210 Electrical and Electronic Principles and Technology

Figure 14.1

Figure 14.2

and hence maximum e.m.f. is again induced. However,

using Fleming’s right-hand rule, the induced e.m.f. is in

the opposite direction to that in position (c) and is thus

shown as −E . In positions (b), (d), (f) and (h) some

flux is cut and hence some e.m.f. is induced. If all such

Figure 14.3

positions of the coil are considered, in one revolution

of the coil, one cycle of alternating e.m.f. is produced

as shown. This is the principle of operation of the a.c.

generator (i.e. the alternator).

14.3 Waveforms

If values of quantities which vary with time t are plotted

to a base of time, the resulting graph is called a wave-

form. Some typical waveforms are shown in Fig. 14.3.

Waveforms (a) and (b) are unidirectional waveforms,

for, although they vary considerably with time, they flow

in one direction only (i.e. they do not cross the time axis

and become negative). Waveforms (c) to (g) are called

alternating waveforms since their quantities are con-

tinually changing in direction (i.e. alternately positive

and negative).

A waveform of the type shown in Fig. 14.3(g) is called

a sine wave. It is the shape of the waveform of e.m.f.

produced by an alternator and thus the mains electricity

supply is of ‘sinusoidal’ form.

One complete series of values is called a cycle (i.e. from

O to P in Fig. 14.3(g)).

The time taken for an alternating quantity to complete

one cycle is called the period or the periodic time, T,

of the waveform.

The number of cycles completed in one second is called

the frequency, f, of the supply and is measured in hertz,

Hz. The standard frequency of the electricity supply in

Great Britain is 50 Hz

T = 1

f

or f = 1

T