Industrial Electronics N2
Industrial Electronics N2
Industrial Electronics N2
R B J van Heerden
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TROUPANT
./
Publishers
Copyright © 1996 by R.B.J van Heerden
All rights reserved. No part of this publication may be
reproduced or transmitted in any form or by any means
without prior written permission by the publisher.
ISBN: 978 1 91978050 4; eISBN: 978 1 43080256 3
First edition 1998
Second impression 2003
Third impression 2005
Forth impression 2007
Fifth impression 2011
Sixth impression 2012
Seventh impression 2012
Published by
Troupant Publishers
Suite 10, Private Bag X12
Cresta, 2118
Cover design by Alix Gracie
Set in 9.5 on 12pt Times New Roman
Setting by Roelf van Heerden using Corel VENTURA 5.0
This textbook is not a revised edition of my Electronics N2 textbook.
I have made as much use of that text as I could, but most of the explanations offer a new approach to the
Industrial Electronics N2 syllabus. After leaving the department of Education in 1989, I spent more than
three years in the private sector, involved with computer-based training, and later taught at a high school. It
was worrying to see in the private sector how little students, who had passed the grade, really knew about
the subject. The reason is that too much emphasis is placed on passing the examination and not enough on
learning the subject itself. Students told me that they would have preferred the textbooks to have had more
explanations in them, which would have allowed them to later go and read about the subject themselves. It
is with this suggestion in mind that I have given more explanations ofthe subjects, sometimes going beyond
the limits of the syllabus.
It is a fact that lower grade students hardly ever read other textbooks or magazines. Many of the new
generation students travel far each day and have no access to libraries to do additional reading. Classes are
also bigger today and the lecturer does not have time in class to go back to basics. With the explanations in
this textbook, students can now read about the subject in their own textbook and in their own time.
An information
infonnation sheet similar to the one accompanying the examination paper, is also included in the
appendix to this book to assist lecturers and students. I find that students always ask for these information
infonnation
sheets and sometimes it is very difficult to get hold of the proper list of formulas.
fonnulas.
I would like to thank all my friends who encouraged me to write another book, and especially Basil van
Rooyen, who had the confidence in me to publish this book.
THE AUTHOR
co~rrE~rrs
co~rrE~rrs
1.
1.
1.1
1.1
1.2
1.2
1.3
1.3
1.4
1.4
1.5
1.5
1.6
1.6
1.7
1.7
1.8
1.8
1.9
1.9
ATOMIC THEORY
ATOMIC THEORY
Matter
Matter
Elements
Elements
The atom
The atom
Valency electrons
Valency electrons
Energy levels
Energy levels
Free electrons
Free electrons
Covalent bonds
Covalent bonds
Conductors
Conductors
Insulators
Insulators
Exercise 1.1
Exercise 1.1
2.1
2.1
2.2
2.2
2.3
2.3
2.3.1
2.3.1
2.3.2
2.3.2
2.3.3
2.3.3
2.3.4
2.3.4
2.4
2.4
2.5
2.5
2.5.1
2.5.1
2.5.2
2.5.2
2.. 5.3
2.. 5.3
2.6
2.6
2.7
2.7
2.7.1
2.7.1
2.7.2
2.7.2
2.
2.
DIRECT CURRENT
DIRECT CURRENT
Electrical current
Electrical current
Voltage
Voltage
Resistance
Resistance
Resistivity
Resistivity
Insulators
Insulators
Determination of resistance
Determination of resistance
Definition
Definition
Ohm's law
Ohm's law
Resistance in series and parallel
Resistance in series and parallel
The series circuit
The series circuit
The parallel circuit
The parallel circuit
Series-parallel circuit
Series-parallel circuit
Power
Power
Kirchoff's laws
Kirchoff's laws
Current law
Current law
Voltage law
Voltage law
Exercise 2.1
Exercise 2.1
6
6
7
7
7
7
7
7
7
7
7
7
8
8
8
8
9
9
9
9
10
10
11
11
13
13
14
14
14
14
14
14
14
14
3.
3.
3.1
3.1
3.2
3.2
3.3
3.3
VOLTAGE
VOLTAGE
The sine wave
The sine wave
Frequency
Frequency
Simple alternating current generator
Simple alternating current generator
17
17
17
17
18
18
1
1
1
1
1
1
2
2
3
3
3
3
3
3
4
4
4
4
4
4
Maximum and peak-to-peak values
Maximum and peak-to-peak values
of a sine wave
of a sine wave
Rms and average values of a
Rms and average values of a
sine wave
sine wave
Form and crest factors
Form and crest factors
Instantaneous value
Instantaneous value
The mid-ordinate rule
The mid-ordinate rule
Phase angle
Phase angle
Ac circuits with resistance
Ac circuits with resistance
Ac circuits with inductance
Ac circuits with inductance
Ac circuits with capacitance
Ac circuits with capacitance
Impedance
Impedance
The series XL circuit
The series XL circuit
The series Xc circuit
The series Xc circuit
The series Xc. XL and R circuit
The series Xc. XL and R circuit
Resonance
Resonance
Exercise 3.1
Exercise 3.1
19
19
20
20
20
20
22
22
23
23
23
23
24
24
25
25
26
26
26
26
28
28
28
28
30
30
30
30
MEASURING INSTRUMENTS
4.
MEASURING INSTRUMENTS
4.
Introduction
4.1
Introduction
4.1
How a meter works
4.2
How a meter works
4.2
4.2.1 Sensitivity
4.2.1 Sensitivity
The voltmeter
4.3
The voltmeter
4.3
4.3.1 Circuit loading
4.3.1 Circuit loading
The ammeter
4.4
The ammeter
4.4
4.4.1 Circuit loading
4.4.1 Circuit loading
The ohmmeter
4.5
The ohmmeter
4.5
Reading meter scales
4.6
Reading meter scales
4.6
Multirange meters
4.7
Multirange meters
4.7
4.7.1 The ammeter
4.7.1 The ammeter
4.7.2 The voltmeter
4.7.2 The voltmeter
4.7.3 The ohmmeter
4.7.3 The ohmmeter
4.7.3.1 Series ohmmeter
4.7.3.1 Series ohmmeter
4.7.3.2 Shunt ohmmeter
4.7.3.2 Shunt ohmmeter
4.7.3.3 Multirange ohmmeter
4.7.3.3 Multirange ohmmeter
Multimeter principles
4.8
Multimeter principles
4.8
Precautions and care
4.9
Precautions and care
4.9
32
32
32
32
33
33
33
33
34
34
35
35
35
35
35
35
36
36
36
36
36
36
38
38
39
39
39
39
40
40
41
41
41
41
42
42
3.4
3.4
3.5
3.5
3.6
3.6
3.7
3.7
3.8
3.8
3.9
3.9
3.10
3.10
3.11
3.11
3.12
3.12
3.13
3.13
3.13.1
3.13.1
3.13.2
3.13.2
3.13.3
3.13.3
3.14
3.14
19
19
4.9.1
4.9.2
4.9.3
Ammeter
Voltmeter
Ohmmeter
Exercise 4.1
5.
SEMICONDUCTOR DIODES
5.1
5.2
5.3
5.4
5.5
5.6
5.6.1
5.7
5.8
5.9
5.10
5.11
5.12
5.13
5.14
5.15
Introduction
Characteristics of materials
N-type semiconductors
P-type material
The P-N junction
Bias
Bias on the P-N junction
Diode characteristics
Zener diodes
Point-contact diodes
Varactor diodes
Photodiodes
Light-emitting diodes (LEDs)
Half-wave rectification
Full-wave rectification
Filter circuits
Exercise 5.1
42
42
42
43
45
45
46
47
48
49
49
50
51
52
52
52
53
53
55
56
57
6.
SEMICONDUCTOR TRANSISTORS
6.1
6.2
6.3
6.4
6.4.1
6.4.2
6.4.3
Introduction
The basic junction transistor
Simple amplifiers
The three basic circuits
The common emitter circuit
The common base circuit
The common collector circuit
Exercise 6.1
7.
TRANSDUCERS
7.1
7.2
7.3
7.4
Introduction
The bimetallic strip
The thermocouple
Thermistors
59
59
62
63
63
64
64
65
67
67
68
69
7.5
Light dependent resistors (LDRs)
Exercise 7.1
8.
SYNCHRO SYSTEMS
8.1
8.2
8.3
Introduction
The synchro system
Advantages of synchro systems
over mechanical systems
Synchro torque tr~smitters and
synchro indicators
Synchro torque differential transmitter
Synchro control transformer
Synchro torque transmitters and
indicators
Synchro schematics
Magnetic fields
Simple transformer theory
Lenz's law
Synchro transmitter-indicator as a team
Differential synchro
Transformer action in a
differential transmitter
Subtracting by means of the
differential transmitter
Addition
Differential receiver
Control transformer
Exercise 8.1
8.4
8.5
8.6
8.7
8.8
8.9
8.10
8.11
8.12
8.13
8.13.1
8.13.2
8.13.3
8.13.4
8.13.5
9.
THE DECIBEL
9.1
9.2
9.3
9.4
9.5
Introduction
Calculating gain or loss
Power gain or loss
Multistages
Voltage and current gain or loss
Exercise 9.1
APPENDIX: Formula list
70
71
72
72
73
73
73
74
75
75
76
77
77
78
79
80
80
81
82
82
83
85
85
86
86
88
89
90
1\ }.,fOJV\IC ~ft-IEOR.Y
1.1 Matter
Matter is anything that takes up space. It cannot be
created or destroyed. It is possible to change its state
from one form to another. Until recently, it was
thought that there were only three forms of matter,
but it has been proved that there are four: solid,
liquid, gas and plasma. Take ice for example: it is a
solid; heat it and it becomes water, which is a liquid;
heat it further and it becomes steam, which is a gas.
The temperature thus 4etermines the state of the
matter. Plasma is the fourth form of matter. (We are
not referring to blood plasma.) Plasma consists of
ionised particles, and emits light, like lightning or
the gas in a gas-discharge chamber.
• A solid does not usually change its natural state
unless it is subjected to pressure or other influences. Solids can be subdivided into metals and
nonmetals, which we shall refer back to later.
• A liquid normally takes the form of its container,
and, if the volume of the liquid is less than that of
the container, it will only partly fill the container.
• A gas will always fill its container, but with a
decrease or increase in pressure.
forms when two hydrogen atoms combine with one
oxygen atom to form a molecule, H 20.
• A molecule is the smallestpart ofa compound that
retains the characteristics of the original compound without breaking up into atoms.
1.3 The atom
protons
neutrons
+tt
H
1.2 Elements
Fig. 1.1
Elements are substances that consist of only one
type of atom, such as iron, copper, germanium and
silicon. A compound or an alloy is formed when
one or more elements react chemically. The most
common compound that exists is water, which
The atom is the smallest part of an element that can
take part in a normal chemical reaction. The known
elements are classified in a table known as the
periodic table. It contains important information
like atomic number, atomic symbol and density.
There are 103 known elements.
Fig. 1.1 represents the simplest atom, the hydrogen atom, with its symbol "H", while fig. 1.2
shows the different shells, electrons, and the nucleus which consists of protons and neutrons. The
electrons revolve around the nucleus in fixed orbits
or shells.
electrons in an atom, which keeps the atom electrically neutral.
The atomic number always indicates the amount
ofprotons or electrons in the atom. The mass of
the protons differs considerably from that of the
electrons. If the mass of the proton is taken as
one, then the mass of the electron is in the order
of 5,488 x 10-4.
When an electron is removed from an atom, there
is no significant influence on the atom as a whole,
except that the charge of the atom changes.
electrons~
shells
1.4 Valency electrons
Those electrons in the outermost shell, or the shell
farthest from the nucleus ofan atom, are often called
valency electrons. In this study, we are concerned
primarily with the behaviour of valency electrons
since they can, under certain conditions, leave their
"parent" atoms. The number ofvalency electrons in
atoms also determines several important electrical
and chemical characteristics of the substance made
up of these atoms.
Consider an atom of germanium, which has an
atomic number of32.
nucleus (32 protons, 41 neutrons)
Fig. 1.2
first shell [K]
An electron is usually represented by the symbol e.
The orbits ofthe electrons are called the K, L, M, N,
etc., orbits. When an electron is in one of its orbits,
it will not move to another, higher energy orbit
unless it is given enough energy by external means.
Each orbit can take up only a certain number of
electrons. The number is determined by the formula
2n 2 where n represents the orbit number; in the first
orbit, it is 2 x 1 x 1 = 2 and in the second orbit it is
2 x 2 x 2 = 8.
An exception is the so-called inert gases, which
have a maximum of eight electrons in the outer
shell. These elements are also called non-active
elements.
The nucleus, which consists of protons and
neutrons, has been mentioned. The protons have
a positive charge while the neutrons have no
charge at all. The electron has a negative charge.
There is always the same amount of protons and
second shell [L)
)5( ~:.-.--,
fourth--~·
shell[N]
...
....... -e-· . .
,
"o
Fig. 1.3
It can be seen that the K shell contains only two
electrons, the L shell has eight and the M shell has
18. This leaves only four electrons for the N shell.
Therefore, germanium has four valency electrons.
2
Ifthe valency electrons are easily removed from the
atom, the element is called a conductor. When electrons are removed from the atom, it gains a positive
charge. This positively charged atom is called a
positive ion or a cation. The process of removing or
adding electrons is called ionisation. A negative ion
or anion results when electrons are added to an
atom; such an atom has a negative charge.
When the valency electrons are not easily removed, the element is an insulator. There is a
group between conductors and insulators, namely
the semiconductors. This group will be discussed
later.
recombination, they soon release the acquired energy and once again become part of an atom.
1.7 Covalent bonds
Some atoms cannot exist on their own as a stable
element. The hydrogen atom is an example. Such an
atom must combine either with another atom like
itselfor with a completely different atom. Hydrogen
gas, for instance, consists of two hydrogen atoms
(H 2). The gas is lighter than air and is readily available. It is used to send weather balloons into the air.
It is highly inflammable and dangerous to use.
When two hydrogen atoms combine, a bond is
formed that is known as a covalent bond, which
means the atoms share their free electrons with each
other (see fig. 1.4).
1.5 Energy levels
A stable (in balance) atom has a certain amount of
energy, which is equal to the sum ofthe
of the energies of
its electrons. Electrons, in turn, have different energies called energy levels. The energy level of an
electron is proportional to its distance from the
nucleus. Hence, the energy levels of electrons in
orbits farther from the nucleus are higher than those
closer to the nucleus.
If the last orbit is not completely filled with electrons, then that orbit is called the valency band. The
electrons in that band are known as the valency
electrons. It is these electrons that are important to
us, because they determine whether an element is a
conductor, a semiconductor or an insulator.
1.6 Free electrons
e
When external energy such as heat, light or electrical energy is applied to certain materials, the electrons. within the atoms of these materials gain
energy. This may cause the electrons to move to a
higher energy level, Le. to move farther from the
nuclei of their atoms. When an electron has moved
to the highest possible energy level, or the outermost
shell, it is least attracted by the positive charges of
the protons within the nucleus ofthe atom. Ifenough
energy is then applied to the atom, some of the
outermost shell's electrons (valency electrons) will
leave the atom. These electrons are calledfree electrons.
Free electrons remain in the mobile state for only
a comparatively short time. By a process known as
Fig. 1.4
Note that oxygen has only six valency electrons. To
complete the last orbit, the atom needs two more
electrons. When oxygen combines with hydrogen,
one oxygen atom must combine with two hydrogen
atoms so that it obtains two more electrons in the
last orbit. This forms a complete orbit, and the result
is H 20, which is one molecule of water.
3
1.8 Conductors
2.
A conductor is a material containing a large number
offree electrons that can pass through the material
quite easily under the influence of a driving force,
called voltage. (We will learn about this in module
2.) In such materials, the valency electrons in the
outermost shell can be quite easily removed from
their parent atoms by the above-mentioned force.
3.
4.
5.
6.
• A conductor is a material having many free electrons.
Three good electrical conductors are silver, copper
and aluminium. In fact, metals generally are good
conductors. Certain gases are also used as conductors under special conditions. For example, neon
gas, argon gas, mercury vapour and sodium vapour
are used in various types of lamps.
7.
8.
9.
10.
11.
1.9 Insulators
12.
Electrical insulation is material which does not easily conduct current. Such materials contain valency
electrons which are tightly bound to the nuclei of
their atoms. As a result, it requires an unusually high
voltage to produce significant numbers of free electrons. Such materials are also called insulators,
non-conductors or dielectrics.
Typical insulating materials include glass, porcelain, mica, rubber, plastics, paper and wood. These
materials are used to electrically isolate conductors
so that the current which they carry will not leak off
or pass through unwanted conductor materials.
There is no sharp, well-defined dividing line separating conductors from insulators. All insulating
materials will break down and conduct current if a
sufficiently high voltage is applied across them.
13.
14.
15.
16.
17.
18.
19.
All insulating materials will break down and
conduct current if a sufficiently high ... is
applied to them.
21.
The ability of a material to act as an insulator
is measured in terms of its ... .
Describe the composition of an atom.
How do atoms differ from one another?
What is
a) an element;
b) a compound;
c) a molecule?
22.
23.
24.
Make simple labelled sketches and describe
the following:
a) an atom;
b) an element;
c) electrons;
d) a cation;
e) a covalent bond;
f) ionisation.
25.
26.
4
The process by which atoms either gain ,or
lose electrons is called ... .
A conductor is a material through which electrons can flow ... .
In a conductor material, there are many ... .
In addition to metals, certain ... are also
used as conductors.
20.
Exercise 1.1
1.
Electrons move about the nucleus of an atom
in paths which are usually referred to as ....
The nucleus of an atom consists of particles
called ... and ... .
Atoms differ from one another only in the
number of . .. and ... which they contain.
The number of protons in the nucleus of an
atom is known as the atomic ... ofthat atom.
When all the atoms within a substance are
alike, the substance is called a chemical ... .
Common examples of chemical elements are
. .. , .... and ....
Different elements can combine to form a
... .
substance called ~ ....
A. .. is the smallest particle of a compound
which retains all the properties of that compound.
Electrons are basic ... charges, while protons are basic ... charges.
A... atom is one which contains the same
number of . .. and ... .
The electrons in the outermost shell of an
atom are often called the ... electrons.
The energy ... of an electron is determined
by its distance from the nucleus of an atom.
If a neutral atom gains electrons, it becomes
a ... ion.
If a neutral atom loses electrons, it becomes
a ... ion.
Define the atomic number of an atom.
Explain what is meant by a neutral atom.
27.
28.
29.
30.
31.
What are valency electrons?
Explain the relationship between electron energy levels and free electrons.
How does an atom become
a) a negative ion;
b) a positive ion?
Define an electrical conductor and name at
least three good conductor materials.
32.
33.
5
Describe the movement of electrons through
a conductor.
Define electrical insulation and name five
common insulating materials.
Under what condition can a material which is
normally an insulator become a conductor?
2.1 Electrical current
electrons move through the conductor from the negative terminal to the positive terminal; this conduction
process lasts until the chemical reaction is exhausted.
In module 1, the basics ofthe atom were discussed. We
mentioned electrons circulating the nucleus and also
learned about valency electrons in the outer orbital.
Electrons further away from the nucleus are more
easily removed than those nearer to the nucleus, and
conductors easily emit or replace their free electrons.
In practice, nonnal room temperature is enough to free
the valency electrons in a good conductor.
It must always be remembered that an atom is
3
very small. For example, 1 cm (lcm x 1 em x 1cm)
24
of copper consists of approximately 10 atoms.
The electron is even smaller than the atom. If only
one out of every 100 atoms in a cubic centimetre of
copper is removed from the metal, there will be a
vast number of electrons moving freely in the copper at room temperature. If this small piece of
copper is stretched out in the form ofa wire, and one
side is made positive and the other side is made
negative, most ofthese electrons will be attracted to
the positive side, and pushed from the negative side
at the same time.
This movement ofelectrons in one direction along
the conductor is known as current·flow. (Fig. 2.1)
An electrical cell has the ability to set electrical
energy free. This is normally achieved by a chemical
reaction within the cell. The cell normally has two
terminals, one positive and the other negative. The
negative terminal has an excess of electrons, while
the positive terminal has a shortage of electrons.
When a conductor is connected to the terminals,
applied
voltage
tI
+
electron
current
electron
current
i
_---. _-... _.--.' e--.
----.
--...
e--+
-~
_--+
e~e~e~
e--+
e-...
Fig. 2.1
The electrons within the cell move from positive to
negative and in the outer circuit from negative to
positive. It is the movement ofelectrons in the outer
circuit that is important, in contrast with conventional current flow, which flows from positive to
negative in the outer circuit. This may sound confusing but will soon become clear.
When one electron starts to move, all the other
electrons also start to move one by one. This can be
compared to a locomotive pulling trucks: when the
locomotive starts pulling, all the trucks start moving, and the second one moves to where the first one
was, etc. All the trucks cover the same distance. The
positions differ in that all the trucks at a station are
in different positions. The difference with electrical
6
2.3.2 Insulators
movement is that the electrons are not linked together, but forces that cause movement are imposed
on the electrons.
The unit used to measure current flow is the
ampere (symbol A). If a current of 1 A flows
through a conductor, about 6,26 x 1018electrons pass
any point in one second. Current flow is usually
indicated by means ofan I in a circuit, with an arrow
pointing in the direction of the current flow.
The ampere can be subdivided into smaller units.
3
There are, for instance, I 000 or 10 milliampere
(rnA) in one ampere. There are 106microamperes (JlA)
in one ampere, 10 3 Jl
J..l in one rnA, or 1 rnA = 10-3 A.
If the resistance of a material is too high for the
conduction of current, then t'le material is called an
insulator. Just as there are good and bad conductors,
there are good and bad insulators. There are several
factors that determine the quality ofan insulator: the
material of which it is made, the temperature, humidity, etc.
2.3.3 Determination of resistance
There are four factors that determine the resistance
of a material:
• the kind ofmaterial (the resistivity, r in ohm-metres);
2.2 Voltage
• the length (l in metres);
2
• the cross-sectional area (a in m or square metres);
From what we have learned so far, it is clear that the
higher the resistance of a conductor, the more difficult it will be for electrons to flow through the
conductor, and vice versa, provided that the source
of electricity is kept constant. The source of electricity is known as voltage (V) or the electromotive
force (emt). Voltage is measured in volts. The different methods for the generation of voltage are
considered later.
• the temperature of the conductor (t, usually in
kelvin or DC).
To determine the resistance of a conductor at a
constant temperature, the following formula must
be used:
R=£i
R=Ei
a
............ '
Q)
Where R is in ohms (n)
I is in metres (m)
p is in ohm-metres (n.m)
a is in square metres (m 2)
2.3 Resistance
• Remember that a is the cross-sectional area and
not the diameter of the conductor.
There are good and bad conductors, but a perfect
conductor does not exist. The process whereby an
electron travels through a conductor with difficulty,
and does not move instantly, but in fact very slowly
from point A to point B, is known as resistance.
Resistance is expressed as R and measured in ohms
(symbol Q).
Example 2.1
A conductor is 1 m long and has a diameter of 0,2
mm. Its resistivity is 0,001 7 Iln.m.
J..ln.m. The conductor
is round. Determine the resistance of the conductor
in ohm.
2.3.1 Resistivity
I
R == -P and a
a
We already know that the availability of free electrons determines the conductivity of a conductor.
This characteristic also has a special name: resistivity (p-Greek rho). The unit of resistivity is the
ohm-metre (n.m). It is sometimes known as the
con- ductivity of a conductor and is determined by
the material ofwhich a conductor is made.
rr.d2
=-
4
therefore: R
0,0017 x 10-6 x 1 x 4
1£
rr. x
(0,2 xX10- 3)2
0,001 7 x 10 -h
1t
== 0,054113 n
7
X
1x 4
x 0,2 X 10-h
= 54,113 rnn
P 14
/4
=-''2
rr. d
You can see from this example how low the resistance of a copper conductor of 1 m is.
Milli-ohm and ohm are known quantities; thousands and millions ofohms are known as kilo-ohms
and mega-ohms and are written as follows:
• The voltage necessary to force a given amount of
current through a circuit is equal to the product of
the current and the resistance of the circuit.
• 1 000 ohm as 1 kQ;
• 1 200 ohm as 1,2 kn (and sometimes just Ik2);
• 1 200 000 ohm as 1,2 MQ (or just 1M2).
Where V = voltage
I = current in amperes
R = resistance in ohms
• The current in a circuit is equal to the voltage
applied to the circuit divided by the resistance of
the circuit.
@
V=lxR
2.3.4 Definition
1=~
l=~
The definition of the ohm (not Ohm's law) is:
• A conductor has a resistance of one ohm when a
voltage of one volt across it causes a current of
one ampere to flow through it.
Voltage is applied across a conductor and causes the
current to flow through the conductor. The amount
of current is detennined by the resist~nce of the
conductor as well as the voltage applied to the
colMklctor.
coJMklctor.
As already stated, this is true only for one temperature. To detennine the resistance at different
temperatures, the temperature coefficient (a) must
be used. This is expressed in O/oC.
n/oc. The formula is:
R, = Ro(l +uoL\,)
............................. @
@)
R
• The resistance of a circuit is equal to the voltage
applied to the circuit divided by the amount of
current in the circuit.
R=~
~
I
Ohm's law shows that the current is directly propor"'' '
As can be seen in equation 4, the R in the denominator shows that with the voltage V constant, the
current I is inversely proportional to the resistance R.
If the resistance increases, then the current will
If
decrease in the same ratio; similarly, a decrease in
resistance results in an increase in current.
An easy way to remember Ohm's law fonnulas is
by means of a triangle as in fig. 2.2.
tional to the voltage.
Q)
Where Ro is the resistance at O°C
Rl the resistance at t °c
°C
U
0. o
0 is the temperature coefficient at DoC
~t the change in temperature
Ie ..,
2.4 Ohm's law
The name Ohm's law is given to a formula which
relates the voltage, current and resistance i~ a circuit. A knowledge ofthis relationship is essential if
the operation of circuits is to be understood.
In a circuit supplied by a source of dc
de voltage, the
opposition to the current is the resistance. There is,
in fact, a definite relationship between the voltage,
the current and the resistance. This relationship was
discovered by Georg Simon Ohm in 1827 and is
known as Ohm's law. It can be stated in three ways:
V=IxR
Fig. 2.2
8
V
1=R
V
R=I
To use this triangle, cover the quantity you want and
the relationship of the other two will indicate how
the chosen quantity can be calculated.
Ohm's law is the most important law in electricity
and electronics; before you go any further, make
sure you know how to use it.
When resistive components are connected in series, the current in the circuit must overcome the
resistance of each component as it passes through
the complete circuit. The total resistance to current
in the circuit is then, in effect, equal to the sum of
the various resistances in the circuit or
R1
= R) + ~ + R3 + . . . Rn
Where R{
2.5
Resistance in series and parallel
2.5.1 The series circuit
R) , R12 , R3
••••••••••••
®
total resistance
=
• ••
resistances in the circuit
Example 2.2
There is only one path for electrons to flow in a
series circuit. The path consists ofthe conductor and
the components that are connected one after another
as in fig. 2.3.
A 270,
27 n, a 1500
150 n and a 2 7000
700 n resistor are connected
in series. Calculate the total resistance.
RI=R,+~+R3
=
= 27 + 150+ 2 700
= 2877 n
to voltage
source
Since the magnitude of the current flowing through
each component of a series circuit is the same, the
circuit voltage must be distributed among the components of the circuit in direct proportion to their
resistance in order for the current to be maintained.
The sum of the voltage drops in any series circuit
is always equal to the voltage that is applied to the
circuit. This relationship, known as Kirchoff's law
.for voltage, is expressed by the following formula:
+
(a)
to voltage
source
~
=V
R1
+ VR2 + VR3
Where ~
VR1 , VR2 , VR3
+
= total (applied) voltage
= voltage drops across
circuit components
(b)
Example 2.3
Fig. 2.3
A 90 volt voltage source is connected in series with
a 20 0, a 100 n and a 180 n resistor as in fig. 2.4.
Calculate the voltage drop across each resistor.
To solve this problem, it is first necessary to
determine the magnitude of the current in the
circuit:
I fthe circuit is broken or opened at any point, it becomes
inoperative, as there is no longer a continuous path
through which electrons can move; see fig. 2.3 (b).
Electrons are not consumed as they flow through
a circuit. There is as much current movingfrom any
point in a series circuit as there is moving to that
point. Therefore, the same magnitude of current
passes through all of the components in a series
circuit.
V
1=- (Ohm's law)
R
90
=~=03 A
20+100+180
20 + 100 + 180 300
'
9