Electrical
Workmanship
Student’s Book
FET FIRST
NQF Level 4
S. Jowaheer FET FIRST Electrical Workmanship NQF Level 4 Student’s Book
© S. Jowaheer, 2008
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First published 2008 by
Troupant Publishers (Pty) Ltd
P O Box 4532
Northcliff
2115
Distributed by Macmillan South Africa (Pty) Ltd
Cover design by René de Wet
Typeset by Lebone Publishing Services, Cape Town
Edited by Brendan Peacock
Artwork by Sean Strydom
Proofread by Irene Cornelissen
ISBN: 978-1-920311-22-3, eISBN: 978-1-430801-64-1
While every effort has been made to ensure the information published in this work is accurate,
the authors, editors, publishers and printers take no responsibility for any loss or damage suffered
by any person as a result of reliance upon the information contained therein. The publishers
respectfully advise readers to obtain professional advice concerning the content.
Acknowledgements: Material in this book has been taken from the works of
B. Brown, V. Nicholson, R. van Zyl, L. Caren Johnson and A. Thorne.
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Contents
Topic 1: Typical electrical installations
1
Summative assessment
143
Module 1: Electrical installations 2
Topic 5: Safety and first aid
147
Module 5: Safety
148
Unit 5.1: Safety and hazards
Unit 5.2: Working in elevated positions
Unit 5.3: Power tool and electrical equipment
safety
Unit 5.4: Safety with machinery
Unit 5.5: Personal protective equipment (PPE)
Summative assessment
148
160
166
178
183
195
Module 6: Acts and regulations
196
Unit 1.1: Electric circuit diagrams
Unit 1.2: IEC symbols and SI units
Unit 1.3: AC theory and network analysis
Unit 1.4: Electromagnetic theory
Unit 1.5: Basic regulations
Summative assessment
2
10
20
37
45
50
Topic 2: Domestic appliances
53
Module 2: Operating and maintaining
domestic appliances
54
Unit 2.1: Operating principles of domestic
appliances
Unit 2.2: Maintenance of domestic appliances
Unit 2.3: Regulations and wiring of stove plates
Unit 2.4: Replacing components Summative assessment
54
65
80
83
87
Topic 3: Low voltage transformers and
switchgear
89
Module 3: Testing and inspecting of low
voltage transformer and switchgear
90
Unit 3.1: Worksite procedures
Unit 3.2: Low-voltage transformers
Unit 3.3: Low-voltage switchgear
Summative assessment
91
107
111
116
Topic 4: Electrical machines and control
gear
117
Module 4: Installing and commissioning
electrical machines and control gear
118
Unit 4.1: Unit 4.2: Unit 4.3:
Installation of motors and important
regulations
118
Connecting motors
128
Inspection, maintenance and cleaning
of electric machines and control gear 136
Unit 6.1: Occupational Health and Safety
Act 85 of 1993 (OHSA)
Unit 6.2: The Mine Health and Safety
Act of 1996 (MHSA)
Unit 6.3: NOSA
Unit 6.4: Safety, health and the environment
(SHE) principles
Summative assessment
212
221
Module 7: Safety checks in the workplace
222
Unit 7.1: Risk assessment and control
procedures
Summative assessment
222
229
Module 8: Understanding and applying
first aid
230
Unit 8.1: First aid concepts
Unit 8.2: Rendering first aid
Unit 8.3: Human anatomy and physiology
Unit 8.4: Assessing an accident scene
Summative assessment
230
238
255
259
275
PoE Guideline Glossary 277
284
196
204
210
Topic 1
Typical electrical
installations
Module 1
Electrical installations
Overview
In this module you will:
• Read and interpret electric circuit diagrams
• Use and describe electrical and mechanical quantities correctly
• Understand and use DC theory and network analysis in solving
RLC circuits
• Understand the application of electromagnetic theory in electric
machines and transformers
• Have a basic knowledge of and be able to interpret and apply
SABS 0142 SANS 10142 regulations.
Unit 1.1: Electric circuit diagrams
Unit outcomes
By the end of this unit you should be able to:
• Discuss basic electric circuit diagrams.
• Read and interpret electric circuit diagrams.
The ability to read and understand information contained on electric
circuit diagrams is essential to perform most electrical-related jobs.
To know how to read a diagram it is necessary to be familiar with the
standard conventions, rules and basic symbols used on the various
types of diagrams.
Electrical diagrams are designed to present functional information
about the electrical design of a system or component, for example:
• Relay-contactor diagrams
• House wiring diagrams
• Electrical machine diagrams
• Low-voltage switchyard diagrams
Basic symbols
Switches
A switch is used to open or close a circuit. When the circuit is open
current flows, while breaking (or opening) the circuit will stop the
current from flowing. There are different types of switches depending
on how many wires go into the switch and how many come out of it.
You have studied such switches in Level 2 and Level 3.
The four basic types of switches are:
• Single-pole single-throw (SPST)
Module 1: Electrical installations
• Single-pole double-throw (SPDT)
• Double-pole single-throw (DPST)
• Double-pole double-throw (DPDT)
Fig. 1.1: Single-pole single-throw (SPST)
Some common types of switch symbols are shown here – these
are single-pole and double-pole, but remember that a switch can
have as many poles as necessary to perform its function. The
term “throw” refers to the number of circuits that each pole of a
switch can complete or control.
Fig. 1.2: Single-pole double-throw (SPDT)
Single-pole single-throw (SPST)
An on-off switch allows current to flow only when it is in the
closed (on) position.
Single-pole double-throw (SPDT)
A two-way changeover switch directs the flow of current to one
of two routes according to its position. Some SPDT switches have
a central off position and are described as ‘on-off-on’.
Fig. 1.3: Double-pole single-throw (DPST)
Double-pole single-throw (DPST)
This is a dual on-off switch, which is often used to switch
mains electricity because it can isolate both the live and neutral
connections.
Double-pole double-throw (DPDT)
This switch can be wired up as a reversing switch for a motor.
Some DPDT switches have a central off position.
Fig. 1.4: Double-pole double-throw
(DPDT)
Push switches or buttons
Push switches or buttons are also used and the two basic
types are:
• Push to make.
• Push to break.
Push to make
A push switch allows current to flow only when the
button is pressed. An example that you should be
familiar with is the doorbell button. Its contacts are
normally open (NO).
Fig. 1.5: Push button, normally open (NO)
Fig. 1.6: Push button, normally closed (NC)
Push to break
This type of push switch is normally closed (on). It is open
(off) only when the button is pressed. Its contacts are normally
closed (NC).
Figure 1.7 depicts the symbol for a multi-position switch:
Fig. 1.7: Multi-position switch
Module 1: Electrical installations
Guidelines for drawing circuit diagrams
A circuit diagram should be drawn in such a way that it allows the
reader to identify its purpose. When drawing circuit diagrams you
should:
• Use the correct symbols.
• Use a suitable symbol orientation.
• Pay attention to the arrangement of symbols on the diagram.
• Pay attention to the routing of interconnections.
• Make sure your drawing is neat and tidy.
Relay coil
Relay contactor diagrams
Control relays
These types of relays are used as auxiliary devices to control circuits
and large motor starters, contactor coils, small loads such as small
motors, solenoids and other relays.
Fig. 1.8: Relay coil
Basic contact (make)
A magnetic relay is operated by an electromagnet, which opens or
closes an electrical contact when the electromagnet is energised.
Contactors
Magnetic contactors are electromagnetically operated switches that
provide a safe and convenient means for connecting and interrupting
branch circuits
Fig. 1.9: Basic contact (make)
Basic contact (break)
In the margin are some basic symbols that you need to be familiar with.
Fig. 1.10: Basic contact (break)
Reading and interpreting electric circuit
diagrams
To read and interpret electrical diagrams properly,
the condition or state of each component must first
be understood. In diagrams the details of individual
relays and contacts are always drawn in the deenergised state (that is, in the “off ” condition). Each
relay (with its contact(s) that it operates) is assigned a
letter or number. Figure 1.11 shows a simple diagram
consisting of a coil labelled m1 on the drawing.
Figure 1.12 shows another basic circuit consisting of
a coil labelled CR1 and two lamps: green (G) and red
(R) respectively.
When the double-pole switch is closed, current flows
through from L1 to the normally closed contact of
CR2 and then through (R) the red lamp. When the
normally open push button is closed, the CR1 coil is
energised and closes the normally open CR1 contact
to energise (G) the green lamp, at the same time
switching off the red lamp. When the push button is
released the red lamp comes on again.
240 Volt AC
transformer
120 Volt AC circuit
start
fuse stop
relay overloads
10A switch switch
holding
M1
M1 contacts
Fig. 1.11: Basic relay and contacts circuit
L1
N
relay
CR1
CR1
CR2
G
G =green
lamp
R =red lamp
R
Fig. 1.12: Simple relay control diagram
Module 1: Electrical installations
Figure 1.13 shows basic No-Voltage protection circuitry.
When there is no voltage the starter will drop but will not
automatically restart itself. The control circuit is achieved
through the stop button and the holding contact M
connected between 2 and 3 on the diagram. To restart the
motor the start button must be pressed again.
Figure 1.14 shows a tumble dryer heater circuit.
stop
1
L1
start
2
timer
heater
motor speed
SW
O.L. (overload)
M
M
T1
M
control
limit
thermostat thermostat
3
L2
T2
M
L3
3
phase
motor
T3
Fig. 1.13: No-Voltage protection circuitry
Fig. 1.14: Tumble dryer heater circuit
Wiring diagrams
A wiring diagram shows every wire terminal connection and all the
component circuitry. These diagrams are essential, especially when
fault-finding.
timer motor
BR
switch (sw)
BU
B
BU
W
BR
Legend
B – Black
BU – Blue
BR – Brown
W – White
Fig. 1.15: Wiring diagram for a motor timer
Assessment activity 1.1
Work in groups of five
Refer to Figure 1.11 and answer the following questions:
1. What type of transformer is being used?
2. What is the rating of the fuse used?
3. How many emergency stop switches are there in the circuit?
4. How many start switches are there in the circuit?
5. Is contact labelled M1 normally open (NO) or a normally closed (NC)?
Module 1: Electrical installations
House wiring
Words &
Terms
Lighting circuits
To wire up a lighting circuit,
accessories such as cables, screw
connectors, lamp-holder and a switch
are required. All circuits must include
a protection device such as a circuit
breaker and the switch must be
placed on the live side of the circuit.
The following circuit diagrams show
the correct way to wire sub-circuits.
Do not install a single-pole
switch in the neutral conductor
of the circuit.
A batten lamp holder or a lamp
holder suspended by a flexible
cord is a luminaire.
One luminaire control from one switch
L
lumin
Note
bulb
circuit breaker
switch
N
Fig. 1.16: One luminaire controlled from one switch
Two luminaires controlled from one switch
L
N
Fig. 1.17: Two luminaires controlled from one switch
Two luminaires controlled from one switch
L
N
Fig. 1.18: Two luminaires controlled from one switch
One luminaire controlled from two switches
Sometimes it is necessary to control a light independently from two
switches. Such configuration is necessary for staircases, where you
have a switch at the bottom and top of the stairs. Two-way switches are
necessary for this type of configuration, shown in the circuit diagram
in Figure 1.19.
Module 1: Electrical installations
aire: appliance
that distribute
s, filters
or transforms
the light
transmitted fr
om one
or more lamps
and that
includes all th
e parts
necessary for
supporting,
fixing and prot
ecting
the lamps bu
t not the
lamps themse
lves, and,
when necess
ary, circuit
auxiliaries toge
ther with the
means for co
nnecting them
to the supply.
(Source:
SANS 101421:2006)
The live wire is connected to terminal
A of the first two-way switch. The
movement of the switch makes contact
L
from the common terminal A to either
terminal B or terminal C. Another
two-way switch is positioned farther
away from the first one. Two wires
are run from B to B1 and C to C1.The
N
diagram shows the circuit in open position
– movement of either switch will make the
circuit and the lamp will light.
C
A
two way
switch
B
bulb
C1
A1
B1
Fig. 1.19: One luminaire control from two switches
In a room that contains a fixed bath or shower cubicle, luminaires must
be totally enclosed (or parts of the lamp holder) if they are within a
distance of 2,5 m from the bath or the shower cubicle. They must also
be constructed of, or shrouded in, insulating material.
Socket outlet circuits
L
A socket outlet must be controlled by means of a
switch on each live conductor.
Note
Earthing in the luminaire
circuits has been removed for
diagram clarity.
circuit breaker
E
The socket outlet is connected in such a way that
each socket outlet is supplied from the previous
one. Based on the size of the installation a
different circuit breaker will control each section
of the installation, so using commonsense is of
utmost importance. This type of circuit is also
known as radial circuit.
socket
outlet
switch
N
In a ring circuit the final socket outlet is wired
Fig. 1.20: Two sockets supplied from one circuit breaker
back to the supply, so any socket outlet is supplied
from two directions. This is not a common method of installation in
South Africa.
A socket outlet must not be installed within a radius of 2 m of a water
tap (in the same room), unless the socket outlet:
• Has earth leakage protection.
• Is connected to a safety supply.
Geyser circuits
A double-pole switch must be installed within arm’s reach of the
geyser, unless the geyser is designed with an isolator built in. Every
geyser should also be fitted with a relief value to allow for expansion
and as an outlet for steam in case the thermostat fails to regulate the
temperature.
Geysers are required
to be bonded and
dedicated circuits
L
must be provided.
Remember that
N
there may be more
E
than one water
heater on each
circuit.
circuit
breaker
ripple
relay
double-pole switch
thermostat
element
geyser
Fig.1.21: A geyser circuit including isolator and ripple relay
Module 1: Electrical installations
Stove circuits
Any circuit that supplies a cooking appliance
through fixed wiring, a stove coupler or an
industrial-type socket outlet must have a
readily accessible switch disconnector. The
switch disconnector may supply more than
one appliance.
L1
L
L2
N
L3
E
E
bridged
together
i.e. joined
N
Recommended sizes of conductors
for domestic installations
back of
stove
Fig. 1.22: Single-phase stove circuit including isolator
Table 1.1 shows examples of recommended
conductor sizes:
Note
Circuits
Size of wire
Lights
1,5 mm2
Socket outlet
2,5 mm2
Geyser
4 mm2
Stove
8/10 mm2
L1, L2 and L3 are joined or
bridged together.
Table 1.1: Examples of recommended conductor sizes
Distribution boards
Figure 1.23 shows the wiring for the distribution board, but it should be
noted that in this case the earth leakage has built-in overload protection.
If, however, the earth leakage that you are using does not have overload
protection facilities then an additional circuit breaker should be used.
Sometimes only certain circuits are protected by earth leakage, for
example, if only socket outlets are protected then the distribution
board will require two neutral bars. Your lecturer will demonstrate the
different types of distribution board wirings.
main circuit breaker or earth
leakage relay
neutral bar
line
Note
Each distribution board must
be controlled by a switchdisconnector.
Note
Surge protection devices, as
shown in Figure 1.24, should
be installed at least in the
main distribution board of an
electrical installation.
1 A 20 A 35 A 10 A 20 A
N
L
N
socket
lights
stove
L
line
geyser
bel
L N E
from meter box
earth bar
Fig. 1.23: Distribution wiring, all circuits on earth leakage
Module 1: Electrical installations
Fig. 1.24: A
single-phase surge
protection device
Assessment activity 1.2
Work in groups of two.
1. With reference to Fig 1.19 and Fig 1.21, explain in your own words how the circuit operates.
2. Draw a simple circuit diagram to show how a single-phase surge protection device is installed in
a main distribution board.
3. List three items that a designer of an electrical installation should be aware of.
4. In SANS 10142-1 the word ‘shall’ is used. Explain the meaning of the word.
5. Name at least three parts that need to be bonded in an electrical installation.
6. Demonstrate to your partner by means of a suitable sketch the meaning of ‘arm’s reach’.
7. Your partner does not understand Regulation 6.16.3.1.1 (Switch disconnector). Explain this
regulation in simpler words to him or her.
8. Draw a floor plan of your electrical workshop, including dimensions.
9. Draw an electrical plan of your workshop showing various electrical components and their
locations, clearly showing the electrical legend used.
10.Draw a circuit diagram for the following subcircuits:
10.1
One luminaire control from two switches.
10.2 Three socket outlets supplied from one circuit breaker.
(Assume you have to practically wire up the above subcircuit. Make a list of tools and materials
required for the successful execution of the task.)
Module 1: Electrical installations
Unit 1.2: IEC symbols and SI units
Unit outcomes
By the end of this unit you should be able to:
• Use and describe International Electrotechnical Commission
(IEC) and Système international d’unités (SI) symbols, units and
abbreviations for electrical and mechanical quantities correctly.
Overview
Graphical symbols appear everywhere, such as on public information
and safety signs. Misunderstanding or misinterpreting the correct
meaning of these symbols could have fatal consequences, which is why
the same IEC symbols are used worldwide to ensure understanding.
A typical symbol with which we are all familiar is the power symbol
(see Figure 1.25) which indicates that a control activates or deactivates
a particular device. It consists of a line and circle.
Examples:
• The power on (line) symbol, appearing on a button or one end of a
toggle switch, indicates that the control places the equipment into a
fully powered state.
• The power off (circle) symbol on a button or toggle indicates that
using the control will disconnect power to the device.
• The power on-off symbol (line within a circle), is used on buttons
that switch a device both on and off.
Fig. 1.25: Power symbol
Electrical wiring symbols
Table 1.2 shows the most common electrical wiring symbols. These
symbols are used to represent wiring, components and apparatus in
circuit diagrams.
10
Single-pole switch
Refers to
alternating current
Push-button switch
Two-way switch
Refers to direct
current
Generator
Double pole
isolator
Motor
Transformer
AC motor
Cell
Coil
Cross over
DC motor
Earth connection
Module 1: Electrical installations
Circuit breaker
Capacitor
Resistor
Fuse
Lamp
Battery
Bell
Table 1.2: Electrical wiring symbols
Systems of measurement
How do we measure things, and why do we do it? Measuring
allows us to be accurate about what we say and do. As a student
you will need to make measurements and perform calculations and
the end results can be meaningless unless they are numerically and
dimensionally correct and have the proper accuracy. For example,
one can say that the length of the classroom is 10. Ten what? Units
of measurement provide a common way of understanding what the
quantity is that is being described.
Words &
Terms
There are different ways of measuring things:
• We can measure things that do not have a value that can be
expressed as a number – such as colour or hair texture, clothing size.
These things are often measured by what they are like in relation to
other things. For example, size 16 is larger than size 10.
• Some measurement systems, such as measuring temperature
using a Celsius scale, describe the extent of difference between
two values.
• In other measurement systems all the units of measurement are
uniform. Some units of measurement use other units to describe
what is being measured. For example, velocity is described as
metres per second – in other words by using units of distance
and time.
units: a particul
ar physical
quantity, defin
ed and
adopted by co
nvention,
with which ot
her particular
quantities of
the same kind
are compared
to express
their value
physic
al quantity: a
quantity that
can be used in
the mathemat
ical equations
of science an
d technology.
Measurement is a key aspect of electrical engineering because it is
essential for efficient production in engineering:
• Measurements are usually of physical quantities – things such as
distances, sizes, temperature or energy.
• Measurements are expressed according to standard units.
• Measurements are usually given as real numbers.
• Almost all measurements involve a certain amount (or likelihood) of
error, and calculations and designs take this into account.
In Electrical Workmanship Level 2 and Level 3 you looked at different
tools used for measuring certain values such as thermometers,
tachometers and voltmeters.
The most commonly used system of measurement is the metric system:
• There are base units for each physical quantity, such as the metre
(for distance) and the gram (for mass). These units are used globally.
Module 1: Electrical installations
11
• All units are related by powers of ten and are identified by prefixes.
This makes conversion of units easier. For example, it is easy to
convert by simply moving the decimal point – 1,456 metres is 1456
millimetres or 0,001456 kilometres.
• Today the current international standard metric system is the
International System of Units or Système international d’unités
(shortened to SI).
The international system of units
Did you know?
There are many possible
causes of error that need to
be taken into account when
measuring:
• Carelessness.
There are different types of SI units:
• Base units are the most simple or basic measurements for time,
length, mass, temperature, amount of substance, electric current and
light intensity.
• Derived units are made up by combining base units, for example,
density is kg/m3; velocity is m/s.
• Damaged tools.
• Accuracy of equipment.
The metric system
Length 10 millimetres = 1 centimetre
10 centimetres = 1 decimeter
10 decimetres = 1 metre
10 metres = 1 decametre
10 decametres = 1 hectometre
10 hectometres = 1 kilometre
1 000 metres = 1 kilometre
Area
100 sq. mm = 1 sq. cm
10 000 sq. cm = 1 sq. metre
4 046,86 sq. metres = 1 acre
1 acre = 0,405 hectare
10 000 sq. metres = 1 hectare
100 hectares = 1 sq. kilometre
1 000 000 sq. metres = 1 sq. kilometre
Volume
1 000 cu. mm = 1 cu. cm
1 000 cu. cm = 1 cu. decimetre
1 000 cu. dm = 1 cu. metre
1 million cu. cm = 1 cu. metre
Capacity
10 millilitres = 1 centilitre
10 centilitree = 1 decilitre
10 decilitres = 1 litre
1 000 litres = 1 cu. metre
Mass
1 000 grams = 1 kilogram
1 000 kilograms = 1 tonne
There are seven basic SI units, two supplementary units and many
derived units. The base units are combined to form the derived units.
1. The seven basic SI units are:
Quantity
Unit
Unit Symbol
metre
m
Mass
kilogram
kg
Time
second
s
Electric current
ampere
A
Thermodynamic temperature
kelvin
K
Amount of substance
mole
mol
candela
cd
Length
Luminous intensity
Table 1.3: Seven basic SI units
12
Module 1: Electrical installations
Did you know?
The SI units were
acknowledged by 36
countries at the 11th General
Conference on Weights and
Measures held in France in
1960.
The table below provides details about the different units of
measurements used in science and engineering:
metre: (m)
The metre is the basic unit of length. It is also the length equal to 1 650 763,73 times
the wavelength of the orange line in the spectrum of an internationally specified krypton
discharge lamp. Light travels this distance, in a vacuum, in 1/299792458th of a second.
kilogram: (kg)
The kilogram is the basic unit of mass. The kilogram is the mass of a platinum-iridium
cylinder preserved at the international Bureau of Weights and measures at Sèvres, near
Paris, France. It is the only basic unit that is defined with a prefix (kilo) already in place.
second: (s)
The second is the basic unit of time. It is the length of time taken for 9192631770 periods
of vibration of the caesium-133 atom to occur.
ampere: (A)
The ampere is the basic unit of electric current. It is that current which produces a
specified force between two parallel wires which are 1 metre apart in a vacuum.
kelvin: (K)
The degree kelvin is the basic unit of temperature. The kelvin unit of thermodynamic
temperature is the fraction 1/273,16 of the thermodynamic temperature of the triple
point of water.
mole: (mol)
The mole is the basic unit of substance. A mole (mol) is defined as the amount of the
substance which contains as many particles as there are carbon atoms in 0,012 kg (12 g)
of carbon-12.
candela: (cd)
The candela is the basic unit of luminous intensity. It is the intensity of a source of light
of a specified frequency, which gives a specified amount of power in a given direction.
Table 1.4: Information about units of measurement
There are strict rules about writing SI units of measurements:
• A unit has only one prefix, i.e. there is no such thing as
kilomillimetre.
• If prefixes make a unit bigger they are written in capital letters (M,
G, T, etc.), but when they make a unit smaller they are written in
lower case. (m, n, p, etc.), except for the kilo (k) so it is not confused
with kelvin (K).
• Units are written in lower case (newton, volt, pascal, etc.) when they
are used in full, but with a capital letter (N, V, Pa, etc.) when they
are written as abbreviations, except for the litre which is written as l.
• Units written in abbreviated form are always singular. So ‘m’ could
be either ‘metre’ or ‘metres’, to avoid confusion with ‘ms’ (meaning
‘millisecond’).
Did you know?
André Marie Ampére (1775-1836) was the French
physicist who laid the foundations of electrodynamics.
He was born near Lyons and as a child showed great
aptitude for mathematics. In 1820 he published his
paper on the magnetic effects of electric currents.
The unit of current is named after him.
William Thomson Kelvin (1824-1907) was born in Belfast,
Ireland. The son of a mathematics professor, he graduated
in 1845 at the University of Cambridge and after spending a
year in Paris working, he returned to Glasgow as a professor
of natural philosophy – a position he held for 53 years. We
owe the absolute scale of temperature (°K) to him.
Module 1: Electrical installations
13
Assessment activity 1.3
Work on your own
1. Fill in the table below, with the correct quantity symbol:
Quantity
Quantity symbol
Length
Time
Mass
Luminous intensity
Temperature
Amount of substance
2. Discuss what you know about systems of measurement for:
a) Length
b) Time
c) Mass
Discuss your answer with other class members when you are finished.
Derived units of measurement
Some of the most important derived units of measurements are:
Acceleration
Acceleration is calculated as the metres that an object moves per
second squared.
Force and the newton (N)
This is the SI unit of force. One newton is the force required to give a
mass of 1 kilogram an acceleration of 1 metre per second per second. In
other words, one Newton is one kilogram metre per second squared.
Force, (in newtons) is given as F = m.a (where m is mass in kilograms
and a is the acceleration in metres per second squared).
Gravitational force (otherwise known as ‘weight’) is given as mg,
where g = 9,81 m/s2.
Example 1
Determine the force needed for a body of mass 500 g which is
accelerated at 3 m/s2.
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Module 1: Electrical installations
Data:
mass = 500 g
= 0.5 kg
acceleration = 3m/s2
force = ?
Using:
force = mass × acceleration
= 0.5 × 3
kg.m
= 1.5
s2
= 1.5 N
Work and the joule
The joule (J) is the SI unit of work or energy. Energy is the capacity for
doing work.
One joule is also known as one newton-metre because the joule is
defined as the work done or energy transferred when a force of one
newton is exerted through a distance of one metre in the direction
of the force. Thus, work done in joules = FS (where F is the force in
Newtons and S is the distance in metres).
Resistance and the ohm
The ohm (Ω) is the SI unit of resistance of an electrical conductor. Its
symbol is the capital Greek letter ‘omega’. The ohm is defined as the
resistance between two points in a conductor when a constant electric
potential of one volt applied at two points produces a current flow of
one ampere in the conductor.
 resistance in ohms = R = V (where V is the potential difference
I
across the two points in volts and I is the current flowing between the
two points in amperes).
Pressure and the pascal
The pascal (Pa) is the SI unit of pressure. One pascal is the pressure
generated by a force of 1 newton acting on an area of 1 square metre.
Pressure is often expressed in kilopascals (kPa) in most everyday
calculations, since one pascal is extremely “light” pressure.
Electric potential and the volt
The volt (V) is the SI unit of electric potential, where one volt is one
joule per coulomb. One volt is defined as the difference in potential
between two points in a conductor which, when carrying a current of
one ampere, dissipates a power of one watt.
joules/second
Volts = watts =
amperes
amperes
=
joules
joules
=
ampere.seconds
coulombs
Module 1: Electrical installations
15
Power and the watt
The watt (W) measures power, or the rate of doing work. One watt is a
power of 1 joule per second. Power is defined as the rate of doing work
or transferring energy.
 power in watts P = w (where W is the work done in joules and t is
t
the time in seconds).
 energy, in joules is given as W = Pt.
Summary of terms, units and their symbols:
Quantity
Quantity symbol
Unit
Unit symbol
Acceleration
a
metres per second squared
m/s2 or m.s–2
Force
F
Newton
N
Work
W
joule
J
Resistance
R
ohm

Potential difference
V
Volts
V
Pressure
Pa
Pascal
Pa or kPa
Power
P
watt
W
Supplementary units of measurement
There are two units that are used to measure planes and solid angles.
Name
Symbol
Quantity
Definition
radian
rad
Plane angle
The unit of angle is the angle subtended at the centre of a circle by
an arc of the circumference equal in length to the radius of the circle.
There are 2 radians in a circle.
steradian
sr
Solid angle
The unit of solid angle is the solid angle subtended at the centre of a
sphere of radius r by a portion of the surface of the sphere having an
area r2. There are 4 steradians on a sphere.
Did you know?
Sir Isaac Newton (1642-1727) was an English scientist born on Christmas day,
1642. He studied at Cambridge University and later produced his masterpiece
publication, Philosophiae naturalis principia mathematica, usually called “The
Principia”. This book made him instantly famous across Europe though few
people could understand the work at the time. The unit of force is named after
him.
George Simon Ohm (1787-1854) was a physics teacher who did much of
his research on electricity in a school laboratory. He was born in Erlangen,
Germany, the son of a master locksmith. We owe the unit of resistance to his
work.
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Module 1: Electrical installations
Did you know?
Count Alessandro Volta (1745-1827) was an Italian physicist whose research in
electricity led him to the invention in 1800 of the voltaic pile, the first device to
produce a continuous electric current. The volt is named after him.
James Prescott Joule (1818-1889) was an English physicist and formulator
of the law of conversion of energy. Although a wealthy brewery owner, he
preferred scientific research. The unit of energy is named after him.
James Watt (1736-1819) was the inventor of the first efficient steam engine.
Born in Scotland, he attended local schools and had a short apprenticeship
in London as a scientific instrument maker. He had exceptional manual skills
and mathematical interest. The unit of power is named after him.
Examples of other SI derived units that are expressed in terms of SI
base units and SI supplementary units:
Quantity
SI unit
Name
Symbol
acceleration
metre per second squared
m/s2
angular acceleration
radian per second squared
rad/s2
angular momentum
kilogram meter squared per second
angular velocity
radian per second
area
square metre
density
kilogram per cubic metre
kg/m3
luminance
candela per square metre
cd/m2
magnetic field strength
ampere per metre
A/m
mass flow rate
kilogram per second
kg/s
mass per unit area
kilogram per square metre
kg/m2
mass per unit length
kilogram per metre
kg/m
momentum
kilogram metre per second
rotational frequency
1 per second
specific volume
cubic metre per kilogram
speed
metre per second
m/s
velocity
metre per second
m/s
volume
cubic metre
m3
kg.m2/s
rad/s
m2
kg.m/s
s–1
m3/kg
Table 1.5: Other SI derived units
Module 1: Electrical installations
17
Assessment activity 1.4
Work in groups of five
1. Match Column A to Column B:
Column A (Quantity)
Column B (Unit Symbol)
1.1 Acceleration
(a) Pa
1.2 Force
(b) W
1.3 Power
(c) m/s2
1.4 Energy
(d) N
1.5 Pressure
(e) J
1.6 Volume
(f) m3
1.7 Area
(g) m2
2. If density is defined as mass per unit volume, derive the unit symbol for density.
SI unit conversion
SI units make it easy to convert when switching from different
units that have the same base but a different prefix, by using simple
multiplication or division.
SI units may be made larger or smaller by using prefixes (which denote
multiplication or division by a particular amount). The most common
multiples (with their meanings) are listed below:
Symbol
Prefix
From the base unit...
T
tera
multiply by 1 000 000 000 000
× 1012
G
giga
multiply by 1 000 000 000
× 109
M
mega
multiply by 1 000 000
× 106
k
kilo
multiply by 1 000
× 103
h
hecto
multiply by 100
× 102
d
deci (a tenth)
divide by 10 (or multiply by 0,1)
× 10–1
c
centi (a hundredth)
divide by 100 (or multiply by 0,01)
× 10–2
m
milli (a thousandth)
divide by 1 000 (or multiply by 0,001)
×10–3

micro (a millionth)
divide by 1 000 000
×10–6
n
nano
divide by 1 000 000 000
×10–9
p
pico
divide by 1 000 000 000 000
×10–12
Table 1.6: Most common multiples and their meanings
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Module 1: Electrical installations
Example
You will need to know the following as well:
10 mm = 1 cm
100 mg = 1 g
1 000 ml = 1 l
100 mm = 1 m
1 000 g = 1 kg
1 000 cm3 = 1 l
1 000 m = 1 km
1 000 kg = 1 ton
Remember that:
• When you change from small units to large units you divide.
• When you change from large units to small units you multiply.
Example 2
Convert 2 kilometres to metres.
Kilometres are larger units than metres so we need to multiply by the
number of metres in a kilometre, which is 1 000.
 2 km= 2 × 1 000 m
= 2 000 m
Example 3
Convert 250 mm to cm.
Millimetres are smaller units than centimetres, so we need to divide by
the number of millimetres in a centimetre, which is 10.
 250 mm = 250
10
= 25 cm
The following will help you to convert from mm to km and vice versa:
÷100 ÷1 000
÷10
mm
 cm

m
 km



×10
×100 ×1 000
Sometimes you will need to compare measurements. First, change all
the measurements to the same units. You can only compare like units
with like units.
Example 4
Which is heavier? 1 kg of rice or 2 000 g of pap
To find the answer, we will need to use the same unit for both:
Rice = 1 kg=1 000 g
Pap = =2 000 g
\ Pap is heavier than rice.
Example 5
Convert 100 km to miles.
Since 8 km is approximately equal to 5 miles
\ 1 km = 5 = 0,625 miles
8
hence 100 km = 100 × 0,625
Think about it
When the changes
occurred from “old” units
to “new” units (from the
imperial units to metric
units), people needed to
do conversion from the
imperial units to metric
units. They were expected
to memorise the conversion
table:
Metric
Imperial
1 kg
25 g
1l
4,5 l
8 km
1m
30 cm
2,54 cm
2,2 pounds
1 ounce
1,75 pints
1 gallon
5 miles
39 inches
1 foot
1 inch
= 62,5 miles
Module 1: Electrical installations
19
Assessment activity 1.5
Work in pairs
1. Explain to your partner the meaning of prefixes.
2. Convert these lengths to centimetres.
a) 6 m
b) 20 mm
3. Convert these lengths to metres:
a) 2 km
b) 200 cm
4. Convert these lengths to millimetres:
a) 1 cm
b) 2 cm
Think about it
5. Convert the following:
5 kg =
8 000 ml =
30 l =
1 km =
20 000 g =
• A prefix alone should
not be used to indicate a
quantity (e.g. “kilohms”,
not just “kilos”).
g
l
• A zero is used before a
decimal quality that is
less than a whole unit.
e.g. 0.3.
ml
m
kg
Unit 1.3: AC theory and network
analysis
Unit outcomes
By the end of this unit, you should be able to:
• Understand the concepts of inductive and capacitive reactance.
• Understand and use AC theory and network analysis in solving RLC
circuits (including both series and simple parallel and series-parallel
calculations).
R
Series AC circuits
Figure 1.26 shows a circuit with a resistance of R ohms and
connected across the terminal of an AC supply.
You have already learned that the magnitude of current is
directly proportional to the magnitude of the voltage, and
inversely proportional to the value of the resistance (this is
known as Ohm’s Law). It also applies to the instantaneous
values of current and voltage in an AC circuit. This means that
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Module 1: Electrical installations
IR
VR
Fig. 1.26: Circuit diagram with resistance only
at any instant when the voltage is zero, the current is also zero and
when the voltage is maximum the current must also be maximum,
since resistance is constant. See Figure 1.27.
VR
VR +
IR
IR
Note
0
time
The term “phase” is used to
indicate the time relationship
between alternating voltage
and current.
–
Fig. 1.27: Voltage and current waveforms
IR
In a purely resistive AC circuit, the current IR and the applied voltage
VR are in phase.
The phasors representing the voltage and current in a resistive circuit
are shown in Figure 1.28. The two phasors are drawn slightly apart so
that they can be distinguished from each other.
VR
Fig. 1.28: Phasor diagram for
resistive circuit
L
Inductance only
Figure 1.29 shows a circuit consisting of a coil having an
inductance of L henrys and negligible resistance.
In any AC circuit that contains only inductance there are three
quantities that can vary, namely:
IL
• The applied voltage.
• The induced back emf.
• The circuit current.
In a purely inductive AC circuit the current IL lags the applied
voltage VL by 90, or the applied voltage VL leads the current IL
by 90. See Figure 1.30.
VL +
IL
0
VL
Fig. 1.29: Circuit diagram with inductance
only
VL
270°
90°
180°
360°
IL
VL
–
Fig. 1.30: Voltage and current waveforms for purely inductive circuit
The phasors diagram for a purely inductive circuit is shown in
Figure 1.31.
IL
Fig. 1.31: Phasor diagram for a
purely inductive circuit
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21
Inductive reactance
In a purely inductive circuit (one that contains a coil or inductor) the
opposition to the flow of alternating current is called the inductive
reactance and is measured in ohms and its symbol is XL.
XL = 2pfL Ω
Where
XL = inductive reactance in ohms.
XL
(Ω)
p = a constant equal to 3,142.
f = frequency of the supply in hertz.
L= inductance in henrys
And
VL= IL × XL
Where
VL= voltage across the inductor in volts.
IL = current through the inductor in amperes.
Example 6
Calculate the inductive reactance of a coil of inductance 0,3 H if it is
connected across a 50 Hz AC supply.
Given
L= 0,3 H
f = 50 Hz
Solution
XL = 2fL Ω
= 2 × 50 × 0.3
= 94,25 Ω
Example 7
Determine the inductance of a coil if the inductive reactance is 15 
and it is connected across a supply having a frequency of 1 kHz.
Given
XL = 15 
f = 1 kHz
Solution
XL = 2fL Ω
L = XL
2rf
= 15 3
1 × 10
= 15 mH
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Module 1: Electrical installations
0
f (Hz)
Fig. 1.32: Graph of inductive
reactance (XL) against frequency (f)
Capacitance only
C
Figure 1.33 shows a circuit consisting of a capacitor C and
connected across an AC supply.
In a purely capacitive AC circuit, the current IC leads the
supply voltage VC by 90. See Figure 1.34.
VC +
Ic
VC
IC
IC
VC
0
t
Fig. 1.33: Circuit diagram with capacitance
only
Note
–
The voltage-current phase
relationship in a capacitor
circuit is exactly opposite to
that in an inductive circuit.
Fig. 1.34: Voltage and current waveforms for purely capacitive circuit
The phasors diagram for a purely capacitive circuit is shown in Figure 1.35.
Capacitive reactance
In a purely capacitive circuit (one that contains a capacitor), the
opposition to the flow of alternating current is called the capacitive
reactance. It is measured in ohms and its symbol is XC.
XC =
IC
Ω
Where
XC= capacitive reactance in ohms.
 = a constant e.g equal to 3,142.
f = frequency of the supply in hertz.
VC
C= capacitance value in farads
Fig. 1.35: Phasor diagram for a
purely capacitive circuit
And
VC= IC × XC
Where
VC= voltage across the capacitor in volts.
XC
(Ω)
IC = current through the capacitor in amperes.
The capacitive reactance is inversely proportional to the frequency
(see Figure 1.36) and the current produced by a given voltage is
proportional to the frequency.
Example 8
A 10 F capacitor is connected across a 230 V, 50 Hz supply. Calculate
the current flowing through the capacitor.
0
f (Hz)
Fig. 1.36: Graph of capacitive
reactance (XC) against frequency (f)
Module 1: Electrical installations
23
Given
C = 10 μF
VC = 230 V
f = 50 Hz
Solution
XC = 1 Ω
2rfC
1
=
2r × 50 × 10 × 10 –6
= 318,31 Ω
IC = VC
XC
= 230
318.31
= 0,723 A
Assessment activity 1.6
Work in pairs
1. State whether the following statements are true or false:
a) In a purely inductive circuit, the opposition to the flow of alternating current is called the
inductive reactance.
b) Inductive reactance is measured in ohms.
c) In a purely capacitive AC circuit, the current IC leads the supply voltage VC by 90.
d) Capacitive reactance is represented by the symbols is XC.
e) The capacitive reactance is inversely proportional to the frequency, and the current
produced by a given voltage is proportional to the frequency.
2. Calculate the inductive reactance of a coil of inductance 0,25 H if it is connected across a 150 Hz
AC supply.
3. A 45 F capacitor is connected across a 230 V, 50 Hz supply. Calculate the current flowing
through the capacitor
Series RL circuits
Figure 1.37 on page 25 shows a series RL circuit consisting of resistance
(R) and inductance (L). The combination is connected across a supply
voltage (V) with a frequency of (f) hertz. I represents the current flowing
through the circuit. The current is the same in all parts of the circuit.
In any AC series circuit the current is common to both the resistor and
the inductor, and is thus taken as the reference phasor as shown in
Figure 1.38. Therefore, the current (I) lags the supply voltage (V) by an
angle between 0 and 90.
The voltage must be added using a voltage triangle
Using Pythagoras’ Law
V2 = VR2 + VL2
24
Module 1: Electrical installations
R
L
V
VL
I
VR
VL

VR
V
I
Fig. 1.38: Phasor diagram
Fig. 1.37: Series RL circuit
V = IZ
Therefore
V=
2
VR + VL
VL = IXL
2
The total opposition to the current flow in any AC circuit is called
impedance (Z). Both resistance and reactance in an AC circuit
oppose current flow. The impedance (Z) of an AC circuit is derived
using the impedance triangle as shown in Figure 1.40.

Therefore
Z= V
I
VR = IR
As can be seen from Figure 1.40:
Fig. 1.39: Voltage triangle
Z2 = R2 + XL2
Z
Therefore
Z=
XL
2
R 2 + XL
Then tan  = XL
R
sin  = XL
Z
and cos  = R
Z
Example 9
A coil with an inductance of
0,2 H is connected in series
with a 3 Ω resistor across a
100 V, 50 Hz supply. Calculate:
a) The impedance.
b) The value of the current through the coil.
c) The phase angle.
d) The voltage across the resistor.
e) The voltage across the inductor.
Given:
L= 0,2 H, R=3 Ω, V= 100 V, f = 50 Hz

R
Fig. 1.40: Impedance triangle
Did you know?
In an AC circuit, the ratio of
the supply voltage to current
is called the impedance (Z).
Module 1: Electrical installations
25
Solution:
Inductive reactance = XL
XL = 2fL Ω
= 2 × 50 × 0,2 Ω
= 62,832 Ω
a) Impedance = Z
2
Z= R 2 + XL
= 3 2 + (62,832) 2
= 62,904 Ω
b) Impedance = Z
2
Z = R 2 + XL
= 3 2 + (62,832) 2
= 62,904 Ω
c) Current I
Using Z = V
I
V
I=
Z
= 100
62, 904
= 1,59 A
d) Phase angle = 
62,832
tan  =
3
= 20,944
 = 87,26 (lagging)
VL = 99,9 V
V = 100 V
e) Voltage across resistor = VR
VR = I × R
= 1,59 × 3
= 4,77 V
f) Voltage across inductor = VL
VL= I × XL
= 1,59 × 62,832
= 99,9V
VR = 4,77 V
I = 1,59 A
Fig. 1.41: Phasor diagram for
example
The phasor diagram is shown in Figure 1.41.
Assessment activity 1.7
Work on your own
1. A coil with an inductance of 0,3 H is connected in series with a 100 Ω resistor across a 10 V, 50 Hz
supply. Calculate:
a) The inductive reactance.
b) The impedance.
c) The value of the current through the coil.
d) The phase angle.
e) The voltage across the resistor.
f) The voltage across the inductor.
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Module 1: Electrical installations
Series RC circuits
C
R
Figure 1.42 shows a series RC circuit consisting
of resistance (R) and capacitance (C). The
combination is connected across a supply voltage
(V) with a frequency of (f) hertz. I represents the
current flowing through the circuit. The current is
the same in all parts of the circuit.
I
VR
The phasor is shown in Figure 1.43. The current (I)
leads the supply voltage (V) by an angle between
0 and 90.
V
The voltages must be added using a voltage triangle.
Using Pythagoras’ Law
Fig. 1.42: Series RC circuit
VR
V2 = VR2 + VC2
Vc
I

VR = IR

Therefore
V=
2
2
VR + VC
The total opposition to the current flow
in any AC circuit is called impedance
(Z). Both resistance and reactance in
an AC circuit oppose current flow. The
impedance (Z) of an AC circuit is
derived using the impedance triangle
as shown in Figure 1.45.
VC
V
V = IZ
VC = IXC
Fig. 1.44: Voltage triangle
Fig. 1.43: Phasor diagram
R

In an AC circuit, the ratio of the supply
voltage to current is called the
impedance (Z).
Therefore
Z= V
I
Z
As can be seen from Figure 1.45:
XC
Fig. 1.45: Impedance triangle
Z2 = R2 + XC2
Therefore
Z=
2
R 2 + XC
Then tan  = XC , sin  = XC and cos  = R
R
Z
Z
Assessment activity 1.8
Work in groups of two
1. A resistor of 10 Ω is connected in series with a capacitor of 350 F. The supply voltage is 230 V,
50 Hz. Calculate:
a) The capacitive reactance.
b) The impedance.
Module 1: Electrical installations
27
c) The current flowing through the circuit.
d) The phase angle.
e) The voltage across the resistor.
f)
The voltage across the capacitor
2. A resistor of 10 Ω is connected in series with a capacitor of 45 F. The supply voltage is 240 V,
50 Hz. Calculate:
a) The capacitive reactance.
b) The impedance.
c) The current flowing through the circuit.
d) The phase angle.
e) The voltage across the resistor.
f)
The voltage across the capacitor.
RLC Series circuits
VL = I X L
Figure 1.46 shows an RLC circuit. It consists of a resistor, an inductor
and a capacitor in series with an AC source.
R
VL – VC
V = IZ
C
L

I
VR
VC
VL
VR – I R
I
VC = I XC
Fig. 1.47: Phasor diagram
when XL> XC
V
VL = I X L
Fig. 1.46: Series RLC circuit
VR = I R
I

In this type of circuit there are three possible phasor diagrams, as
follows:
• XL> XC (See Figure 1.47.) The circuit is inductive and has a lagging
phase angle.
• XC > XL (See Figure 1.48.) The circuit is capacitive and has a leading
phase angle
• XL =XC (See Figure 1.49.) The applied voltage and the current I are
in phase. This is called series resonance and will not be discussed
because it is not part of the curriculum.
According to Pythagoras and because the impedance (Z) is the phasor
sum of R, XL and XC,
When XL> XC then impedance Z =
V = IZ
VC – V L
VC = I X C
Fig. 1.48: Phasor diagram
when XC > XL
VL = I X L
R 2 + (XL – XC) 2 Ω
And tan  = XL – XC
R
When XC > XL then impedance Z =
And tan  = XC – XL
R
V = IR
I
R 2 + (XC – XL) 2 Ω
VC = I X C
Fig. 1.49: Phasor diagram
when XL = XC
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Module 1: Electrical installations
Example 10
An RLC circuit consists of a 10 Ω resistor, an
inductor of 0,2 H and a capacitor of 45 F. The
circuit is connected across a 240 V, 50 Hz supply.
Calculate:
a) The impedance of the circuit.
b) The total current.
c) The voltage drop across all the components.
d) The phase angle.
The circuit diagram is shown in Figure 1.50.
R = 10 Ω
I
VR
L = 0,2 H
VL
C = 45 F
VC
240 V
50 HZ
Fig. 1.50: Circuit diagram for example
Given:
L= 0,2 H, R=10 Ω, V= 240 V, f = 50 Hz
Solution:
a) Inductive reactance = XL
XL = 2fL Ω
= 2 × 50 × 0,2 Ω
= 62,832 Ω
Capacitive reactance = XC
XC = 1
2rfC
1
=
(2r × 50 × 20 × 10 –6)
= 70,736 Ω
Note: XC > XL
Therefore,
Impedance Z =
R 2 + (XC – XL) 2 Ω
10 2 + (70, 736 – 62, 832) 2
Z=
Z = 12,746 Ω
b) The total current I
I = V
Z
= 240
12, 746
= 18,829 A
c) Voltage drop across resistance VR
VR = I × R
= 18,829 × 10
= 188,29 V
Voltage across the inductor VL
VL = I × XL
= 18,829 × 62,832
= 1183,06 V
Module 1: Electrical installations
29