Electrical Quantities and Circuits | IGCSE Physics

This extensive slide deck provides a detailed exploration of electrical quantities and circuits for IGCSE Physics. It covers key electrical quantities, including charge, current, voltage (potential difference), resistance, power, energy, electromotive force (EMF), and internal resistance. The presentation also explains series and parallel circuits, with in-depth discussions on Ohm’s Law, Kirchhoff’s Laws, electrical components, circuit calculations, and practical applications. Packed with illustrative diagrams, worked examples, and exam-style questions, this resource is ideal for IGCSE students, teachers, and independent learners preparing for exams.

1. ELECTRICITY
& CIRCUITS

2. Open Virtual lab
https://phet.colorado.edu/en/simulations/circuit-
construction-kit-dc
BLESSING NDAZIE ELECTRICITY 2

3. Positive & negative charges
•There are two types of electric charge:positiveandnegative
•Inside an atom, there are
•negatively chargedelectrons
•positively chargedprotons
•neutral (no charge)neutrons
•Atoms contain equal numbers of protons and electrons as they
have equal and opposite charges
•These charges cancel out so the overall charge of an atom is
zero.
BLESSING NDAZIE ELECTRICITY 3

4. Structure of an atom
BLESSING NDAZIE ELECTRICITY 4
The number of negative electrons in an atom balances the number of positive protons

5. Attraction and repulsion
•When two charges are close together,
they exert aforceon each other, this
could be:
•Attractive(the objects get closer
together)
•Repulsive(the objects move further
apart)
BLESSING NDAZIE ELECTRICITY 5

6. •Whether two objects attract or repel
depends on theircharge
•If the charges are theopposite, they willattract
•If the charges are thesame, they willrepel
BLESSING NDAZIE ELECTRICITY 6
Electric forces between charges
Opposite charges attract, like charges repel

7. BLESSING NDAZIE ELECTRICITY 7
•Positive chargesrepelother positive charges andattractnegative charges
•Negative chargesrepelother negative charges andattractpositive charges
•Electric charge is measured in units calledcoulombs (C)
Attraction and Repulsion Summary

8. •Remember the saying “opposites attract” when answering
questions about forces between charged particles.
•While electrostatic forces share many similarities with
magnetic forces, they are different phenomena– do
notconfuse the two!
BLESSING NDAZIE ELECTRICITY 8
Tip

9. BLESSING NDAZIE ELECTRICITY 9
Worked Example

10. Charging by friction
BLESSING NDAZIE ELECTRICITY 10
Open Virtual Lab
https://phet.colorado.edu/en/simul
ations/balloons-and-static-
electricity

11. Charging by friction
•When certain insulating solids are rubbed against
each other, they can becomeelectrically charged
•This is calledcharging by friction
•The charges remain on the insulators and cannot
immediately flow away
•One gains a netpositive chargeand the other gains a
netnegative charge
•An example of this is a plastic or polythene rod being
charged by rubbing it with a cloth
•Both the rod and cloth are insulating materials
BLESSING NDAZIE ELECTRICITY 11

12. Charging solids by friction
BLESSING NDAZIE ELECTRICITY 12
A polyethene rod may be given a charge by rubbing it with a cloth

13. •When an uncharged cloth is rubbed against an
uncharged polythene rod
•Electronsaretransferredawayfromthecloth totherod
•The cloth has lost electrons so it becomes positively charged
•The polythene rod has gained electrons so it becomes negatively
charged
•Theseoppositely chargedobjects are alsoattractedto each
other
•When an uncharged cloth is rubbed against an
uncharged acetate plastic rod, however
•Electronsaretransferredawayfromthe acetaterod
tothecloth
•The cloth has gained electrons so it becomes negatively charged
•The rod has lost electrons so it becomes positively charged
BLESSING NDAZIE ELECTRICITY 13
Charging solids by friction

14. BLESSING NDAZIE ELECTRICITY 14
Electrons are transferred away from the acetate rod to the cloth but transferred
away from the cloth to the polythene rod
Charging solids by friction

15. •At this level, if you are asked to explain how charge is gained
or lost, you must referenceelectrons. If an object gains
electrons, it gains negative charge and if it loses electrons it
loses negative charge (and hence, gains positive charge)
•Remember when charging by friction, it is only
theelectronsthat can move, not any 'positive' charge,
therefore if an insulator gains a negative charge, the other
insulator must have gained a positive charge
BLESSING NDAZIE ELECTRICITY 15
Tips and Tricks

16. BLESSING NDAZIE ELECTRICITY 16
Worked Example

17. BLESSING NDAZIE ELECTRICITY 17
Worked Example

18. •Experiment 1: investigating electrostatic charging by friction
•The aim of this experiment is to investigate how insulating
materials can be charged by friction
•Variables
•Independent variable= Rods of different material
•Dependent variable= Charge on the rod
•Control variables:
•Time spent rubbing the rod
•Using the same type of cloth
•Using the same length of rod
BLESSING NDAZIE ELECTRICITY 18
Demonstrating electrostatic charges

19. BLESSING NDAZIE ELECTRICITY 19

20. Method
BLESSING NDAZIE ELECTRICITY 20
Apparatus for investigating charging by friction

21. 1.Take a polythene rod, hold it at its centre and rub both ends
with a cloth
2.Suspend the rod, without touching the ends, from a stand
using a cradle and nylon string
3.Take a second polythene rod and rub one end with a
different cloth
4.Bring the second polythene rod close to the suspended rod
5.Record any observations of the suspended rod's motion, i.e.
whether it is attracted or repelled by the second rod
6.Repeat using an acetate rod and rods of different materials
BLESSING NDAZIE ELECTRICITY 21
Method

22. BLESSING NDAZIE ELECTRICITY 22

23. Analysis of results
•When two insulating materials are rubbed together, negative
charge (electrons) will transfer from one insulator to the other
•A polythene rod gains anegativecharge when rubbed with a
cloth
•This is because electrons are transferred to the polythene from the
cloth
•An acetate rod gains apositivecharge when rubbed with a cloth
•This is because electrons are removed from the acetate by the cloth
BLESSING NDAZIE ELECTRICITY 23

24. Transfer of electrons between charged
insulators
BLESSING NDAZIE ELECTRICITY 24
Electrons are transferred to the polythene rod giving it a negative charge,
and they move from the acetate rod giving it a positive charge

25. •If the material isrepelledby the polythene rod, then the
materials have thesame charge
•For example, the polythene rod would be repelled by a second
polythene rod, as they have the same charge
•If the material isattractedto the polythene rod, then they
haveopposite charges
•For example, the polythene rod would be attracted to an acetate
rod, as they have opposite charges
BLESSING NDAZIE ELECTRICITY 25
Transfer of electrons between charged
insulators

26. Evaluating the experiment
•Reduce the effects of environmental factors (e.g. close
windows to reduce drafts) to ensure the motion of the
polythene rod is due to electric forces only
•Make sure not to touch the ends of the rods once they have
been charged(if the ends are touched, the rods
willdischargeand the forces will no longer be present)
•Produce greater deflections by rubbing the rods for a longer
period to transfer more charge (ensuring that the time spent
rubbing each rod is the same)
BLESSING NDAZIE ELECTRICITY 26

27. Detecting charge using a gold-leaf
electroscope
BLESSING NDAZIE ELECTRICITY 27
Experiment 2:

28. Variables
•Independent variable= Rods of different material
•Dependent variable= Charge on the rod
BLESSING NDAZIE ELECTRICITY 28

29. Equipments
BLESSING NDAZIE ELECTRICITY 29
Equipment Purpose
Gold-leaf electroscope to detect charge
Polythene and acetate rods (or
strips)
to observe the effects of these on the gold-leaf
electroscope when charged
Cloths (one per material) to charge the rods (or strips) by rubbing them

30. BLESSING NDAZIE ELECTRICITY 30
1.Before beginning the experiment, ensure
the plate of the electroscope is uncharged
by touching it with your finger. The leaf
should hang straight down next to the
stem
2.Charge a polythene rod by rubbing it
with a cloth
3.Bring the charged rod towards the plate
of the electroscope and record any
observations
4.Bring the charged rod away from the
plate of the electroscope and record any
observations
5.Touch the charged rod to the plate of the
electroscope and record any observations
6.Repeat using an acetate rod
The gold-leaf electroscope is a device consisting
of a metal plate, a metal stem and a thin gold
leaf. The stem and leaf are housed in an airtight
container to prevent draughts.
Methods

31. Example results table
charged material action gold leaf rises or
falls
movement of
electrons
polythene moved towards plate
polythene moved away from plate
polythene touched plate
acetate moved towards plate
acetate moved away from plate
acetate touched plate
BLESSING NDAZIE ELECTRICITY 31

32. Analysis of results 1/2
•When a charged object is brought near the plate of the
electroscope, the leafrises
•The negatively charged polythene rodrepelselectrons away from the
surface of the plate down the stem and leaf, giving them
anegativecharge, hence, they repel
•The positively charged acetate rodattractselectrons to the surface of
the metal plate from the stem and leaf, giving them apositivecharge,
hence, they repel
•When the charged object is moved away from the plate, the
leaffalls
•Electrons in the electroscope are no longer repelled or attracted by the
rod so they redistribute themselves
•The stem and leaf become electricallyneutral
BLESSING NDAZIE ELECTRICITY 32

33. Analysis of results 2/2
•When a charged objecttouchesthe plate of the electroscope,
the leafstays risen
•The charge from the rod is transferred to the metal plate and travels
down the stem and leaf of the electroscope
•The stem and leaf therefore carry thesame chargeand repel each
other
•The electroscope has beencharged
•When a finger touches the plate, the leaffalls
•The charge from the electroscope is transferred to the person and
travels to the earth
•The stem and leaf become electrically neutral
•The electroscope has beendischarged
BLESSING NDAZIE ELECTRICITY 33

34. Evaluating the experiment
•Make sure not to touch the ends of the rods once they have
been charged(if the ends are touched, the rods willdischarge)
•When the electroscope is charged by contact with a rod, it
should stay risen. If it doesn't, repeat the process but ensure
to press harder and draw the rod along the edge of the plate
BLESSING NDAZIE ELECTRICITY 34

35. Examiner Tips and Tricks
•Experimental demonstrations, such as the one above, are
different from experiments in which you have to take
measurements. In the case of this demonstration your results
are yourobservations.
•When describing a demonstration you shouldstate a
conclusion– in other words, explain what you expect to
happen and what it means.
BLESSING NDAZIE ELECTRICITY 35

36. Electric Fields
BLESSING NDAZIE ELECTRICITY 36
Open Virtual Lab
https://phet.colorado.edu/sims/html/charges-
and-fields/latest/charges-and-fields_all.html

37. Electric fields
•An electric field is defined as:
A region of space in which an electric charge
experiences a force
•The direction of an electric field line is ;
The direction of the force on a positive
charge at that point
•Field lines always goes from positive to
negative
•Charged objectscreateelectric fields
around themselves
•This is similar to how magnets create magnetic
fields
•An electric field is avectorquantity as it has
bothmagnitude(strength) anddirection
BLESSING NDAZIE ELECTRICITY 37

38. Electric field patterns
•Electric field lines are
•used to represent thedirectionandmagnitudeof an electric field
•always directed from thepositivechargetothenegativecharge
•Field pattern around a point charge are radial
BLESSING NDAZIE ELECTRICITY 38

39. Electric field around a point charge
•Around apoint charge, the electric field lines are directly
radially inwards or outwards:
•If the charge ispositive(+), the field lines are radiallyoutwards
•If the charge isnegative(-), the field lines are radiallyinwards
BLESSING NDAZIE ELECTRICITY 39

40. Electric field lines around positive and
negative point charges
BLESSING NDAZIE ELECTRICITY 40
Electric field lines around a point charge are directed away from a positive charge and
towards a negative charge

41. Electric field around a charged
conducting sphere
•The field lines around a charged conducting sphere are similar
to that of a point charge
•This is because the charges on the surface of the sphere will be evenly
distributed
•The charges are the same, so they repel
•The surface is conducting, allowing them to move
•Field lines arealways perpendicular(at right angles)to the
surface of a conducting sphere
BLESSING NDAZIE ELECTRICITY 41

42. Electric field lines around a positively
charged sphere
BLESSING NDAZIE ELECTRICITY 42
The electric field pattern
around a conducting can
be demonstrated using a
Van der Graaff generator

43. Electric field between two parallel plates
•The electric field between
two parallel plates is
auniform electric field
•The field lines are:
•directed from thepositiveto
thenegativeplate
•parallel
•straight lines
BLESSING NDAZIE ELECTRICITY 43
Electric field lines between two
oppositely charged parallel plates
Electric field lines between two parallel plates are directed
from the positive to the negative plate. A uniform electric field
has equally spaced field lines

44. BLESSING NDAZIE ELECTRICITY 44
Worked Example

45. BLESSING NDAZIE ELECTRICITY 45

46. Investigating Electrical
Conductors & Insulators
BLESSING NDAZIE ELECTRICITY 46

47. Conductors
•Aconductoris a material that allowscharge(usually electrons) to flow
through it easily
•Some examples of conductors are:
•silver
•copper
•aluminium
•steel
•The best conductors tend to bemetals
•On the atomic scale, metallic conductors are made up of positively
charged metal ions with their outermost electronsdelocalised
•This means the electrons are free to move
•Metals conduct electricity very well because:
•Current is the rate of flow of electrons
•So, the more easily electrons are able to flow, thebetterthe conductor
BLESSING NDAZIE ELECTRICITY 47

48. Metallic lattice structure
BLESSING NDAZIE ELECTRICITY 48
The lattice structure of a conductor with positive metal ions and delocalised electrons

49. Insulators
•Aninsulatoris a material that hasno free chargesand,hence
doesnotallow the flow of charge through it very easily
•Some examples of insulators are:
•rubber
•plastic
•glass
•wood
•Some non-metals, such as wood, allowsomecharge to pass
through them
•Although they are not very good at conducting, they do conduct a
little in the form ofstaticelectricity
•For example, two insulators can build up charge on their surfaces and if
they touch this would allow that charge to be conducted away
BLESSING NDAZIE ELECTRICITY 49

50. Conductors and insulators
BLESSING NDAZIE ELECTRICITY 50
Different materials have different properties of conductivity

51. Investigating electrical conductors &
insulators
•Aim of the experiment
•The aim of this experiment is to distinguish between good
and bad conductors using a gold leaf electroscope
•Variables
•Independent variable= Different materials
•Dependent variable= Electrical conductivity of materials
BLESSING NDAZIE ELECTRICITY 51

52. Equipment
Equipment Purpose
Gold-leaf electroscope to distinguish between electrical conductors and
insulators
Polythene rod to charge the electroscope by contact
Cloth to charge the rod by friction
Different conducting and
insulating materials (metal,
plastic, glass, wood)
to observe the effects of these on the gold-leaf
electroscope when uncharged
BLESSING NDAZIE ELECTRICITY 52

53. Method
1.Before beginning the experiment, ensure the plate of the
electroscope is uncharged by touching it with your finger.
The leaf should hang straight down next to the stem
2.Charge a polythene rod by rubbing it with a cloth
3.Touch the charged rod to the plate of the electroscope.
The leaf should stay risen if the electroscope has been
successfully charged
4.Touch the plate of the charged electroscope with the first
object to be tested and record any observations
5.Repeat for different materials
BLESSING NDAZIE ELECTRICITY 53

54. Example results table
material gold leaf falls quickly or
slowly
good or bad conductor
metal
plastic
glass
graphite
wood
fabric
rubber
BLESSING NDAZIE ELECTRICITY 54

55. Analysis of results
•Good conductors, such as metals, allow charge to flow through
them easily
•Therefore, a good conductor will cause the leaf to fallquicklyas it
allows charge to flow to or from the plate
•Thefasterthe leaf falls, thebetterthe conductor
•Poor conductors, such as glass, do not allow charge to flow as
easily
•Therefore, a poor conductor will cause the leaf to fallslowlyas the
charge is unable to flow as well
•If the leaf does not move at all, the material is agood insulator
BLESSING NDAZIE ELECTRICITY 55

56. Table of conductors and insulator
good conductors poor conductors (insulators)
metal plastic
graphite glass
wood
rubber
fabric
BLESSING NDAZIE ELECTRICITY 56

57. Evaluating the experiment
An electrometer (electronic instrument capable of measuring
electric charge) could be used instead of an electroscope to
allow for numerical comparisons between good and poor
conductors
BLESSING NDAZIE ELECTRICITY 57

58. Current
BLESSING NDAZIE ELECTRICITY 58
Open Virtual Lab
https://phet.colorado.edu/en/simul
ations/balloons-and-static-
electricity

59. Current
•Electric current is defined as
•The rate of flow of electric charge within a circuit
•In most cases, these charged particles are electrons, which are
negatively charged entities. The movement of these electrons
constitutes an electric current, which enables the transfer of
energy through electrical circuits.
•Current flows
•when acircuitis formed e.g. when a wire connects the two
oppositely charged terminals of a cell
•from thepositiveterminal to thenegativeterminal of a
cell
BLESSING NDAZIE ELECTRICITY 59

60. BLESSING NDAZIE ELECTRICITY 60
Charge flows from the positive terminal to the negative terminal
Current

61. BLESSING NDAZIE ELECTRICITY 61
Worked Example

62. BLESSING NDAZIE ELECTRICITY 62
Worked Example

63. Measuring current
•Current can be measured using
anammeter
•Ammeters must be connected
inserieswith the component
being measured
•Ammeters can be
•digital (with an electronic read
out)
•analogue (with a needle and scale)
BLESSING NDAZIE ELECTRICITY 63
An ammeter can be used to measure the current
around a circuit

64. Analogue ammeters
•Typical ranges are 0.1-1.0 A and 1.0-5.0 A
for analogue ammeters
•Always double check exactly where the
marker is before an experiment, if not at
zero, you will need to subtract this from all
your measurements. They should be checked
forzero errorsbefore using
•They are also subject toparallax error
•Always read the meter from a position
directly perpendicular to the scale
BLESSING NDAZIE ELECTRICITY 64

65. Digital ammeters
•Digital ammeters can measure very small currents, in mA or
µA
•Digital displays show the measured values as digits and are
more accurate than analogue displays
•They’re easy to use because they give a specific value and are
capable of displaying more precise values
•However digital displays may 'flicker' back and forth between values
and a judgement must be made as to which to write down
•Digital ammeters should be checked forzero error
•Make sure the reading is zero before starting an experiment, or
subtract the “zero” value from the end results
BLESSING NDAZIE ELECTRICITY 65

66. Electrical conduction in metals
•The wires in an electric circuit are made ofmetalbecause it is a
goodconductorof electriccurrent
•In the wires, the current is a flow ofnegativelychargedelectrons
BLESSING NDAZIE ELECTRICITY 66

67. •Electric current can be defined more precisely as:
The charge passing a point in a circuit per unit time
•Current is measured in units ofamperesoramps (A)
•1 amp is equivalent to a charge of 1 coulomb flowing in 1 second, or 1 A
= 1 C/s
•This means the size of an electric current is the amount of charge passing
through a component each second
•Current, charge and time are related by the equation:

•Where:
•Q= charge, measured in coulombs (C)
•t= time, measured in seconds (s)
•The current, charge and time equation can be rearranged with the help of
the following formula triangle:
•I= current, measured in amps (A)
Calculating current
BLESSING NDAZIE ELECTRICITY 67

68. Current charge time formula triangle
BLESSING NDAZIE ELECTRICITY 68

69. Worked Example
•When will 8 A of current pass through an electrical circuit?
•A. When 8 J of energy is used by 1 C of charge
•B. When a charge of 4 C passes in 0.5 s
•C. When a charge of 8 C passes in 0.1 s
•D. When a charge of 1 C passes in 8 s
BLESSING NDAZIE ELECTRICITY 69

70. Examiner Tips and Tricks
•Electric currents in everyday circuits tend to be quite small, so
it's common for examiners to throw in aunitprefixlike 'm'
next to quantities of current, e.g. 10 mA (10 milliamperes).
Make sure you can convert these into standard units, e.g. 10
mA = 10 × 10
-3
A.
•Make sure to only use the triangle to help yourearrangethe
equation that links charge, current and time. Don't draw it if
you are asked to write out the equation in full, such
asQ=I×t, as you may lose marks for doing so.
•Check out this revision note onspeed, distance and timeif you
need a reminder on how to use formula triangles.
BLESSING NDAZIE ELECTRICITY 70

71. BLESSING NDAZIE ELECTRICITY 71

72. BLESSING NDAZIE ELECTRICITY 72
Worked Example

73. Conventional current
•Current is the flow ofpositivecharge i.e. from
thepositiveterminaltothenegativeterminal
of a cell
•This is known asconventional current
•This is in the opposite direction toelectron flow
•Electrons are negatively charged, so they flow from
thenegativeterminaltothepositiveterminal of a
cell
BLESSING NDAZIE ELECTRICITY 73

74. Conventional current and electron flow
BLESSING NDAZIE ELECTRICITY 74

75. BLESSING NDAZIE ELECTRICITY 75

76. BLESSING NDAZIE ELECTRICITY 76

77. Direct & alternating current
•There aretwotypes of current
•direct current (d.c.)
•alternating current (a.c.)
BLESSING NDAZIE ELECTRICITY 77

78. Direct current
•A direct current (d.c.) is defined as
•A steady current, constantly flowing in the same direction in
a circuit, from positive to negative
•The potential difference across a cell in a d.c. circuit travels
inone direction only
•The current travels from the positive terminal to the negative
terminal
•A d.c. power supply has afixedpositive terminal and a fixed
negative terminal
•Electriccells, orbatteries, produce direct current (d.c.)
BLESSING NDAZIE ELECTRICITY 78

79. Alternating current
•An alternating current (a.c.) is defined as
•A current that continuously changes its direction, going back
and forth around a circuit
•An alternating current power supply has two identical terminals
thatchangefrom positive to negative and back again
•The alternating current always travels from the positive terminal to the
negative terminal
•Therefore, the currentchanges directionas the polarity of the terminals
changes
•Thefrequencyof an alternating current is the number of times
the current changes direction back and forth each second
•In the UK,mains electricityis analternatingcurrent with a frequency of
50 Hz and a potential difference of around 230 V
BLESSING NDAZIE ELECTRICITY 79

80. Graphs of direct current and alternating
current
BLESSING NDAZIE ELECTRICITY 80

81. Comparing direct and alternating current
Direct current (d.c.) Alternating current (a.c.)
continuous and in one direction constantly changing direction
produced by cells and batteries produced by electrical generators i.e. mains
electricity
involves a positive and negative terminalinvolves two identical terminals
BLESSING NDAZIE ELECTRICITY 81

82. BLESSING NDAZIE ELECTRICITY 82

83. Examiner Tips and Tricks
•If asked to explain the difference between alternating
and direct current, sketch the graphs shown above: a
well-sketched (and labelled) graph can earn you full
marks.
BLESSING NDAZIE ELECTRICITY 83

84. BLESSING NDAZIE ELECTRICITY 84

85. BLESSING NDAZIE ELECTRICITY 85

86. BLESSING NDAZIE ELECTRICITY 86

87. Electromotive force
BLESSING NDAZIE ELECTRICITY 87

88. Electromotive force
•Think of e.m.f like the total energy that
pushes electric charges (electrons) through
a circuit.
•It is provided by a battery or power source
•e.m.f. is the name given to the potential
difference of the power source in a circuit
•Even if the circuit is open the e.m.f is still
present
•Defined as: The electrical work done by a
source in moving a unit charge around a
complete circuit
•measured in volts (V)
BLESSING NDAZIE ELECTRICITY 88
The e.m.f. is the voltage supplied by a
power supply: 12 V in the above case

89. Calculating electromotive force
BLESSING NDAZIE ELECTRICITY 89
•The definition of e.m.f. can also be expessed using the
equation:

•Where
•E= electromotive force (e.m.f.), measured in volts (V)
•W= energy transferredto the chargesfrom the power
source, measured in joules (J)
•Q= charge moved, measured in coulombs (C)
•This equation should be compared to the definition of
potential difference as the two are closely related

90. Potential difference
BLESSING NDAZIE ELECTRICITY 90

91. Potential difference
•The work done by a unit charge
passing through a component
•Think of it as the energy used/lost
by the charges as they move through
the circuit
•Also measured in units ofvolts (V)
•The potential difference between
two points in a circuit is related to
the amount ofenergy
transferred/lost by the electrons
between those points
BLESSING NDAZIE ELECTRICITY 91
The potential difference is the difference in the
electrical potential across each component: 5 volts for
the bulb (on the left) and 7 volts for the resistor (on
the right)

92. Potential difference
•As electrons flow through a cell,
theygainenergy
•For example, in a 12 V cell, every
coulomb of charge passing through the
cell gains 12 J of energy
•As electrons flow through a circuit,
theyloseenergy
•For example, after leaving the 12 V cell,
each coulomb of charge will transfer 12
J of energy to the wires and
components in the circuit
BLESSING NDAZIE ELECTRICITY 92
The potential difference is the difference in the
electrical potential across each component: 5
volts for the bulb (on the left) and 7 volts for
the resistor (on the right)

93. BLESSING NDAZIE ELECTRICITY 93

94. Measuring potential difference
•Potential difference can be measured using
avoltmeter
•Voltmeters must be set up inparallelwith the
component being measured
•This is because potential difference is
thedifferencein electrical potential between two
points
•Therefore, a voltmeter has to be connected totwo
pointsin the circuit
•Voltmeters can be
•digital (with an electronic read out)
•analogue (with a needle and scale)
BLESSING NDAZIE ELECTRICITY 94
Potential difference can be measured
by connecting a voltmeter in parallel
between two points in a circuit

95. Analogue voltmeters
•Analogue voltmeters are subject toparallax
error
•Always read the meter from a position directly
perpendicular to the scale
•Typical ranges are 0.1-1.0 V and 0-5.0 V for
analogue voltmeters although they can vary
•Always double-check exactly where the marker is
before an experiment, if not at zero, you will need
to subtract this from all your measurements
•They should be checked forzero errorsbefore
using
BLESSING NDAZIE ELECTRICITY 95
Voltmeters can be either analogue
(with a scale and needle)

96. Digital voltmeters
•Digital voltmeterscan measure very small potential
differences, in mV or µV
•Digital displays show the measured values as digits and
are more accurate than analogue displays
•They’re easy to use because they give a specific value
and are capable of displaying more precise values
•However digital displays may 'flicker' back and forth between
values and a judgement must be made as to which to write
down
•Digital voltmeters should be checked forzero error
•Make sure the reading is zero before starting an experiment, or
subtract the “zero” value from the end results
BLESSING NDAZIE ELECTRICITY 96
digital (with electronic
read-out)

97. Examiner Tips and Tricks
•When you are building a circuit in class, alwaysconnect the
voltmeter last.Make the whole circuit first and check it works.
•Only then pick up the voltmeter. Connect two leads to your
voltmeter. Now connect the leads so that they are one on each
side of the component you are measuring. This will save you a lot
of time waiting for your teacher to troubleshoot your circuit!
•You might sometimes see potential difference called voltage. Both
mean the same thing, but it is best to use the term potential
difference. This can be particularly useful when thinking about
voltmeters as the potential difference describes
adifferencebetweentwopoints, therefore the voltmeter has to
be connected betweentwopoints in the circuit.
BLESSING NDAZIE ELECTRICITY 97

98. Calculating potential difference
BLESSING NDAZIE ELECTRICITY 98
•Potential difference, energy transferred and charge are related by the
equation:

•Where:
•V= potential difference, measured in volts (V)
•W= energy transferred to the components, measured in joules (J)
•Q= charge moved, measured in coulombs (C)
•One volt is equivalent to the transfer of 1 joule of electrical energy by 1
coulomb of charge, or 1 V = 1 J/C
•This can be rearranged using the formula triangle below:

99. Energy charge and potential difference
formula triangle
BLESSING NDAZIE ELECTRICITY 99

100. Worked Example
The normal operating voltage for a lamp is 6 V.
Calculate how much energy is transferred in the lamp
when 4200 C of charge flows through it.
BLESSING NDAZIE ELECTRICITY 100

101. Answer:
Step 1: List the known quantities
•Voltage,V =6 V
•Charge,Q= 4200
Step 2: State the equation linking potential difference, energy and
charge
•The equation linking potential difference, energy and charge is:

Step 3: Rearrange the equation and substitute the known values

W =6 × 4200 = 25 200 J
•Therefore,25 200 Jof energy is transferred in the lamp
BLESSING NDAZIE ELECTRICITY 101

102. BLESSING NDAZIE ELECTRICITY 102
•EMF is the total energy supplied to push the
charges.
•Potential difference is the energy lost or
used by the charges as they move through
components (like a bulb, resistor, or motor)

103. BLESSING NDAZIE ELECTRICITY 103

104. BLESSING NDAZIE ELECTRICITY 104

105. Examiner Tips and Tricks
•Don't be confused by the symbol for voltage (thesymbolV)
being the same as its unit (thevolt, V). Remember that one
volt is equivalent to 'a joule per coulomb'.
•Make sure to learn this equation and understand how it is
similar (and different) to the equation for e.m.f.
BLESSING NDAZIE ELECTRICITY 105

106. Ohm's law
BLESSING NDAZIE ELECTRICITY 106

107. Resistance
•Resistanceis defined as: The opposition to current/movement
of electrons
•Resistance occurs because the freeelectronsflowing in the
circuit (current)collidewith the metal ions in the wire
•These collisionsslow downthe electrons, or, in other
words,resisttheir flow
•Thehigherthe resistance of a circuit, thelowerthe current
•This means that good conductors have alowresistance and insulators
have ahighresistance
•The resistance of a circuit can beincreasedby adding resistors
(or variable resistors) to it
•Every electrical component has a resistance, even wires
•In exam questions, the resistance of the wires and batteries are
assumed to be negligible
BLESSING NDAZIE ELECTRICITY 107

108. The effect of resistance on the current in
a circuit
BLESSING NDAZIE ELECTRICITY 108

109. Ohm's law
BLESSING NDAZIE ELECTRICITY 109
•Current,I, potential difference,V,and resistance,R, all affect one
another
•Changing anyoneof these in a circuit, changesallof them
•Current and resistance areinversely proportional
•If the resistance is doubled, current will halve
•This relationship is described by the following equation, known
as Ohm's law

•Where
• R= resistance, measured in ohms (Ω)
• V= potential ifference, measured in volts (V)
• I= current, measured in amperes or amps (A)

110. Consequences of Ohm's law
•Resistors are used in circuits to control either:
othe current in branches of the circuit (through certain components)
othe potential difference across certain components
•This is due to the consequences of Ohm's Law
oThe current in an electrical conductor decreases as its resistance
increases (for a constant p.d.)
oThe p.d. across an electrical conductor increases as its resistance
increases (for a constant current)
BLESSING NDAZIE ELECTRICITY 110

111. Worked Example
•A 12 Ω resistor has a current of 0.3 A flowing through it.
•Determine the potential difference across the resistor.
BLESSING NDAZIE ELECTRICITY 111

112. Answer:
BLESSING NDAZIE ELECTRICITY 112

113. BLESSING NDAZIE ELECTRICITY 113

114. BLESSING NDAZIE ELECTRICITY 114

115. Current-voltage graphs
•The relationship between current and potential difference of a
component can be shown on a current-voltage (I-V)graph
•When the relationship between current and potential
difference islinear:
•theI-Vgraph is astraight linewhich passes through theorigin
•the resistance isconstant
•these are known asohmic resistors
•When the relationship between current and voltage isnon-
linear:
•theI-Vgraph that isnota straight line
•the resistance isnotconstant
•these are known asnon-ohmic resistors
BLESSING NDAZIE ELECTRICITY 115

116. •These are resistors that follow Ohm’s Law, which
states that voltage (V) is directly proportional to
current (I) if the temperature remains constant.
•This means if you double the voltage, the
current also doubles.
•The graph of voltage vs. current for an ohmic
resistor is a straight line.
Examples of Ohmic Resistors:
•Metallic wires (like copper or nichrome at
constant temperature)
•Standard resistors used in circuits
BLESSING NDAZIE ELECTRICITY 116
Ohmic Resistors

117. I-V graph for ohmic conductors
•The relationship between
current and voltage for a wire
or fixed resistor is linear,
ordirectly proportional, which
means
•the IV graph is a straight line, so
voltage and current increase (or
decrease) by thesameamount
•the slope of the graph is
constant, so resistance
isconstant
BLESSING NDAZIE ELECTRICITY 117

118. Non-Ohmic Resistors
•These do not follow Ohm’s Law, meaning the relationship
between voltage and current is not linear.
•Their resistance changes depending on conditions like
temperature, light, or voltage.
•The graph of voltage vs. current for a non-ohmic resistor is
curved, showing that resistance is changing.
•Examples of Non-Ohmic Resistors:
•Filament Bulb – As it heats up, resistance increases.
•Diodes & LEDs – Only allow current to flow in one
direction, with resistance changing significantly.
•Thermistors – Resistance changes with temperature.
•If you see a resistor that behaves predictably and follows a
straight-line graph, it’s ohmic. If it behaves differently
depending on voltage or conditions, it’s non-ohmic.
BLESSING NDAZIE ELECTRICITY 118

119. I-V graph for a filament lamp
•The relationship between current and voltage for
a filament lamp is non-linear, ornotdirectly
proportional, which means
•theIVgraph is not a straight line, so voltage and
current donotincrease (or decrease) by the same
amount
•the slope of the graph is not constant, so
resistancechanges
•TheIVgraph for a filament lamp shows as voltage
increases
•the current increases at a proportionallyslowerrate
•the resistanceincreases;the flatter the slope, the
higher the resistance
BLESSING NDAZIE ELECTRICITY 119

120. •As current through a filament lamp increases, the
resistanceincreasesbecause:
•the higher current causes thetemperatureof the
filament to increase
•the higher temperature causes the atoms in the metal
lattice of the filament tovibratemore
•this causes an increase in resistance as it becomes
more difficult forfreeelectrons(the current) to pass
through
•since resistanceopposesthe current, this causes it to
increase at aslowerrate
I-V graph for a filament lamp
BLESSING NDAZIE ELECTRICITY 120

121. I-V graph for a diode
•A diodeallows current to flow inonedirection
only
•This is calledforward bias
•In the reverse direction, the diode has veryhigh
resistance, and thereforenocurrent flows
•This is calledreverse bias
•When the current is in the direction of the
arrowhead symbol, this isforward bias
•On the IV graph, this is shown by a sharp increase in
voltage and current on the right side of the graph
•This shows the resistance is verylow
•When the diode is switched around, this
isreverse bias
•On the IV graph, this is shown by a zero reading of
current or voltage on the left side of the graph
•This shows the resistance is veryhigh
BLESSING NDAZIE ELECTRICITY 121
The current is zero at all potential differences in the
negative quadrants because current only flows one
way through a diode; this gives the diode I-V graph its
distinct shape

122. Current-voltage (I-V) graph for a
resistor and a filament lamp
BLESSING NDAZIE ELECTRICITY 122
•Components withlinearI-Vgraphs
(ohmic resistors) include:
•fixed resistors (at constant
temperature)
•wires (at constant temperature)
•Components withnon-linearI-Vgraphs
(non-ohmic resistors) include:
•filament lamps
•diodes
•LDRs
•thermistors

123. Examiner Tips and Tricks
•In your IGCSE exam, you could be asked to recognise,
sketch or explain the I-V graphs for a wire / fixed
resistor (ohmic conductors), a filament lamp and a
diode.
BLESSING NDAZIE ELECTRICITY 123

124. Resistance of a wire
•As electrons pass through a wire, theycollidewith the metal
ions in the wire
•These collisions transfer energy away from the kinetic store of
the electrons, which causes them toslow down
•The energy from the electrons is transferred to the kinetic
store of the vibrating metal ions
•This causes the vibration of the ions to increase (increased
temperature)
•As the vibration of the ions increases, the more the electrons
collide with them (increased resistance)
BLESSING NDAZIE ELECTRICITY 124

125. Resistance of a wire
BLESSING NDAZIE ELECTRICITY 125

126. Electron collisions in a metal wire
BLESSING NDAZIE ELECTRICITY 126
Electrons collide with metal ions, which resist their flow

127. Effect of length and cross-sectional area
on resistance
•If the wire is longer, each electron will collide with more
ions, and so there will be more resistance:
•The longer a wire, thegreaterits resistance
•If the wire is thicker (greater diameter) there is more space
for the electrons and so more electrons can flow:
•The thicker a wire, thesmallerits resistance
BLESSING NDAZIE ELECTRICITY 127

128. Effect of length and cross-sectional area
on resistance
•The relationship between resistance, length and cross-
sectional area can be represented mathematically
•Resistance isdirectlyproportional tolength
•Doubling the length will double the resistance and vice versa
•Resistance isinverselyproportional tocross-sectional
area(width, or thickness)
•Doubling the cross-sectional area will halve the resistance
BLESSING NDAZIE ELECTRICITY 128

129. Effect of length and cross-sectional area
on resistance
BLESSING NDAZIE ELECTRICITY 129
The mathematical relationship between length and width of
the wire and the resistance

130. Electrical Energy
BLESSING NDAZIE ELECTRICITY 130

131. Energy transfer in electrical circuits
•As charge (electrons) flows around a
circuit, energy is transferred from the
power source to the various components
•As electrons pass through the power supply,
energy is transferred to the electrons
•As the electrons pass through each
component, energy is transferred from the
electrons to the component
•The component will often dissipate some of
that energy to the surroundings
BLESSING NDAZIE ELECTRICITY 131
Charge gains energy from the power
supply, and transfers the energy to
the components

132. Energy transfers in common household
appliances (The Motors)
•Some domestic appliances transfer energy from
the chemical store of cells and batteries, such as
mobile phones, laptops, and remote controls
•Most larger household appliances transfer
energy electrically from the mains supply
•Lots of household appliances contain motors
•Vacuum cleaners: to create the suction to suck in
dust and dirt off carpets
•Washing machines: to rotate the drum to wash (or
dry) clothes
•Refrigerators: to compress the refrigerant chemical
into a liquid to reduce the temperature
•Energy is transferred electrically from the mains
supply to the kinetic store of the motor in the
appliance
BLESSING NDAZIE ELECTRICITY 132

133. Energy transfers in a washing machine
BLESSING NDAZIE ELECTRICITY 133

134. Energy transfers in common household
appliances (The Heaters)
•Lots of household appliances contain heaters
•Toasters: to heat up food
•Kettles: to boil water
•Boiler in a central heating system: hot water is pumped from the
boiler so the radiator can heat up a room
•Energy is transferred electrically from the mains supply to the
thermal store of the heater.
BLESSING NDAZIE ELECTRICITY 134

135. Energy transfers in a Toaster
BLESSING NDAZIE ELECTRICITY 135

136. Electrical energy equation
•The amount of energy transferred by an electrical appliance
depends on:
•how long the appliance runs for
•the power rating of the appliance
•Electrical energy can be calculated using the following
equation:
BLESSING NDAZIE ELECTRICITY 136
•Where:
• E= energy, measured in joules (J)
• I= current, measured in amps (A)
• t= time, measured in seconds (s)
• V= potential difference, measured in volts (V)

137. Worked Example
A washing machine runs a cycle for 3 hours and 16 minutes.
The potential difference of the mains supply is 230 V. A current
of 10.0 A flows through the washing machine for the duration
of the cycle.
Determine the amount of energy transferred from the mains
supply during the cycle. Give your answer in MJ.
BLESSING NDAZIE ELECTRICITY 137

138. Answer:
BLESSING NDAZIE ELECTRICITY 138

139. Answer:
BLESSING NDAZIE ELECTRICITY 139

140. Electrical Power
BLESSING NDAZIE ELECTRICITY 140

141. Electrical power equations
•Thepowerof an appliance is defined as:
•The rate at which energy is transferred by an appliance
•Power can be calculated in terms of energy:
BLESSING NDAZIE ELECTRICITY 141
•Where:
•P= power, measured in watts (W)
•The watt is equivalent to joules per second (J/s)
• E= energy transferred, measured in joules (J)
• t= time, measured in seconds (s)

142. Electrical power equations
•Power can also be calculated in terms of work done:
BLESSING NDAZIE ELECTRICITY 142
•Where:
• W= work done, which is equivalent to energy transferred,
measured in joules (J)
•The power of an electrical device is theenergy transferred per
secondby the device

143. Electrical power equations
•The power dissipated by an electrical component can be
calculated by:
BLESSING NDAZIE ELECTRICITY 143
•Where:
•P= dissipated power, measured in watts (W)
•I= current, measured in amps (A)
•V= potential difference, measured in volts (V)

144. Worked Example
•Two lamps are connected in series to a 150 V power supply.
•Which statement most accurately describes what happens?
•A. Both lamps light normally
•B. The 15 V lamp blows
•C. Only the 41 W lamp lights
•D. Both lamps light at less than their normal brightness
BLESSING NDAZIE ELECTRICITY 144

145. BLESSING NDAZIE ELECTRICITY 145

146. Examiner Tips and Tricks
•When doing calculations involving electrical power,
remember the unit is Watts W, therefore, you
shouldalwaysmake sure that the time is inseconds
BLESSING NDAZIE ELECTRICITY 146

147. Measuring energy usage
•Energy measured in joules
•Electrical energy transferred is often calculated with units of
joules
•One joule is equivalent to one-watt second
•Consider an average lightbulb with a power of 60 W, which is
left on for 6 hours in a house
•1 hour is 3600 s
•The energy transferred over this time is 1.296 × 10
6
J
•This number is large and that is only one lightbulb for a single
day
•A household uses many appliances all year round; the energy
transferred per month in joules would be inconveniently large
BLESSING NDAZIE ELECTRICITY 147

148. Measuring energy usage
•Energy measured in kilowatt-hours
•To make these large values more relatable to daily use:
•Power can be measured in kilowatts (kW)
•Time can be measured in hours (h)
•In this case, energy has units of kilowatt-hours (kW h)
•The lightbulb from before receives 3.6 kW h of energy over the 6
hours
•This value is much easier to understand for consumers and
energy providers; thinking in terms of hours of use is more
practical than seconds
BLESSING NDAZIE ELECTRICITY 148

149. Calculating with kWh
•As has been stated previously, the equation for energy
transferred is:
BLESSING NDAZIE ELECTRICITY 149
•But here, different units are considered:
• E= energy transferred, measured in kilowatt hours (kW h)
• P= power of the appliance, measured in kilowatts (kW)
• t= time, measured in hours (h)

150. •The usual unit of energy is joules (J), which is one watt-second
•To find the number of joules in 1 kW h, convert the power and time to
watts and seconds
•1000 watts multiplied by 3600 seconds is equal to 1000 multiplied by
3600, in watt-seconds
•Therefore, 1 kWh = 3.6 × 106 J
•To convert from kW h to J
•To convert from J to kW h:
•The kW h is a large unit of energy, and is mostly used for energy in
homes, businesses and factories
BLESSING NDAZIE ELECTRICITY 150

151. Worked Example
A cooker transfers 1.2 × 10
9
J of energy electrically to the
thermal store of the heating element during its use over a year.
Assume that 1 kW h costs 14.2 p.
100 p = £1 (100 pence = 1 pound)
Calculate the cost of using the oven for the year.
BLESSING NDAZIE ELECTRICITY 151

152. Answer:
BLESSING NDAZIE ELECTRICITY 152

153. Circuit components
BLESSING NDAZIE ELECTRICITY 153

154. Circuit symbols
•Circuit symbols are used in circuit diagrams to represent
circuitcomponents
•You will be expected to knowwhat each component isandhow it
behavesin a circuit
BLESSING NDAZIE ELECTRICITY 154

155. Circuit symbols
BLESSING NDAZIE ELECTRICITY 155

156. Circuit symbols
BLESSING NDAZIE ELECTRICITY 156

157. Types of circuit components
Power supplies
•Cells, batteries, power supplies and generators allsupply
currentto the circuit
Resistors
•Potential dividers, fixed and variable resistors, thermistors and
light-dependent resistors (LDRs) are all used tocontrol current
Meters
•Ammeters and voltmeters are used to measure the current and
potential difference
•Ammeters are always connected in series whilst voltmeters are always
connected in parallel
BLESSING NDAZIE ELECTRICITY 157

158. Switches and functional components
•Switches open and close a circuit and determine whether current can flow
•Functional components perform specific roles when current passes through
them:
•Motors rotate
•Lamps emit light
•Heaters transfer thermal energy
•Bells emit a sound
Electromagnetic components
•Magnetising coils, relays and transformers use electromagnetic effects
•Relays use a small current in one circuit to switch on a much larger current in another
•Transformers 'step up' and 'step down' current and potential difference
Fuses
•Protect expensive components from current surges and act as a safety
measure against fire
BLESSING NDAZIE ELECTRICITY 158
Types of circuit components

159. Thermistors
•A thermistor is anon-
ohmicconductor and a temperature-
dependent resistor
•The resistance of a thermistor
changes depending on
itstemperature
•As the
temperatureincreasesthe
resistance of a
thermistordecreasesand vice
versa
Types of circuit components
BLESSING NDAZIE ELECTRICITY 159

160. Light-dependent resistors
•A light-dependent resistor (LDR) is a
non-ohmic conductor and sensory
resistor
•Its resistance automatically changes
depending on the light energy falling
onto it (illumination)
•As thelight intensity increases,
theresistanceof an LDRdecreases
BLESSING NDAZIE ELECTRICITY 160

161. Diodes
•Diodes are occasionally drawn
with a horizontal line running
through the middle of them
•Diodes only allow current to flow
through them inonedirection
(see the diagram below)
•This is the direction that the triangle
points in the diagram
•Light emitting diodes (LEDs)
behave the exact same way, but
they emit light when current flows
through them
BLESSING NDAZIE ELECTRICITY 161

162. Series circuits
What is a series circuit?
•A series circuit contains
asinglecomplete loop
BLESSING NDAZIE ELECTRICITY 162
In this circuit, the switch, battery and both
lamps are in a single loop, making it a series
circuit

163. Current in a series circuit
•In a series circuit, the current is thesame value at any point
•This is because the number of electrons per second that passes
through one part of the circuit is the same number that passes
through any other part
•This means thatallcomponents in a closed-loop have the same
current
BLESSING NDAZIE ELECTRICITY 163
The current is the same at each
point in a series circuit

164. Factors affecting current in a series circuit
•The amount of current flowing around a series circuit depends
on two things:
•Thevoltageof the power source
•Theresistanceof the components in the circuit
•Increasingthevoltageof the power source
drivesmorecurrentaround the circuit
•So, decreasing the voltage of the power source reduces the current
•Increasingthenumberof components in the
circuitincreasesthetotalresistance
•Hencelesscurrentflows through the circuit
BLESSING NDAZIE ELECTRICITY 164

165. Factors affecting current in a series circuit
BLESSING NDAZIE ELECTRICITY 165
Current will increase if the voltage of the power supply increases, and decreases
if the number of components increases (because there will be more resistance)

166. Current in parallel circuits
•What is a parallel circuit?
•A parallel circuit consists of
multiple loops containing circuit
components
BLESSING NDAZIE ELECTRICITY 166
The bulbs are each in a separate loop in
this circuit, making it a parallel circuit

167. What is the rule for current in a
parallel circuit?
•In a parallel circuit, the currentsplitsalong eachbranchat a
junction
•Some of it goes down one branch and the rest goes down the other
•This means that the current from the source islargerthan the
current in each branch
BLESSING NDAZIE ELECTRICITY 167

168. Lighting circuits
•A lighting circuit is used to supply power to multiple light
sources
•Office lights are a common example, as multiple identical bulbs must
have the same brightness
•Lighting circuits are constructed inparallelbecause:
•Bulb's all have the same potential difference and therefore the same
brightness
•If one bulb breaks, the rest continue to function as current passes
along each branch independently
•This also means lamps can be switched off and on individually
without breaking the whole circuit
BLESSING NDAZIE ELECTRICITY 168

169. Calculating current in parallel circuits
•The currentbeforea junction is equal to
thesumof currents along each
branchafterthe junction
•At ajunctionin aparallelcircuit(where
two or more wires meet) the current
isconserved
•This means the amount of current flowing
into the junction is equal to the amount of
current flowing out of it
•This is becausechargeis conserved
•Note that the current does not always
split equally – often there will be more
current in some branches than in others
•The current in each branch will only be
identical if theresistanceof the
components along each branch areidentical
BLESSING NDAZIE ELECTRICITY 169
Current from the power supply (4 A) is split
along each branch (2 A). These current
combine again at the other side

170. Calculating current in parallel circuits
•Current behaves in this way because it is theflow of electrons:
•Electrons are physical matter – they cannot be created or destroyed
•This means the total number of electrons (and hence current) going
around a circuit must remain the same
•When the electrons reach a junction, however, some of them will go
one way and the rest will go the other
BLESSING NDAZIE ELECTRICITY 170
Current is split at a
junction into
individual branches

171. Worked Example
BLESSING NDAZIE ELECTRICITY 171

172. BLESSING NDAZIE ELECTRICITY 172

173. BLESSING NDAZIE ELECTRICITY 173

174. Examiner Tips and Tricks
•The direction of current flow is important when considering
junctions in a circuit. You should remember that current flows
from thepositiveterminal to thenegativeterminal of a cell /
battery. This will help determine the direction current is
flowing round a circuit.
BLESSING NDAZIE ELECTRICITY 174

175. Potential difference in series circuits
•In a series circuit, the sum of potential
differences across the components is
equal to the total e.m.f.
(electromotive force) of the power
supply
BLESSING NDAZIE ELECTRICITY 175
In a series circuit the components
share the e.m.f. of the power supply

176. Worked Example
BLESSING NDAZIE ELECTRICITY 176

177. Answer:
BLESSING NDAZIE ELECTRICITY 177

178. Potential difference in a parallel circuit
•The potential difference
acrosseachbranch of a parallel
circuit is the same as the e.m.f. of
the power source
•It is important to notice that the
potential difference in a parallel
circuit is equal across eachbranch
•In the example above, if one branch
in the circuit contained multiple
components, the 12 V would
besplitbetween the components
on that branch
BLESSING NDAZIE ELECTRICITY 178
The power source has an e.m.f .of 12 V and there
is a potential difference of 12 V across each
branch

179. Resistors in series & parallel
BLESSING NDAZIE ELECTRICITY 179

180. Combination of resistance in series
•When two or more components are connected inseries:
•Thecombinedresistance of the components is equal to thesumof
individual resistances
BLESSING NDAZIE ELECTRICITY 180

181. Combination of resistance in parallel
•When resistors are connected in parallel,
thecombinedresistance isless thanthe resistance of any of
the individual components
•If two resistors of equal resistance are connected in parallel,
then the combined resistance will halve
BLESSING NDAZIE ELECTRICITY 181

182. Determining resistance in parallel
•To determine the combined resistance of any combination of
two resistors, you must use the equation:
BLESSING NDAZIE ELECTRICITY 182

183. •The method to calculate the resistance:
•First find the value of1/R(by adding1/R
1+ 1/R
2)
•Next find the value ofRby using the reciprocal button on your
calculator (labelled eitherx
-1
or1/x, depending on your calculator)
BLESSING NDAZIE ELECTRICITY 183

184. BLESSING NDAZIE ELECTRICITY 184

185. BLESSING NDAZIE ELECTRICITY 185

186. Variable potential dividers
•When two resistors are connected in
series, the potential difference across
the power source is shared between
them
•A potential divider is a circuit
whichsplitspotential difference from a
power source, so only afractiongoes to
a component (a voltmeter, in the
diagram below)
BLESSING NDAZIE ELECTRICITY 186

187. Variable potential dividers
•The potential difference across each resistor depends upon its
resistance:
•The resistor with thelargest resistancewill have agreater potential
differencethan the other one
•If theresistanceof one of the resistors isincreased, it will get
agreatershare of the potential difference, whilst theotherresistor
will get asmallershare
•If one resistor is avariable resistor, the potential difference
across the other resistor can bealtered
•This means the potential difference across any componentin
parallelwith that resistor can also be altered
BLESSING NDAZIE ELECTRICITY 187

188. Resistors as Potential Dividers
•When two resistors are connected in series, the power source's
e.m.f. is split between the resistors
•This potential difference splits in thesame ratioas the resistance of
the two resistors
•The ratio of potential differences across each resistor can be
found using the following equation:
BLESSING NDAZIE ELECTRICITY 188

189. Electrical hazards
•Mains electricity can be dangerous if safety
procedures are not followed
•Voltages as low as 50 V can pose a serious risk of
electrocution
•Common electrical hazards include:
•damaged insulation
•overheating cables
•damp conditions
•excess current from overloading of plugs, extension
leads, single and multiple sockets when using a mains
supply
BLESSING NDAZIE ELECTRICITY 189

190. Electrical danger sign
•The risk of
electrocution is
indicated by hazard
signs but other risks
which would not be
signposted are listed
below
BLESSING NDAZIE ELECTRICITY 190

191. •Damaged insulation
If the insulation around an electrical cable is damaged, the metal part
of the wire may become exposed
If a person touches the exposed wire, they could be subjected to a
lethal electric shock
There is also a chance that current will flow between the exposed wire
and any piece of metal it comes into contact with
•Overheating of cables
If an excess of current flows in a wire, this can lead to overheating
This could cause the insulation to melt, or even cause a fire
BLESSING NDAZIE ELECTRICITY 191
Electrical hazards

192. •Damp conditions
•Damp conditions can be dangerous in the presence of electricity since
water is an electrical conductor
•If moisture comes into contact with a live wire, this could set up
•a short circuit within the device, which could cause a fire
•a conductive path for current to flow through a person to the earth, which could
cause electrocution
•Excess current from overloading
•An excessive current may flow if too many plugs, extension leads or sockets
are connected to the mains supply
•The heat created could cause the insulation to melt, or even cause a fire
BLESSING NDAZIE ELECTRICITY 192
Electrical hazards

193. Electrical fire due to excessive current
BLESSING NDAZIE ELECTRICITY 193
Too many appliances plugged into an extension lead can cause overheating and fire

194. Mains Circuits
•All electrical appliances are connected to the mains supply
•A mains circuit consists of:
•a live wire
•a neutral wire
•an earth wire
•The insulation covering each wire is colour-coded for easy
identification:
•Live wire –brown
•Neutral wire –blue
•Earth wire –green and yellow stripes
BLESSING NDAZIE ELECTRICITY 194

195. Live, neutral & earth wires
BLESSING NDAZIE ELECTRICITY 195

196. BLESSING NDAZIE ELECTRICITY 196
A mains-powered appliance in the UK contains live, neutral and earth wires
Live, neutral & earth wires

197. The live wire
The purpose of the live wire isto carry the
alternating current from the mains supply
to a circuit
It is the most dangerous of the three wires
If it touches the appliance without the
earth wire, it can cause electrocution
BLESSING NDAZIE ELECTRICITY 197

198. The neutral wire
The purpose of the neutral wire isto
form the opposite end of the circuit to
the live wire to complete the circuit
Because of its lower voltage, it is much
less dangerous than the live wire
BLESSING NDAZIE ELECTRICITY 198

199. The earth wire
The purpose of the earth wire isto act as a safety wire to
stop the appliance from becoming live
This prevents electric shocks from occurring if the
appliance malfunctions or the live wire breaks off and
touches the case of the plug
In order to protect the user or the device, there are
several safety features built into domestic appliances,
including:
•double insulation
•earthing
•fuses
•circuit breaker
BLESSING NDAZIE ELECTRICITY 199

200. Double insulation
•The conducting part of a wire is
usually made of copper or some
other metal
•If this comes into contact with a
person, this poses a risk of
electrocution
•For this reason, wires are covered
with an insulating material, such as
rubber
BLESSING NDAZIE ELECTRICITY 200

201. Double insulation
•Some appliances do not have metal cases and
so there is no risk of them becoming electrified
•Such appliances are said to bedouble
insulated, as they have two layers of insulation:
•Insulation around the wires themselves
•A non-metallic case that acts as a second layer of
insulation
•Double insulated appliances do not require an
earth wire or have been designed so that the
earth wire cannot touch the metal casing
BLESSING NDAZIE ELECTRICITY 201

202. Earthing
•Many electrical appliances have metal cases
•This poses a potential safety hazard:
•If a live wire (inside the appliance) came into contact with the case, the
case would become electrified and anyone who touched it would risk
being electrocuted
•The earth wire is an additional safety wire that can reduce this risk
•If this happens:
•The earth wire provides alow resistance path to the earth
•It causes asurge of current in the earth wireand hence also in the live
wire
•The high current through the fuse causes it tomelt and break
•This cuts off the supply of electricity to the appliance, making it safe
BLESSING NDAZIE ELECTRICITY 202

203. Fuses & trip switches
•Fusesandtrip switches(circuit breakers) are safety devices
designed tocut off the flow of electricityto an appliance if
the current becomestoo large(due to a fault or a surge)
BLESSING NDAZIE ELECTRICITY 203

204. Fuses
•Fusesare used to protectindividual appliances
•Fuses are located in theplug
•Fuses usually consist of a glass cylinder containing a thin
metalwire
•A fuse without an earth wireprotectsthe circuit and the
cabling for a double-insulated appliance
•If the current in the wire becomes too large:
•The wireheats upandmelts
•This causes the wire tobreak, breaking
thecircuitandstoppingthecurrent
BLESSING NDAZIE ELECTRICITY 204

205. Circuit symbol of a fuse
BLESSING NDAZIE ELECTRICITY 205
•Fuses haveratings, which signify themaximum currentthat
can flow through the fuse wire without it melting
•If the currentexceedsthat value, the fusewire meltsand
theindividual applianceisdisconnectedfrom the mains
supply
•Fuses come in values of3 A,5 Aand13 A
•The correct fuse to use is the value just above the current
required for the appliance

206. Choosing the correct fuse
•Suppose an appliance uses 3.1 amps
•A 3 amp fuse would betoo small- the fuse would
blow as soon as the appliance was switched on
•A 13 amp fuse would betoo large- it would allow
an extra 10 amps to pass through the appliance
before it finally blew
•A 5 amp fuse would be themost
appropriatechoice, as it is the next size up
BLESSING NDAZIE ELECTRICITY 206

207. Trip switches
•The current enters the house at theconsumer
unit(sometimes referred to as a 'fuse box')
•The consumer unit consists of a series oftrip
switches(or circuit breakers) which control the
amount of current supplied to each circuit within the
house
•When the current is too high the switch 'trips'
(automatically flicks to the off position)
•This stops the current flowing in that circuit
BLESSING NDAZIE ELECTRICITY 207

208. Example of a domestic circuit
BLESSING NDAZIE ELECTRICITY 208
The consumer unit distributes current to all the circuits in the house

209. Trip switches…
•The mainadvantagesof trip switches are:
•they provide protection from current surges or faults
•they can be reset when the problem is fixed
BLESSING NDAZIE ELECTRICITY 209