SECTION 4

Electricity and
magnetism
Topics
4.1 Simple magnetism and magnetic fields
4.2 Electrical quantities
4.3 Electric circuits
4.4 Practical electricity
4.5 Electromagnetic effects
4.6 Uses of an oscilloscope
 4.1 Simple magnetism and
magnetic fields
FOCUS POINTS
★ Describe forces between magnets and magnetic materials and between magnetic poles and understand
the meaning of various terms associated with magnetism.
★ State the differences between temporary and permanent magnets and between magnetic and non-
magnetic materials.
★ Describe, draw and state the direction of magnetic fields.
★ Know that the spacing of the magnetic field lines represents the relative strength of a magnetic field.
★ Describe how magnetic field lines can be plotted using a compass or iron filings.
★ Know the different uses of permanent magnets and electromagnets.

A familiar example of a magnet is a compass needle with one north-seeking pole. You will find that
all magnets have two poles: like poles repel, unlike poles attract. A magnet can induce magnetism
in certain materials such as iron and steel and is surrounded by a magnetic field which exerts a
force on another magnet. The pattern of magnetic field lines can be made visible with the aid of iron
filings. Electromagnets are formed from coils of wire through which an electrical current is passed
that allows the strength of the magnet to be varied and turned on and off easily. They are used
in many electrical devices from doorbells to motors. You will learn that permanent magnets and
electromagnets have differing properties and uses.
In a magnetic field, the closer the field lines are at a point, the stronger is the magnetic field.

Properties of magnets North and south poles

A magnet has two poles; a north pole (N pole) and
Magnetic materials a south pole (S pole). If a magnet is supported so
Some materials, known as ferromagnets, can be that it can swing in a horizontal plane it comes
magnetised to form a magnet. In their unmagnetised to rest with one pole, the N pole, always pointing
form they are attracted to a magnet. roughly towards the Earth’s north pole. A magnet
can therefore be used as a compass.
Magnetic poles
The poles are the places in a magnet to which Law of magnetic poles
magnetic materials, such as iron filings, are If the N pole of a magnet is brought near the
attracted. They are near the ends of a bar magnet N pole of another magnet, repulsion occurs.
and occur in pairs of equal strength. Two S (south-seeking) poles also repel. By contrast,
N and S poles always attract.
The law of magnetic poles summarises these facts
and states:
Like poles repel, unlike poles attract.
The force between magnetic poles decreases as their
separation increases.

176
 Magnetisation of iron and steel

Induced magnetism Magnetisation of iron

When a piece of unmagnetised magnetic material
touches or is brought near to the pole of a
and steel
permanent magnet, it becomes a magnet itself. Chains of small iron nails and steel paper clips can
The material is said to have magnetism induced in be hung from a magnet (Figure 4.1.3). Each nail
it. Figure 4.1.1 shows that a N pole in the permanent or clip magnetises the one below it and the unlike
magnet induces a N pole in the right-hand end of poles so formed attract.
the magnetic material. If the iron chain is removed by pulling the top
nail away from the magnet, the chain collapses,
magnetic showing that magnetism induced in iron is
material
temporary. When the same is done with the steel
chain, it does not collapse; magnetism induced in
S N S N steel is permanent.

permanent induced Key definitions

magnet magnet
Temporary magnets made of soft iron, lose their
▲ Figure 4.1.1 Induced magnetism magnetism easily
Permanent magnets made of steel, retain their magnetism
This can be checked by hanging two iron nails from
the N pole of a magnet. Their lower ends repel each
other (Figure 4.1.2a) and both are repelled further
from each other when the N pole of another magnet N S
is brought close (Figure 4.1.2b).
S N
b iron nails
a
S S N S
S N
steel paper
clips
N S
S N

N N N S
iron
S N
nails

N S
greater
repulsion ▲ Figure 4.1.3 Investigating the magnetisation of iron
repulsion and steel
N
Magnetic materials such as iron that magnetise
easily but readily lose their magnetism (are easily
demagnetised) are said to be soft. Those such as
steel that are harder to magnetise than iron but
stay magnetised are hard. Both types have their
   uses; very hard ones are used to make permanent
▲ Figure 4.1.2 Magnetic repulsion magnets.

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 4.1 Simple magnetism and magnetic fields

Magnetic and non-magnetic S N bar magnet

materials line of force

Magnetic materials such as iron, steel, nickel N

and cobalt are attracted by a magnet and can cork

be magnetised temporarily or permanently.
Non-magnetic materials such as aluminium and bowl of
water
wood are not attracted by a magnet and cannot
be magnetised. magnetised
S steel needle
or rod
Key definitions
Magnetic materials materials that can be magnetised by ▲ Figure 4.1.4 Detecting magnetic force
a magnet; in their unmagnetised state they are attracted
by a magnet
It is useful to consider that a magnetic field has
a direction and to represent the field by lines of
Non-magnetic materials materials that cannot be force. It has been decided that the direction of a
magnetised and are not attracted by a magnet
magnetic field at a point should be the direction of
the force on a N pole. To show the direction, arrows
Magnetic fields are put on the lines of force and point away from a
N pole towards a S pole.
The space surrounding a magnet where it produces
a magnetic force is called a magnetic field. Key definition
The force around a bar magnet can be detected and Direction of a magnetic field at a point the direction of
shown to vary in direction, using the apparatus in the force on the N pole of a magnet at that point
Figure 4.1.4. If the floating magnet is released near
the N pole of the bar magnet, it is repelled to the
S pole and moves along a curved path known as Strength of magnetic fields
a line of force or a field line. It moves in the A magnetic field is stronger in regions where the
opposite direction if its south pole is uppermost. field lines are close together than where they are
further apart.

Test yourself
1 Which one of these statements is true? Copy the diagram and mark on the position of all the
A magnet attracts poles if the magnets
A plastics a attract each other
B any metal b repel each other.
C iron and steel 3 In Figure 4.1.8a on the next page, is the magnetic
D aluminium. field stronger or weaker at X than at a point closer to
2 Two bar magnets are positioned side by side as one of the magnets? Explain your answer.
shown in Figure 4.1.5. The north pole is marked on
one of the magnets.

▲ Figure 4.1.5

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 Magnetic fields

Practical work
Plotting lines of force A typical field pattern is shown in Figure 4.1.7.

Plotting compass method

A plotting compass is a small pivoted magnet
in a glass case with non-magnetic metal walls
(Figure 4.1.6a).
a
S N

compass
needle

▲ Figure 4.1.7 Magnetic field lines around a bar magnet

b The combined field due to two neighbouring

C magnets can also be plotted to give patterns like
n those in Figure 4.1.8. In part a, where two like
s
poles are facing each other, the point X is called a
B
neutral point. At X, the field due to one magnet
A cancels out that due to the other and there are no
plotting
S N compass lines of force.
a
▲ Figure 4.1.6

Lay a bar magnet on a sheet of paper. Place

the plotting compass at a point such as A
(Figure 4.1.6b), near one pole of the magnet. In
Figure 4.1.6b it is the N pole. Mark the position N X N
of the poles (n, s) of the compass by pencil
dots B, A. Move the compass so that pole s is
exactly over B, mark the new position of n by
dot C.
Continue this process until the other pole of the b
bar magnet is reached (in Figure 4.1.6b it is the
S pole). Join the dots to give one line of force and
show its direction by putting an arrow on it. Plot
other lines by starting at different points round
the magnet. S N

▲ Figure 4.1.8 Field lines due to two neighbouring

magnets

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 4.1 Simple magnetism and magnetic fields

Iron filings method

a
Place a sheet of paper on top of a bar magnet and
sprinkle iron filings thinly and evenly onto the
paper from a ‘pepper pot’.
Tap the paper gently with a pencil and the filings
should form patterns showing the lines of force.
Each filing turns in the direction of the field when
the paper is tapped.
This method is quick but no use for weak fields.
1 Sketch the field lines around a bar magnet
marking on the N and S poles and the
direction of the field lines.
2 Figure 4.1.9 shows typical iron filings patterns
obtained with two magnets. Why are the b
patterns different?
3 What combination of poles would give the
observed patterns in Figure 4.1.9 a and b?

▲ Figure 4.1.9 Field lines round two bar magnets shown

by iron filings

Going further

Magnetisation and demagnetisation Solenoids (see Topic 4.5) can be used to magnetise and
demagnetise magnetic materials (Topic 4.5.4); dropping
A ferromagnetic material can be magnetised by placing
or heating a magnet also causes demagnetisation.
it inside a solenoid and gradually increasing the direct
Hammering a magnetic material in a magnetic field
current (d.c.). This increases the magnetic field strength
causes magnetisation but in the absence of a field it
in the solenoid (the density of the field lines increases),
causes demagnetisation. ‘Stroking’ a magnetic material
and the material becomes magnetised. Reversing
several times in the same direction with one pole of a
the direction of current flow reverses the direction
magnet will also cause it to become magnetised.
of the magnetic field and reverses the polarity of the
magnetisation. A magnet can be demagnetised by
placing it inside a solenoid through which an alternating
current (a.c.) is passed and gradually reduced.

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 Electromagnets

Practical work

Simple electromagnet
An electromagnet is a coil of wire wound wooden
on a soft iron core. A 5 cm iron nail and 3 m electromagnet stand
of PVC-covered copper wire (SWG 26) are
needed.
a Leave about 25 cm at one end of the wire (for
connecting to the circuit) and then wind about paper clips
50 cm as a single layer on the nail. Keep the
turns close together and always wind in the
same direction. Connect the circuit of Figure
4.1.10, setting the rheostat (variable resistor,
see p. 199) at its maximum resistance.
Find the number of paper clips the A

electromagnet can support when the current (0–2 A)

(2–3 V)
is varied between 0.2 A and 2.0 A. Record the (0–15 Ω)
results in a table.
Deduce how the strength of the electromagnet ▲ Figure 4.1.10
changes when the current is increased. c Place the electromagnet on the bench and
b Add another two layers of wire to the nail, under a sheet of paper. Sprinkle iron filings on
winding in the same direction as the first layer. the paper, tap it gently and observe the field
Repeat the experiment. pattern. Compare the pattern with that given
Deduce how the strength of the electromagnet by a bar magnet.
has been changed by increasing the number d Use a plotting compass to find which end of
of turns of wire. the electromagnet is a N pole.
4 Name two variables which you might think
could affect the strength of an electromagnet.
5 How could you use a compass to determine which
end of the current-carrying coil is a north pole?

Electromagnets coil soft iron core

An electromagnet is formed from a coil of wire

through which an electrical current is passed that
allows the strength of the magnet to be varied. S

The magnetism of an electromagnet is temporary N

and can be switched on and off, unlike that of a field
permanent magnet. It has a core of soft iron which line
current
is magnetised only when there is current in the direction
surrounding coil.
The strength of an electromagnet increases if ▲ Figure 4.1.11 C-core or horseshoe electromagnet
(i) the current in the coil increases In C-core (or horseshoe) electromagnets, condition
(ii) the number of turns on the coil increases (iii) is achieved (Figure 4.1.11). Note that the
(iii) the poles are moved closer together. coil on each limb of the core is wound in opposite
directions.
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 4.1 Simple magnetism and magnetic fields

Uses of permanent magnets

and electromagnets
Permanent magnets made from magnetic materials
such as steel retain their magnetism, so can be
used in applications where the magnetic field does
not need to be varied. These include a compass,
computer hard disk, electric motor (see Topic 4.5.5)
electricity generator (see Topic 4.5.2), microphone,
loudspeaker and many more everyday devices such
as credit and debit cards.
An advantage over an electromagnet is that it
does not require a current to maintain its magnetism.
Electromagnets are temporary and are used
where one wants to be able to vary the strength
of the magnetic field (by varying the current) and
switch it on and off. As well as being used in cranes
to lift iron objects, scrap iron, etc. (Figure 4.1.12),
electromagnets are an essential part of many electrical
devices such as electric bells, magnetic locks, relays ▲ Figure 4.1.12 Electromagnet being used to lift scrap
and practical motors and generators (see Topic 4.5.3). metal.

Going further

Magnetic shielding At most places on the Earth’s surface a magnetic

compass points slightly east or west of true north,
Any ferromagnetic material can be used for magnetic
i.e. the Earth’s geographical and magnetic north
screening of sensitive electronic equipment. Steel is
poles do not coincide. The angle between magnetic
often used as it is cheap, readily available and works
north and true north is called the declination (Figure
well in strong magnetic fields. Mu-metal, a nickel-
4.1.14). In Hong Kong in 2020 it was about 3º W of N and
iron soft ferromagnetic material, is more effective for
changing slowly.
weaker magnetic fields but is more expensive.
geographical
Earth’s magnetic field north

If lines of force are plotted on a sheet of paper with magnetic

north
no magnets nearby, a set of parallel straight lines is
obtained. They run roughly from S to N geographically
(Figure 4.1.13), and represent a small part of the Earth’s
magnetic field in a horizontal plane.

declination
north

▲ Figure 4.1.14 The Earth’s geographical and magnetic

▲ Figure 4.1.13 Lines of force due to the Earth’s field poles do not coincide.

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 Exam-style questions

Revision checklist
After studying Topic 4.1 you should know and After studying Topic 4.1 you should be able to:
understand: ✔ state the properties of magnets, describe induced
✔ like magnetic poles repel, unlike magnetic poles magnetism and distinguish between the magnetic
attract properties of iron and steel
✔ the difference between magnetic and non- ✔ recall that a magnetic field is the region round a
magnetic materials, and permanent and magnet where a magnetic force is exerted and is
electromagnets represented by lines of force whose direction at
✔ how to map the magnetic field around a bar magnet, any point is the direction of the force on a N pole
by the plotting compass and iron filings methods. ✔ recall that the magnetic field is strongest in
regions where the field lines are closest
together.

Exam-style questions
1 Copy Figure 4.1.15 which shows a plotting 2 a Describe an experiment using a plotting
compass and a magnet. compass to map the magnetic field lines
a Label the N pole of the magnet. [1] around a bar magnet. [4]
b Sketch the magnetic field line on which the b Explain why permanent magnets are used in
compass lies. [2] some applications and electromagnets
c State the direction of the magnetic in others. [4]
field line. [1] c Give two uses of a permanent magnet. [2]
[Total: 10]
3 a Explain how magnetic forces arise. [2]
b Where are the magnetic field lines
strongest around a bar magnet? [2]
c State how you would recognise from a pattern
of magnetic field lines where the field is
i strongest
ii weakest. [2]
[Total: 6]
▲ Figure 4.1.15

[Total: 4]

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4.2 Electrical quantities
4.2.1 Electric charge
FOCUS POINTS
★ Understand that there are positive and negative charges and that opposite charges attract and like
charges repel.
★ Explain the charging of solids by friction.
★ Describe an experiment to determine whether a material is an electrical conductor or an insulator.
★ Explain the difference between electrical conductors and insulators using a simple electron model, and
give examples of each.
★ Know that charge is measured in coulombs.
★ Describe an electric field, explain its direction and describe simple electric field patterns.

Electrostatic charges arise when electrons are transferred between objects by rubbing. Sparks can
fly after you comb your hair or walk across a synthetic carpet when you touch an earthed object,
through which the charge can be neutralised; the discharge can lead you to feel a small electric
shock. A flash of lightning is nature’s most spectacular static electricity effect. There are two types
of electrostatic charge. Like charges repel while opposite charges attract. Charges build up on an
insulator such as plastic and remain static, but for conductors like metals, charges flow away to try
to neutralise charge. Both electrical conductors and insulators have their uses.
Electric charges are surrounded by an electric field which exerts a force on a nearby charge.
This effect is made use of in applications from ink-jet printers to crop sprayers. As with a magnetic
field, an electric field exerts an action-at-a-distance force.

Clothes containing nylon often crackle when they

are taken off. We say they are charged with static
electricity; the crackles are caused by tiny electric
sparks which can be seen in the dark. Pens and
combs made of certain plastics become charged
when rubbed on your sleeve and can then attract
scraps of paper.

Positive and negative charges

When a strip of polythene is rubbed with a cloth
it becomes charged. If it is hung up and another
rubbed polythene strip is brought near, repulsion
occurs (Figure 4.2.2). Attraction occurs when a
rubbed strip of cellulose acetate is brought
near.

▲ Figure 4.2.1 A flash of lightning

184
 4.2.1 Electric charge

nucleus of one proton

thread

one electron moving

around nucleus

paper stirrup

rubbed
polythene
▲ Figure 4.2.3 Hydrogen atom
strips like The production of charges by rubbing can be explained
charges
repel by supposing that friction causes electrons to be
transferred from one material to the other. For example,
when cellulose acetate is rubbed with a cloth, electrons
go from the acetate to the cloth, leaving the acetate
short of electrons, i.e. positively charged. The cloth
now has more electrons than protons and becomes
▲ Figure 4.2.2 Investigating charges negatively charged. Note that it is only electrons which
move; the protons remain fixed in the nucleus.
This shows there are two kinds of electric charge.
That on cellulose acetate is taken as positive (+)
and that on polythene is negative (–). It also
Test yourself
shows that: 1 Two identical conducting balls, suspended on
nylon threads, come to rest with the threads
Like charges (+ and +, or – and –) repel, while unlike making equal angles with the vertical, as shown in
charges (+ and –) attract. Figure 4.2.4.
Which of these statements is true?
The force between electric charges decreases as This shows that
their separation increases. A the balls are equally and oppositely charged
B the balls are oppositely charged but not
Key definitions necessarily equally charged
Positive charges repel other positive charges, but C one ball is charged and the other is uncharged
positive charges attract negative charges D the balls both carry the same type of charge.

Negative charges repel other negative charges, but

negative charges attract positive charges

Charges, atoms and electrons

There is evidence (Topic 5.1) that we can picture
an atom as being made up of a small central
nucleus containing positively charged particles
called protons, surrounded by an equal number of ▲ Figure 4.2.4
negatively charged electrons. The charges on a
2 Explain in terms of electron movement what
proton and an electron are equal and opposite so an happens when a polythene rod becomes charged
atom as a whole is normally electrically neutral, i.e. negatively by being rubbed with a cloth.
has no net charge. 3 Two electrostatic charges are brought close
Hydrogen is the simplest atom with one together.
proton and one electron (Figure 4.2.3). A copper a When one charge is positive and the other is
atom has 29 protons in the nucleus and 29 negative, are they attracted or repelled from
each other?
surrounding electrons. Every nucleus except b When both charges are negative, are they
hydrogen also contains uncharged particles attracted or repelled?
called neutrons.

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 4.2 Electrical quantities

Units of charge Key definition

Charge is measured in coulombs (C) and is defined Coulomb (C) unit of charge
in terms of the ampere (see Topic 4.2.2).
The charge on an electron e = 1.6 × 10 −19 C.

Going further

Practical work

Gold-leaf electroscope not, repeat the process but press harder. The
electroscope has now become negatively
metal cap
charged by contact with the polythene strip,
metal rod from which electrons have been transferred.
insulating
plug
Insulators and conductors
Touch the cap of the charged electroscope
metal plate with different things, such as a piece of
gold leaf paper, a wire, your finger, a comb, a cotton
handkerchief, a piece of wood, a glass rod,
glass window
wooden or a plastic pen, rubber tubing. Record your
metal case results.
earthed by
resting on When the leaf falls, charge is passing to
bench or from the ground through you and the
▲ Figure 4.2.5 Gold-leaf electroscope material touching the cap. If the fall is rapid
the material is a good conductor; if the leaf
A gold-leaf electroscope consists of a metal falls slowly, the material is a poor conductor.
cap on a metal rod at the foot of which is a If the leaf does not alter, the material is a good
metal plate with a leaf of gold foil attached insulator.
(Figure 4.2.5). The rod is held by an
insulating plastic plug in a case with glass The gold-leaf electroscope used in this
sides to protect the leaf from draughts. experiment could be replaced by an
electronic instrument capable of measuring
Detecting a charge electric charge –
Bring a charged polythene strip towards the an electrometer.
cap: the leaf rises away from the plate. When
1 How could you charge a polythene rod?
you remove the charged strip, the leaf falls
2 How could you transfer charge from a
again. Repeat with a charged acetate strip.
polythene rod to a gold-leaf electroscope?
Charging by contact 3 Why does the leaf of the electroscope rise
Draw a charged polythene strip firmly across when it gains charge?
the edge of the cap. The leaf should rise and 4 How can you discharge the electroscope?
stay up when the strip is removed. If it does

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 4.2.1 Electric charge

Electrons, insulators and conductors

In an insulator all electrons are bound firmly to
their atoms; in a conductor some electrons can
move freely from atom to atom. An insulator can be
charged by rubbing because the charge produced
cannot move from where the rubbing occurs, i.e. the
electric charge is static. A conductor will become
charged only if it is held with an insulating handle;
otherwise electrons are transferred between the
conductor and the ground via the person’s body. ▲ Figure 4.2.6 Uniform electric field
Good insulators include plastics such as polythene,
Moving charges are deflected by an electric field
cellulose acetate, Perspex and nylon. All metals and
due to the electric force exerted on them.
carbon are good conductors. In between are materials
The electric field lines radiating from an isolated
that are both poor conductors and (because they
positively charged conducting sphere and a point
conduct to some extent) poor insulators. Examples
charge are shown in Figures 4.2.7a and b: the field lines
are wood, paper, cotton, the human body and the
again emerge at right angles to the conducting surface.
Earth. Water conducts and if it were not present in
materials such as wood and on the surface of, for
example, glass, these would be good insulators.
Dry air insulates well.

Electric fields
When an electric charge is placed near to another
electric charge it experiences a force. The electric
force does not require contact between the two
charges so we call it an ‘action-at-a-distance force’
– it acts through space. The region of space where
an electric charge experiences a force due to other
▲ Figure 4.2.7a Electric field around a charged conducting
charges is called an electric field. If the electric sphere
force felt by a charge is the same everywhere in a
region, the field is uniform; a uniform electric field
is produced between two oppositely charged parallel
metal plates (Figure 4.2.6). It can be represented by
evenly spaced parallel lines drawn perpendicular to the
metal surfaces. The direction of an electric field at a
point, denoted by arrows, is the direction of the force
on a small positive charge placed in the field (negative +
charges experience a force in the opposite direction to
the field). An electric field is a vector quantity as it
has both magnitude (strength) and direction.

Key definition
Direction of an electric field at a point the direction of
the force on a positive charge at that point
▲ Figure 4.2.7b Electric field around a point charge

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 4.2 Electrical quantities

Going further

Dangers of static electricity Sparks from static electricity can be particularly

dangerous when flammable vapour is present.
Sparks occur between electrostatic charges when the
Fuel flowing in a pipeline (particularly a plastic pipe)
electric field is strong enough. Damage can be reduced
experiences friction, which may lead to a build-up of
by providing an easy path for electrons to flow safely
static charge. During refuelling, aircraft, fuel tanker
to and from the earth. For example, a tall building
and pipeline hoses are all earthed to avoid sparks which
is protected by a lightning conductor consisting of a
could ignite the fuel and cause an explosion.
thick copper strip fixed on the outside of the building
connecting metal spikes at the top to a metal plate in Computers and sensitive electronic equipment should
the ground (Figure 4.2.8). also be earthed to avoid electrostatic damage.
Thunderclouds carry charges: a negatively charged
cloud passing overhead repels electrons from the
Uses of static electricity
spikes to the Earth. The points of the spikes are left There are many uses of static electricity in applications
with a large positive charge (charge concentrates on from flue-ash precipitation in coal-burning power
sharp points) which removes electrons from nearby stations, paint and crop spraying to photocopiers and
air molecules, so charging them positively and ink-jet printers.
causing them to be repelled from the spike. In an ink-jet printer tiny drops of ink are forced out of a
This effect, called action at points, results in an fine nozzle, charged electrostatically and then passed
‘electric wind’ of positive air molecules streaming between two oppositely charged plates; a negatively
upwards which can neutralise electrons discharging charged drop will be attracted towards the positive plate
from the thundercloud in a lightning flash. If a flash causing it to be deflected as shown in Figure 4.2.9.
occurs it is now less violent and the conductor gives it The amount of deflection and hence the position at which
an easy path to ground. the ink strikes the page is determined by the charge on
the drop and the p.d. between the plates; both of these
thundercloud are controlled by a computer. About 100 precisely located
drops are needed to make up an individual letter but very
fast printing speeds can be achieved.
stream of
positive air
molecules
ink-jet nozzle

tall spikes
building electrostatic
copper
charging unit
strip

deflecting
plates
negative positive

electrons
repelled path of negatively
to Earth charged ink drop
metal plate
in ground paper
▲ Figure 4.2.8 Lightning conductor ▲ Figure 4.2.9 Ink-jet printer

Test yourself
Test yourself 5 Name
4 Describe the electric field around a negatively a two applications
charged conducting sphere. b two dangers
of static electricity.

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 4.2.2 Electric current

4.2.2 Electric current

FOCUS POINTS
★ Understand that an electric current consists of moving electric charges.
★ Define electric current and use the correct equation in calculations.
★ Describe the use of analogue and digital ammeters and the difference between alternating current (a.c.)
and direct current (d.c.).
★ Describe the role of free electrons in electrical conduction in metals.
★ Know that the flow of electrons in a circuit is in the opposite direction to that of the conventional current
flow.

In the previous topic you learnt about positive and negative static charges and how they were
produced on conductors and insulators. In this topic you will discover that moving charges in a
conductor produce an electric current which is proportional to the rate of flow of charge. Every
electrical appliance you use, from hair dryer to computer, relies on the flow of an electric current.
In a metal the current is produced by the movement of electrons. By convention, electric current is
linked to the flow of positive charge, which is in the opposite direction to the way electrons move.
You will find out how to connect an ammeter to a circuit to measure the size of an electric current
and learn about the different types of current.

An electric current consists of moving electric thread

charges. In Figure 4.2.10, when the van de Graaff
insulating van de Graaff
machine is working, it produces a continuous supply handle generator
metal
of charge which produces an electric field between plates
the metal plates to which it is connected. The table-tennis
ball coated
table-tennis ball shuttles rapidly backwards and with ‘Aquadag‘
forwards between the plates and the very sensitive to make it
conducting
meter records a small current. As the ball touches
each plate it becomes charged and is repelled to the
other plate. In this way charge is carried across the
gap. This also shows that static charges, produced
by friction in the van de Graaff machine, cause a 5 cm
deflection on a meter just as current electricity
produced by a battery does.
In a metal, each atom has one or more loosely
held electrons that are free to move. When a van
de Graaff or a battery is connected across the
ends of such a conductor, the free electrons drift
slowly along it in the direction from the negative
picoammeter
to the positive terminal of a battery. There is then
a current of negative charge. This is how electrical ▲ Figure 4.2.10 Demonstrating that an electric current
conduction occurs in a metal. consists of moving charges

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 4.2 Electrical quantities

Effects of a current The unit of charge, the coulomb (C), is defined in

terms of the ampere.
An electric current has three effects that reveal its One coulomb is the charge passing any point in a
existence and which can be shown with the circuit circuit when a steady current of 1 ampere flows for
of Figure 4.2.11. 1 second. That is, 1 C = 1 A s.
battery
(1.5 V cells)
Key definition
thick Ampere (A) unit of current given by the coulomb per
copper
wire second (C/s)

In general, if a steady current I (amperes) flows for

time t (seconds) the charge Q (coulombs) passing
plotting
compass lamp any point is given by
dilute
sulfuric Q=I ×t
acid
Current must have a complete path (a circuit) of conductors
if it is to flow. When drawing circuit diagrams, components
circuit board
are represented by symbols. Some commonly used symbols
▲ Figure 4.2.11 Investigating the effects of a current are represented in Topic 4.3.1.
Heating and lighting
The lamp lights because the small wire inside (the Worked example
filament) is made white hot by the current. Current flows in an electrical circuit.
Magnetic a A charge of 2 C passes a point in the circuit in 5 s,
The plotting compass is deflected when it is placed calculate the current flowing past that point.
near the wire because a magnetic field is produced I = Q/t = 2 C/5 s = 0.4 A
around any wire carrying a current. b A current of 3 A flows past another point in the circuit in
Chemical 10 seconds. How much charge passes the point in this time?

Bubbles of gas are given off at the wires in the acid Q = I × t = 3 A × 10 s = 30 C

because of the chemical action of the current. Now put this into practice
The ampere and the coulomb 1 A current of 2 A flows past a point in an electrical circuit in
20 s. How much charge passes the point in this time?
An electric current is defined as the charge passing a 2 A charge of 2 C passes a point in an electrical circuit in
point per unit time and can be written in symbols as 7 s. Calculate the current flowing past that point.
I= Q
t
where I is the current when charge Q passes any
Conventional current
point in a circuit in time t. Before the electron was discovered scientists agreed
It shows that current is the rate of flow of charge to think of current as positive charges moving round
in a circuit. a circuit in the direction from positive to negative
The unit of current is the ampere (A). One of a battery. This agreement still stands. Arrows on
milliampere (mA) is one-thousandth of an ampere. circuit diagrams show the direction of what we call
Current is measured by an ammeter. the conventional current, i.e. the direction in which
positive charges would flow. Electrons flow in the
Key definition opposite direction to the conventional current.
Electric current the charge passing a point per unit time
Key definition
charge Q
electric current I = or where Q is the charge flowing pastConventional current
a particular point flowst.from positive to negative; the
in time
time t flow of free electrons is from negative to positive
ere Q is the charge flowing past a particular point in time t.

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 4.2.2 Electric current

Ammeters
An ammeter is used to measure currents. It should
always be placed in series in a circuit with the
positive terminal on the ammeter connected to the
positive terminal of the supply, as described in the
practical work below (see Figure 4.2.13 overleaf).
A simple moving coil ammeter will read d.c. currents
only on an analogue display. It may have two ranges
and two scales in the display.
A multimeter can have either a digital or
analogue display (see Figure 4.1.12a and b) and be
used to measure a.c. and d.c. currents (or voltages
and also resistance). The required function is first
selected, say d.c. current.
When making a measurement on either type
of ammeter a suitable range must be chosen. For
example, if a current of a few milliamps is expected,
the 10 mA range might be selected and the value
of the current (in mA) read from the display; if the
reading is off-scale, the sensitivity should be reduced
by changing to the higher, perhaps 100 mA, range.

▲ Figure 4.2.12b Digital multimeter

Test yourself
6 Explain how electrical conduction occurs in a
metal.
7 Explain how you would connect an ammeter into a
circuit.
8 What is the current in a circuit if the charge
passing each point is
a 10 C in 2 s
b 20 C in 40 s
c 240 C in 2 minutes?
9 How long does it take a charge of 5 C to pass a
point in an electrical circuit where the current
flowing is 2 A?
▲ Figure 4.2.12a Analogue multimeter

Practical work
Measuring current b Connect the circuit of Figure 4.2.13b. The cells
are in series (+ of one to – of the other), as are
a Connect the circuit of Figure 4.2.13a (on a the lamps. Record the current. Measure the
circuit board if possible), ensuring that the + current at B, C and D by disconnecting the
of the cell (the metal stud) goes to the + of the circuit at each point in turn and inserting the
ammeter (marked red). Note the current. ammeter. Record the values of the current in
each position.

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 4.2 Electrical quantities

c Connect the circuit of Figure 4.2.13c. (1.5 V cell) D

The lamps are in parallel. Read the ammeter.
Also measure and record the currents at P, Q
and R. Comment on your results.
A (0–1A) A C

5 In Figure 4.2.13a how could you tell when

current flows?
6 In Figure 4.2.13b (1.25 V)    B
a how many paths are there for current to
flow? ▲ Figure 4.2.13a ▲ Figure 4.2.13b
b would you expect the current to be
different in different parts of the circuit?
7 In Figure 4.2.13c
a how many paths are there for current to A R

flow?
b would you expect the current to be
different in different parts of the circuit?
Q

▲ Figure 4.2.13c

Direct and alternating current In an alternating current (a.c.) the direction of

flow reverses regularly, as shown in the graph in
Difference Figure 4.2.15. The circuit sign for a.c. is given
In a direct current (d.c.) the electrons flow in one in Figure 4.2.16.
direction only. Graphs for steady and varying d.c.
are shown in Figure 4.2.14.
a.c.
current

0
1 1 time/seconds
current

2
steady d.c.

1 cycle
time
▲ Figure 4.2.15 Alternating current (a.c.)
current

▲ Figure 4.2.16 Symbol for alternating current

The pointer of an ammeter for measuring d.c. is

varying d.c.
deflected one way by the direct current. Alternating
time
current makes the pointer move back and forth
about the zero if the changes are slow enough;
▲ Figure 4.2.14 Direct current (d.c.) otherwise no deflection can be seen.

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 4.2.3 Electromotive force and potential difference

Batteries give d.c.; generators can produce either tickertape timer (Topic 1.2) and is relied upon in
d.c. or a.c. mains-operated clocks.
Frequency of a.c. See Topic 4.6 for how an oscilloscope can be used to
measure the frequency of an a.c. signal.
The number of complete alternations or cycles
in 1 second is the frequency of the alternating
current. The unit of frequency is the hertz (Hz). Test yourself
The frequency of the a.c. in Figure 4.2.15 is 2 Hz, 10 Sketch
which means there are two cycles per second, or one a a d.c. current
cycle lasts 1/2 = 0.5 s. The mains supply in many b an a.c. current
countries is a.c. of frequency 50 Hz; each cycle lasts c the circuit symbol used for a.c.
11 An a.c. current has a frequency of 1000 Hz.
1/50th of a second. This regularity was used in the How long does each cycle last?

4.2.3 Electromotive force and potential difference

FOCUS POINTS
★ Define electromotive force.
★ Describe the use of analogue and digital voltmeters.
★ Define potential difference and know that it is measured in volts.
★ Use the correct equations for electromagnetic force and potential difference.

As you will have seen in the previous topic, a complete circuit of conductors is needed for a current
to flow. In this topic you will learn that it is the electromotive force of a supply which provides
the energy needed to move charge around a complete circuit. The supply may vary from a simple
torch battery to your mains electricity supply. There are usually several components in a circuit,
for example lamps, motors or other electrical devices, from which energy is transferred to the
surroundings. The energy transferred from a device can be calculated by introducing the concept of
potential difference. Previously you used an ammeter to measure the current in an electrical circuit;
now you will learn how to use a voltmeter to measure potential difference.

The chemical action inside a battery produces a Key definitions

surplus of electrons at one of its terminals (the Electromotive force e.m.f. the electrical work done by a
negative) and creates a shortage at the other source in moving unit charge around a complete circuit
(the positive). It is then able to maintain a flow
Potential difference p.d. the work done by a unit charge
of electrons, i.e. an electric current, in any circuit passing through a component
connected across its terminals for as long as the
chemical action lasts. Work is done by the battery Electromotive force is measured in volts (V).
in moving charge around the circuit. The e.m.f. of a car battery is 12 V and the domestic
Electromotive force (e.m.f.), symbol E, is mains supply in many countries is 240 V.
defined as the electrical work, w, done by a source There are usually a number of components in an
in moving a unit charge around a complete circuit: electrical circuit through which charge flows. Potential
work done (by a source) difference (p.d.) is defined as the work done by a unit
e.m.f. =
  charge of charge passing through a component:
or work done (on a component)
p.d. =
E=W   charge
Q or
V=W
Q
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 4.2 Electrical quantities

Like e.m.f., potential difference between two ‘bundle’ of

points is measured in volts (V). The term voltage is electrical
sometimes used instead of p.d. energy

Energy transfers and p.d.

In an electric circuit, an electric current transfers
energy from an energy store, such as a battery,
to components in the circuit which then transfer
energy into the surroundings. In the case of a lamp,
energy is transferred to the surroundings by light
and by heating. Mr Coulomb
When each of the circuits shown in Figure 4.2.17
is connected up, it will be found from the ammeter
readings that the current is about the same (0.4 A)
in each lamp. However, the mains lamp with a ▲ Figure 4.2.18 Model of a circuit
potential difference of 230 V applied across it gives In our imaginary representation, Mr Coulomb travels
much more light and heat than the car lamp with round the circuit and unloads energy as he goes,
12 V across it. most of it in the lamp. We think of him receiving
a.c. ammeters (0–1 A) a fresh bundle every time he passes through the
mains lamp battery, which suggests he must be travelling very
(100 W)
car fast. In fact, as we found earlier (Topic 4.2.2), the
side-lamp electrons drift along quite slowly. As soon as the
(6 W)
circuit is complete, energy is delivered at once to
the lamp, not by electrons directly from the battery
but from electrons that were in the connecting
wires. The model is helpful but is not an exact
230 V mains 12 V a.c. supply representation.
▲ Figure 4.2.17 Investigating the effect of p.d. (potential The volt
difference) on energy transfer
The demonstrations of Figure 4.2.17 show that
Evidently the p.d. across a device affects the rate the greater the e.m.f. of a supply, the larger is the
at which it transfers energy. This gives us a way of bundle of energy given to each coulomb and the
defining the unit of potential difference: the volt. greater is the rate at which energy is transferred
from a lamp.
Model of a circuit In general, if W (joules) is the energy transferred
(i.e. the work done) when charge Q (coulombs)
It may help you to understand the definition of
moves around a complete circuit, the e.m.f. E (volts)
the volt, i.e. what a volt is, if you imagine that the
of the supply is given by
current in a circuit is formed by ‘drops’ of electricity,
each having a charge of 1 coulomb and carrying E = W/Q
equal-sized bundles of electrical energy. In Figure or
4.2.18, Mr Coulomb represents one such drop.
W=Q×E
As a drop moves around the circuit it gives up all its
energy which is transferred to other energy stores.
Note that electrical energy, not charge or current, is
used up.

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 4.2.3 Electromotive force and potential difference

The p.d. between two points in a circuit is 1 volt if Voltmeters

1 joule of energy is transferred when 1 coulomb
passes from one point to the other. A voltmeter is used to measure potential
That is, 1 volt = 1 joule per coulomb (1 V = 1 J/C). differences; it should always be placed in parallel
If 2 J is transferred by each coulomb, the p.d. is 2 V. with the component across which the p.d. is to be
In general, if W (joules) is the work done when measured. The positive terminal on the voltmeter
charge Q (coulombs) passes between two points, the should be connected to the side of the component
p.d. V (volts) between the points is given by into which current flows as is shown in the practical
work and Figure 4.2.21 overleaf. A simple moving-
V = W/Q coil voltmeter will read d.c. voltages only on an
or analogue display.
W=Q×V The face of an analogue voltmeter is represented
If Q is in the form of a steady current I (amperes) in Figure 4.2.19. The voltmeter has two scales.
flowing for time t (seconds) then Q = I × t (Topic The 0–5 scale has a full-scale deflection of 5.0 V.
4.2.2) and Each small division on the 0–5 scale represents
0.1 V. This voltmeter scale can be read to the nearest
W=I×t×V 0.1 V. The human eye is very good at judging a half
division, so we are able to estimate the voltmeter
reading to the nearest 0.05 V with considerable
Worked example precision. The 0–10 scale has a full-scale deflection
A lamp is connected to a battery in a circuit and a current
of 10.0 V; each small division on this scale represents
flows. 0.2 V so the precision of a reading is less than on
a Calculate the p.d. across the lamp if 6 J of work are done the 0–5 V scale.
when 2 C of charge pass through the lamp.
From the equation V = W/Q
4
the p.d. across the lamp = W/Q = 6 J/ 2 C = 3 V 2 6
0 8
b If the p.d. across the lamp is increased to 5 V calculate 2
the energy transferred to the lamp when a current of 2 A 2 1 3 10
0 4
flows in the lamp for 5 seconds.
1 5
Q = I × t = 2 A × 5 s = 10 C
Rearranging the equation V = W/Q gives
W = Q × V = 10 C × 5 V = 50 J volts

Now put this into practice

▲ Figure 4.2.19 An analogue voltmeter scale
1 Calculate the p.d. across a lamp in an electric circuit
when 8 J of work are done when a charge of 4 C passes Analogue voltmeters or multimeters are adapted
through the lamp. moving-coil galvanometers (Topic 4.5.5). Digital
2 The p.d. across a lamp is 6 V. multimeters are constructed from integrated
How many joules of energy are transferred when a circuits. On the voltage setting they have a very
charge of 2 C passes through it?
3 The p.d. across a lamp is 6 V. Find the work done when a
high input resistance (10 MΩ); this means they
current of 3 A flows in the lamp for 10 s. affect most circuits very little and so give very
accurate readings.

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 4.2 Electrical quantities

When making a measurement on either an

analogue or digital voltmeter a suitable range must Practical work
first be chosen. For example, if a voltage of a few
millivolts is expected, the 10 mV range might be Measuring voltage
selected and the value of the voltage (in mV) read A voltmeter is an instrument for measuring
from the display; if the reading is off-scale, the voltage or p.d. It looks like an ammeter but has
sensitivity should be reduced by changing to the a scale marked in volts. Whereas an ammeter
higher, perhaps 100 mV, range. is inserted in series in a circuit to measure the
Every measuring instrument has a calibrated current, a voltmeter is connected across that
scale. When you write an account of an experiment part of the circuit where the voltage is required,
(see p. viii, Using scientific skills) you should include i.e. in parallel.
details about each scale that you use.
To prevent damage to the voltmeter make sure
that the + terminal (marked red) is connected
Worked example to the point nearest the + of the battery.
The scales of an analogue voltmeter are shown in a Connect the circuit of Figure 4.2.21a.
Figure 4.2.20. The voltmeter gives the p.d across the lamp.
Read it.
2 4 6
a 1.5 V cell
0 8
1 2 3
2 10
0 4 lamp
1 5 (1.25 V)

volts
V
▲ Figure 4.2.20
voltmeter (0–5 V)
a What are the two ranges available when using the
voltmeter?
The lower scale reads 0–5 V and the upper scale reads b 4.5 V
0–10 V.
b What do the small divisions between the numbers 3 and 4
represent?
0.1 V X Y
L1 L2 L3
c Which scale would you use to measure a voltage of 4.6 V?
The lower scale 0–5 V will give a more accurate reading.
d When the voltmeter reads 4.0 V where should you position
c 1.5 V
your eye to make the reading?
Above the 4 to reduce parallax error.
V1
Now put this into practice
1 Use the scales of the voltmeter shown in Figure 4.2.20.
a What do the small divisions between the numbers 6 L1
and 8 represent? L2
b Which scale would you use to measure a voltage of
5.4 V?
c When making the reading for 4.0 V an observer’s eye V2
is over the 0 V mark. Explain why the value obtained by
this observer is higher than 4.0 V. ▲ Figure 4.2.21

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 4.2.4 Resistance

b Connect the circuit of Figure 4.2.21b. Test yourself

Measure:
12 a Define electromotive force.
i the p.d V between X and Y b Define potential difference.
ii the p.d V1 across lamp L1 13 The p.d. across the lamp in Figure 4.2.22 is
iii the p.d V2 across lamp L 2 12 V. How many joules of electrical energy are
iv the p.d V3 across lamp L 3. transferred into light and heat when
c Connect the circuit of Figure 4.2.21c, so that a a charge of 1 C passes through it
b a charge of 5 C passes through it
two lamps L1 and L 2 are in parallel across c a current of 2 A flows in it for 10 s?
one 1.5 V cell. Measure the p.d.s, V1 and V2
across each lamp in turn.
8 For step b above, calculate the value of
V1 + V2 + V3 and compare with the value of V.
9 For step c above, compare the values of V1
and V2.
12 V
10 If all the lamps shown in Figure 4.2.21b are
identical, what would you expect the p.d. ▲ Figure 4.2.22
across each to be?
11 a Explain where you would connect
and how you would use a voltmeter to
measure the p.d. across a device.
b In the circuit shown in Figure 4.2.21c, if V1
measures 1.5 V, what would you expect
the value of V2 to be?

4.2.4 Resistance
FOCUS POINTS
★ Know the correct equation for resistance and use it correctly to determine resistance using a voltmeter
and an ammeter.
★ Draw and interpret current–voltage graphs.
★ Understand the dependence of the resistance of a metal wire on its length and cross-sectional area.
★ Know that resistance is directly proportional to length and inversely proportional to cross-sectional area
in a metallic electrical conductor.

In this topic you will learn that the ease of passage of electrons depends on the nature of the
material. This effect is measured by resistance. More work has to be done to drive a current through
a high resistance than a low resistance. For the element in an electric fire, a high-resistance wire is
needed so that a large amount of energy is transferred. The opposite is required for the connecting
wires in a circuit, where low-resistance wires are used to reduce energy losses. Current flow is
easier in a wire with a large cross-sectional area so thick wires are used where large currents are
needed, for example in the starter motor in a car or a kitchen oven. The longer a wire, the harder it is
for current to flow; energy loss is reduced by using short connecting wires.

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 4.2 Electrical quantities

Electrons move more easily through some conductors

than others when a p.d. is applied. The opposition Worked example
of a conductor to current is called its resistance.
A good conductor has a low resistance and a poor a If a p.d. of 4.5 V is applied across a lamp, the current
conductor has a high resistance. flowing through the lamp is 1.5 A. Calculate the
resistance of the lamp.
The ohm R=
V
If the current in a conductor is I when the voltage I
across it is V, as shown in Figure 4.2.23a, its 4.5 V
so R = = 3Ω
resistance R is defined by 1.5A

p.d. b A current of 0.5 A flows through a resistance of 5 Ω.

resistance = Calculate the p.d. across the lamp.
current
or V = IR = 0.5 A × 5 Ω = 2.5 V
V
R= Now put this into practice
I 1 The current flowing through a resistor is 0.30 A when a
This is a reasonable way to measure resistance since p.d. of 4.5 V is applied across it.
the smaller I is for a given V, the greater is R. If V is Calculate the value of the resistor.
in volts and I in amperes, then R is in ohms (symbol 2 A current of 0.2 A flows through a resistor of 10 Ω.
Ω, the Greek letter omega). For example, if I = 2 A Calculate the p.d. across the resistor.
when V = 12 V, then R = 12 V/2 A, that is, R = 6 Ω. 3 A p.d. of 12.0 V is applied across a lamp of 24 Ω and the
lamp lights up. Calculate the current passing through the
The ohm is the resistance of a conductor in which lamp.
the current is 1 ampere when a voltage of 1 volt is
applied across it.

I
R
I
Resistors
Conductors intended to have resistance are called
resistors (Figure 4.2.24a) and are made either from
V wires of special alloys or from carbon. Those used
in radio and television sets have values from a few
▲ Figure 4.2.23a ohms up to millions of ohms (Figure 4.2.24b).

V ▲ Figure 4.2.24a Circuit symbol for a resistor

I R

▲ Figure 4.2.24b Resistor

▲ Figure 4.2.23b

Alternatively, if R and I are known, V can be found

from
V = IR
Also, when V and R are known, I can be calculated
from
V
I=
R
The triangle in Figure 4.2.23b is an aid to remembering
the three equations. It is used in the same way as the
‘density triangle’ in Topic 1.4. ▲ Figure 4.2.24c Variable resistor (potentiometer)

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 4.2.4 Resistance

Variable resistors are used in electronics (and are a b

then called potentiometers) as volume and other
controls (Figure 4.2.24c). Variable resistors that
take larger currents, like the one shown in Figure potential
divider
4.2.25, are useful in laboratory experiments. These rheostat
consist of a coil of constantan wire (an alloy of
60% copper, 40% nickel) wound on a tube with a
sliding contact on a metal bar above the tube.
tube metal bar sliding contact
  
terminals
▲ Figure 4.2.26 A variable resistor can be used as a
rheostat or as a potential divider.

coil of constantan wire

terminal

▲ Figure 4.2.25 Large variable resistor ▲ Figure 4.2.27 Circuit symbol for a variable resistor used
as a rheostat
There are two ways of using such a variable resistor.
It may be used as a rheostat for changing the current
in a circuit; only one end connection and the sliding Test yourself
contact are then required. In Figure 4.2.26a moving 14 What is the resistance of a lamp when a voltage of
the sliding contact to the left reduces the resistance 12 V across it causes a current of 4 A?
and increases the current. This variable resistor can 15 Calculate the p.d. across a 10 Ω resistor carrying a
also act as a potential divider for changing the p.d. current of 2 A.
16 The p.d. across a 3 Ω resistor is 6 V. Calculate the
applied to a device; all three connections are then current flowing (in ampere).
used. In Figure 4.2.26b any fraction from the total 17 Calculate the number of coulombs per second
p.d. of the battery to zero can be ‘tapped off’ by passing through a 4 Ω resistor connected across
moving the sliding contact down. Figure 4.2.27 shows the terminals of a 12 V battery.
the circuit diagram symbol for a variable resistor
being used in rheostat mode.

Practical work

Measuring resistance constantan wire. Altering the rheostat changes

both the p.d. V and the current I. Record in a table,
Safety with three columns, five values of I (e.g. 0.10, 0.15,
0.20, 0.25 and 0.3 A) and the corresponding values
l Avoid touching the wire when current is of V (in the range 1.0 V to 4.0 V).
flowing as it may become hot.
Repeat the experiment, but instead of the wire use
The resistance R of a conductor can be found (i) a lamp (e.g. 2.5 V, 0.3 A), (ii) a semiconductor
by measuring the current I in it when a p.d. V diode (e.g. 1 N4001) connected first one way then
is applied across it and then using R = V/I. This is the other way around and (iii) a thermistor (e.g.
called the ammeter–voltmeter method. TH 7). (Semiconductor diodes and thermistors are
Set up the circuit of Figure 4.2.28 in which the considered in Topic 4.3 in more detail.)
unknown resistance R is 1 metre of SWG 34

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 4.2 Electrical quantities

Experiments show that the resistance R of a wire of

a given material is
to three 1.5 V (4.5 V) cells in series
(i) directly proportional to its length l, i.e. R ∝ l
R
(ii) inversely proportional to its cross-sectional
area A, i.e. R ∝ I/A (doubling A halves R).
crocodile
clip
A
Worked example
A copper wire has a diameter of 0.50 mm, a length of 1 km
and a resistance of 84 Ω.
ammeter a Calculate the resistance of a wire of the same material
(0–1 A) and diameter with a length of 500 m.
Let R1 = 84 Ω, length l1 = 1.0 km = 1000 m,
rheostat circuit
(0–25 Ω ) board length l2 = 500 m and R2 the required resistance.
Then since R ∝ l/A and A is constant
R2 I
= 2
R1 I1
I2 500 m
and R2 = R1 × = 42 Ω
= 84 Ω ×
V voltmeter I1 1000 m
(0–5 V) The resistance is halved when the length of the wire is
halved.
▲ Figure 4.2.28 b Calculate the resistance of a wire of the same material
with a diameter of 1.0 mm and a length of 1 km.
12 Work out R for each pair of readings from the Let R1 = 84 Ω, diameter d1 = 0.50 mm, diameter
equation R = V/I. d2 = 1.0 mm and R2 the required resistance.
13 Draw the symbols for a a resistor and If r is the radius of the wire, the cross-sectional area
A = πr 2 = π(d/2)2 = (π/4) d2 , so
b a variable resistor.
14 List the equipment you would need to A1 ( d1 )2 (0.50 mm)2
= = = 0.25
measure the resistance of a wire. A2 ( d2 ) 2
(1.0 mm)2
15 Calculate the resistance of a wire that has a l
Then since R ∝ and l is constant
current of 0.15 A passing through it when the A
p.d. across it is 4.5 V. R2 A1
=
R1 A2
A1
Resistance of a metal wire and R2 = R1 ×
A2
= 84 Ω × 0.25 = 21 Ω

The resistance of a metallic wire

(i) increases as its length increases Now put this into practice
(ii) increases as its cross-sectional area decreases 1 A certain wire has a length of 10 m and a resistance of 60 Ω.
(iii) depends on the material. Calculate the resistance of 20 m of the wire.
2 A certain wire has diameter of 0.20 mm and a resistance
A long thin wire has more resistance than a short
of 60 Ω. Calculate the resistance of a wire of the same
thick one of the same material. Silver is the best material with a diameter of 0.40 mm.
conductor, but copper, the next best, is cheaper
and is used for connecting wires and for domestic
electric cables.
Key definition
Resistance of a metallic wire directly proportional to its
length and inversely proportional to its cross-sectional
area

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 4.2.4 Resistance

I–V graphs: Ohm’s law Filament lamp

The variation of current with voltage is shown for A filament lamp is a non-ohmic conductor at high
various conductors in Figure 4.2.29. temperatures. For a filament lamp the I–V graph
curve flattens as V and I increase (Figure 4.2.29c).
a Ohmic conductor b Semiconductor diode
I I
That is, the resistance (V/I) increases as I increases
and makes the filament hotter.
Variation of resistance with temperature
In a metal, the current in a circuit is carried by
free electrons. When the temperature of the metal
0 V 0 V increases, the atoms vibrate faster and it becomes
more difficult for the electrons to move through
c Filament lamp d Thermistor
I I the material. This means that the resistance of the
metal increases. From Ohm’s law V = IR, so that if
R increases, the p.d. V across the conductor also
increases if a constant current I is to be maintained.
The effect of increasing resistance can be
seen in the I–V curve for a filament lamp (Figure
0 V 0 V 4.2.29c). When the current increases, the metal
▲ Figure 4.2.29 I–V graphs filament heats up and its resistance increases as
is indicated by the curvature of the graph. The
Metallic conductors resistance of semiconductor thermistors decreases
Metals and some alloys give I–V graphs that are a if their temperature rises, i.e. their I–V graph bends
straight line through the origin, as in Figure 4.2.29a, upwards, as in Figure 4.2.29d.
provided that their temperature is constant. I is
directly proportional to V, i.e. I ∝ V. Doubling V Variation of resistance with light intensity
doubles I, etc. Such conductors obey Ohm’s law, The resistance of some semiconducting materials
stated as follows. decreases when the intensity of light falling on
The current in a metallic conductor is directly them increases. This property is made use of in
proportional to the p.d. across its ends if the light-dependent resistors (LDRs) (see Topic 4.3.3).
temperature and other conditions are constant. The I–V graph for an LDR is similar to that shown
They are called ohmic or linear conductors in Figure 4.2.29d for a thermistor. Both thermistors
and since I ∝ V, it follows that V/I = a constant and LDRs are non-ohmic conductors.
(obtained from the slope of the I–V graph).
The resistance of an ohmic conductor therefore does Test yourself
not change when the p.d. does. 18 a Sketch the I–V graph for a resistor of
constant resistance.
Semiconductor diode b How could you obtain a value of the
The typical I–V graph in Figure 4.2.29b shows that resistance from the graph?
current passes when the p.d. is applied in one 19 a Sketch the I–V graph for a filament lamp.
direction but is almost zero when the p.d. is b Explain the shape of the graph.
applied in the opposite direction. A diode has a
small resistance when connected one way round
but a very large resistance when the p.d. is
reversed. It conducts in one direction only and
is a non-ohmic conductor.

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 4.2 Electrical quantities

4.2.5 Electric power

FOCUS POINTS
★ Know and use the correct equations for electrical power and electrical energy.
★ Define the kilowatt-hour (kWh) and use this unit to calculate the cost of using some electrical appliances.

The e.m.f. applied to a circuit drives current around the circuit. In the process, energy is transferred
from the electrical cell or mains supply to the wires and components of the circuit. The total energy
transferred to a device depends on its power consumption and the time span over which it is used.
In this section you will learn how to measure power consumption, the typical power consumption of
some everyday household appliances and how to calculate the cost of electricity usage.

Power in electric circuits To calculate the power P of an electrical appliance

we multiply the current I in it by the p.d. V across it.
In many circuits it is important to know the rate at
which the electric current transfers energy from the A
source to the circuit components.
Earlier (Topic 1.7.4) we said that energy transfers
were measured by the work done and power was
defined by the equation
V
energy transferred
power = work done =
time taken time taken
In symbols

P = W (1)
t ▲ Figure 4.2.30
where W is in joules (J), t in seconds (s) and P is in
J/s or watts (W). For example if a lamp on a 240 V supply has a
From the definition of p.d. (Topic 4.2.3) we saw current of 0.25 A in it, its power
that if W is the work done when there is a steady P = IV = 240 V × 0.25 A = 60 W
current I (in amperes) for time t (in seconds) in a This means that 60  J of energy are transferred to
device (e.g. a lamp) with a p.d. V (in volts) across it, the lamp each second. Larger units of power are the
as in Figure 4.2.30, then kilowatt (kW) and the megawatt (MW) where
W=I×t×V
Substituting for W in (1) gives P = I × t × V 1 kW = 1000 W and 1 MW = 1 000 000 W
t In units
so    P = IV
watts = amperes × volts (3)
or    power = current × voltage
It follows from (3) that since
and in time t the electrical energy transferred is
watts
E = Pt volts = (4)
amperes
so    E = IVt (2) the volt can be defined as a watt per ampere and
or energy = current × voltage × time p.d. calculated from (4).

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 4.2.5 Electric power

If all the energy is transferred to thermal energy in

3V
a resistor of resistance R, then V = IR and the rate
of transfer to thermal energy is given by
P = V × I = IR × I = I 2R
That is, if the current is doubled, four times as much torch
thermal energy is produced per second. Also, A lamp V
P = V 2/R. The thermal energy can be transferred to (0–1 A) (0–5 V)

the surroundings by light and by heating.

Worked example ▲ Figure 4.2.31

A lamp of resistance 12 Ω has a current of 0.5 A flowing Motor
through it.
a Calculate the p.d. across the lamp.
Replace the lamp in Figure 4.2.31 by a small
electric motor. Attach a known mass m (in kg)
p.d. V = IR = 0.5 A × 12 Ω = 6 V
to the axle of the motor with a length of thin
b What is the power of the lamp? string and find the time t (in s) required to raise
P = IV = 0.5 A × 6 V = 3 W = 3 J/s the mass through a known height h (in m) at a
steady speed. Then the power output Po (in W)
c How much energy is transferred to the lamp in 6 s?
of the motor is given by
P = E/t so E = Pt = 3 J/s × 6 s = 18 J
work done in raising mass mgh
Po = =
Now put this into practice time taken t
1 A lamp has a resistance of 12 Ω and a current of 1.0 A
passing through it. If the ammeter and voltmeter readings I and V
a Calculate the p.d. across the lamp. are noted while the mass is being raised, the
b Calculate the power of the lamp. power input Pi (in W) can be found from
c How much energy is transferred to the lamp
in 10 s? Pi = IV
2 A small electric motor attached to a 12 V supply has a
The efficiency of the motor is given by
current of 0.3 A passing through it.
a Calculate the power of the motor in watts. Po
b Give the power of the motor in joules/second. efficiency = × 100%
c How much energy is transferred to the motor in Pi
1 minute?
Also investigate the effect of a greater mass on:
(i) the speed, (ii) the power output and (iii) the
efficiency of the motor at its rated p.d.
Practical work
16 When a p.d. of 30 V is applied across an
Measuring electric power electric motor, a current of 0.5 A flows
through it. Calculate the power supplied to
Lamp the motor.
Connect the circuit of Figure 4.2.31. Note the 17 An electric motor raises a mass of 500 g
ammeter and voltmeter readings and work out through 80 cm in 4 s. Calculate the output
the electric power supplied to the lamp in watts. power of the motor.

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 4.2 Electrical quantities

Going further
Joulemeter
Instead of using an ammeter and a voltmeter to
measure the electrical energy transferred to an
appliance, a joulemeter can be used to measure
it directly in joules. The circuit connections are shown
in Figure 4.2.32.

electrical joulemeter appliance

supply
input output

▲ Figure 4.2.32 Connections to a joulemeter

Paying for electricity

Electricity supply companies charge for the ▲ Figure 4.2.33 Electricity meter with digital display
amount of energy they supply. A joule is a very
Typical powers of some appliances are given in
small amount of energy and a larger unit, the
Table 4.2.1.
kilowatt-hour (kWh), is used.
A kilowatt-hour is the energy used by a 1 kW ▼ Table 4.2.1 Power of some appliances
appliance in 1 hour.
DVD player 20 W Iron 1 kW
1 kWh = 1000 J/s × 3600 s
Laptop computer 50 W Fire 1, 2, 3 kW
= 3 600 000 J = 3.6 MJ Light bulbs 60, 100 W Kettle 2 kW
A 3 kW electric fire working for 2 hours uses 6 kWh of Television 100 W Immersion heater 3 kW
energy – usually called 6 ‘units’. Electricity meters, Refrigerator 150 W Cooker 6.4 kW
which are joulemeters, are marked in kWh: the latest
have digital readouts like the one in Figure 4.2.33. Note that the current required by a 6.4 kW cooker is
given by
Key definition
6400 W
I= P=
Kilowatt-hour (kWh) the energy used by a 1 kW appliance
in 1 hour = 28A
V 230 V
1 kWh = 1000 J/s × 3600 s
This is too large a current to draw from the ring main of
= 3 600 000 J = 3.6 MJ
a house and so a separate circuit must be used.

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 4.2.5 Electric power

Worked example Test yourself

20 How much energy in joules is transferred to a
If the price of 1 kWh (1 unit) of electricity is 10 cents, how
100 watt lamp in
much will it cost to use a 3000 W electric heater for 3 hours?
a 1 second
Convert watts to kilowatts: 3000 W = 3 kW b 5 seconds
c 1 minute?
Electrical energy E = Pt = 3 kW × 3 h = 9 kWh
21 a What is the power of a lamp rated at 12 V 2 A?
Cost of using the heater = 9 kWh × 10 cents = 90 cents b How many joules of energy are transferred per
second to a 6 V 0.5 A lamp?
Now put this into practice
1 If the price of 1 kWh (1 unit) of electricity is 10 cents, how
much will it cost to use a 6.4 kW oven for 2 hours?
2 If the cost of 1 kWh (1 unit) of electricity is 10 cents, how
much will it cost to use a 150 W refrigerator for 12 hours?

Revision checklist
After studying Topic 4.2 you should know and ✔ state the units of charge and current
understand: ✔ recall the relation electric current = charge/time
✔ that positive and negative charges are produced (I = Q/t) and use it to solve problems
by rubbing and like charges repel while unlike ✔ distinguish between electron flow and
charges attract conventional current
✔ what is meant by an electric field and that the ✔ state that e.m.f. and p.d. are measured in volts and
direction of an electric field at a point is the direction that the volt is given by a joule per coulomb
of the force on a positive charge at that point ✔ recall and use the equations e.m.f. = work done
✔ that an electric current in a metal is a flow of free (by a source)/charge (E = W/Q) and p.d. = work
electrons from the negative to the positive terminal done (on a component)/charge (V = W/Q)
of the battery around a circuit ✔ describe an experiment to measure resistance
✔ the difference between d.c. and a.c. and relate the resistance of a wire to its length and
✔ the meaning of the terms electromotive force and diameter
potential difference ✔ state Ohm’s law
✔ how to use ammeters and voltmeters, both ✔ plot and explain I–V graphs for different
analogue and digital conductors
✔ how to solve simple problems using the equation ✔ describe the effect of temperature increase on the
resistance = p.d./current (R = V/I) resistance of a resistor
✔ recall the equations power = current × voltage
After studying Topic 4.2 you should be able to:
(P = IV) and energy = current × voltage × time
✔ explain the charging of objects in terms of the
(E = IVt) and use them to solve simple problems on
motion of negatively charged electrons and
energy transfers
describe simple experiments to show how
✔ define the kilowatt-hour and calculate the cost of
electrostatic charges are produced and detected
using electrical appliances.
✔ give examples of conductors and insulators and
explain the differences between them using a
simple electron model

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 4.2 Electrical quantities

Exam-style questions
1 a Explain in terms of electron movement what P
S
Q R P
S
Q R
happens when a piece of cellulose acetate
becomes positively charged by being
rubbed with a cloth. [3]
A B
b Two positive electrostatic charges are
brought close together. Will they be
repelled or attracted to each other? [1] S
c A positive and a negative electric charge P Q R P Q R

are brought close to each other. Will they

be attracted or repelled from each other? [1] S
d How many types of electric charge C D
are there? [1] ▲ Figure 4.2.34 [Total: 1]
[Total: 6]
2 a Describe an experiment to distinguish 6 Using the circuit in Figure 4.2.35, which of the
between electrical conductors and following statements is correct?
insulators.[4] A When S1 and S2 are closed, lamps A and B are
b Identify two good electrical conductors. [2] lit.
c Identify one electrical insulator. [1] B With S1 open and S2 closed, A is lit and B is
d Explain the difference between electrical not lit.
conductors and insulators in terms of electrons. C With S2 open and S1 closed, A and B are lit.
[3] D With S1 open and S2 open, A is lit and B is not
lit.
[Total: 10]
3 a Explain what is meant by an electric
field.[2]
b Sketch the electric field lines (including S1 A B
their direction) between two oppositely
charged conducting parallel plates. Indicate
the direction in which a positive charge would
move if placed between the plates. [4] S2
c State the units of charge. [1]
▲ Figure 4.2.35 [Total: 1]
[Total: 7]
4 a State the direction of an electric field. [3] 7 a Identify the particles which carry a current
b Draw the field lines around a positively in a metal. [1]
charged conducting sphere. [4] b Explain the difference between direct current
[Total: 7] (d.c.) and alternating current (a.c.). [2]
c Explain where you would connect and how you
5 Study the circuits in Figure 4.2.34. The switch S
would use an ammeter to measure the d.c.
is open (there is a break in the circuit at this
current in a circuit. [3]
point). In which circuit would lamps Q and R light
[Total: 6]
but not lamp P?

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 Exam-style questions

8 a Define electric current. [2]

b An electric current passes through a device. A
i Calculate the current at a point in the L1 L2

circuit where 180 C of charge passes in

1 minute.[2]
ii If the current in the device is 2 A, V1 V2
what charge passes through it
in 1 minute? [3] V

[Total: 7] ▲ Figure 4.2.37 [Total: 10]

9 a If the current in a floodlamp is 5 A,
what charge passes in 12 The graph in Figure 4.2.38 illustrates how the
i 10 s [2] p.d. across the ends of a conductor is related
ii 5 minutes? [2] to the current in it.
b Calculate how long it will take 300 C a State the relationship between V and I
to pass through the floodlight. [3] that can be deduced from the graph,
[Total: 7] giving reasons.[4]
b Calculate the resistance of the conductor. [3]
10 The lamps and the cells in all the circuits of Figure
4.2.36 are the same. If the lamp in a has its full,
normal brightness, what can you say about the
6 +
brightness of the lamps in b, c, d, e and f?
a b c
4 +
p.d./V

+
2
+

d e f 0 1 2 3
current/A

▲ Figure 4.2.38 [Total: 7]

13 a Describe how the resistance of a wire depends
on its length and cross-sectional area. [3]
▲ Figure 4.2.36 [Total: 5] b The resistance of a wire of length 1 m
is 70 Ω. Calculate the resistance of a
11 Three voltmeters V, V1 and V2 are connected as in 20 cm length of the wire. [3]
Figure 4.2.37. c If the 1 m length of wire is replaced with
a If V reads 18 V and V1 reads 12 V, what does a wire of the same material and length
V2 read? [2] but of half the diameter calculate its
b If the ammeter A reads 0.5 A, how much resistance.[4]
electrical energy is changed to heat and light [Total: 10]
in lamp L1 in one minute? [4]
14 Sketch a current–voltage graph of
c Copy Figure 4.2.37 and mark with a + the
a a resistor of constant resistance [3]
positive terminals of the ammeter and
b a semiconductor diode [3]
voltmeters for correct connection. [4]
c a filament lamp. [3]
[Total: 9]

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 4.2 Electrical quantities

15 a Calculate the energy transferred to a 6.4 kW 16 a Below is a list of wattages of various

cooker in 30 minutes. [3] appliances. State which is most likely to be
b Calculate the cost of heating a tank of water the correct one for each of the appliances
with a 3000 W immersion heater for 80 minutes named.
if electricity costs 10 cents per kWh. 60 W 250 W 850 W 2 kW 3.5 kW
[3] i kettle [1]
[Total: 6] ii table lamp [1]
iii iron [1]
b Calculate the current in a 920 W appliance
if the supply voltage is 230 V. [4]
[Total: 7]

Alternative to Practical
17 a Give an expression relating the resistance 18 Plan an experiment to find how the resistance
of a metal wire to the p.d. across it and the of a wire varies with its length. You are provided
current flowing through it. [1] with a battery, ammeter, voltmeter, connecting
b Describe how you could measure the wires (attached to crocodile clips) and different
resistance of a wire; include the equipment lengths of wires of varying material.
you would need. [4] You should:
c In an experiment to determine the resistance – draw a diagram of the circuit you would use
of a wire the following values were obtained to determine the resistance of a wire being
for the current through the wire and the p.d. tested
across it. – explain briefly how you would carry out the
investigation, including the measurements you
Current/A p.d./V would take
0.04 2.0 – state the key variables that you would control
0.08 4.0 – give a suitable table, with column headings,
0.12 6.0 to show how you would display your readings.
[Total: 6]
0.16 8.0
0.20 10.0
0.24 12.0

i Plot a graph of p.d. versus current. [3]

ii Determine the value of the resistor. [2]
[Total: 10]

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 4.3 Electric circuits
4.3.1 Circuit diagrams and components
FOCUS POINTS
★ Draw and interpret circuit diagrams containing a variety of different components and understand how
these components behave in the circuit.

You will find that electrical circuits can contain many different types of components. The circuit
configuration is expressed by circuit diagrams. Conventional symbols represent the different types
of components. Such diagrams are used in the design of circuits and the analysis of their behaviour.

Some of the symbols used for the various parts of an

electric circuit are shown in Figure 4.3.1. So far you
have encountered cells, batteries, lamps, resistors, connecting wires crossing
wires joined
ammeters and voltmeters. In this section you will wire (not joined)
be introduced to some more of the components
+ –
frequently used in electric circuits including
thermistors, light-dependent resistors (LDRs), relays, cell battery (two or more cells) switch
light-emitting diodes (LEDs) and semiconductor
diodes. + +
A V

ammeter lamp voltmeter

resistor fuse
variable resistor
▲ Figure 4.3.1 Circuit symbols

4.3.2 Series and parallel circuits

FOCUS POINTS
★ Understand that current in a series circuit is the same at any point.
★ Calculate the currents and p.d.s in series and parallel circuits.
★ Understand how to construct and use series and parallel circuits.
★ Calculate the combined e.m.f. of two or more sources in series and of two identical sources in parallel.
★ Understand that the sum of the currents into a junction equals the sum of the currents out of the junction.
★ Calculate the effective resistance of two resistors in parallel and the combined resistance of two or more
resistors in series.
★ Know that in a lighting circuit there are advantages to connecting lamps in parallel.

209
 4.3 Electric circuits

In the preceding topic you learned about the concepts of current, p.d. and resistance and how they
are related to each other in simple circuits. Electrical circuits can branch and reconnect. The net
effect depends on the way the components are connected. The sum of the currents into a junction
equals the sum of the currents out of the junction. This means that there are different effects
when resistors follow each other (in series) from those when they lie on parallel wires. There are
significant advantages in connecting lamps in parallel in a lighting circuit.

A circuit usually contains several components and

the effect of connecting components together
in series and parallel configurations will be now
be considered. A R

Current in a series circuit

In a series circuit, such as the one shown in Figure
4.3.2, the different parts follow one after the other Q
and there is just one path for the current to follow.
The reading on an ammeter will be the same whether
it is placed in the position shown or at B, C or D. P
That is, current is not used up as it goes around the ▲ Figure 4.3.3 Currents in a parallel circuit
circuit.
The current at every point in a series circuit is Practical work associated with currents in series and
the same. parallel circuits can be found in Topic 4.2.2.
D Key definitions
Series circuit components connected one after another;
current is the same in each component
Parallel circuit components are connected side by side
A C and the current splits into alternative paths and then
recombines.

Current at a junction
B
Electric current in a circuit cannot be stored.
▲ Figure 4.3.2 Current in a series circuit This means that when circuits join or divide, the
total current going into a junction must be equal
Current in a parallel circuit to the total current leaving the junction. A simple
In a parallel circuit, such as the one shown in example of this is provided by the splitting and re-
Figure 4.3.3, the lamps are side by side and there joining of the current when it goes into and comes
are alternative paths for the current. The current out of a parallel circuit.
splits: some goes through one lamp and the rest
through the other. The current from the source is Potential difference in a series
larger than the current in each branch. For example, circuit
if the ammeter reading was 0.4 A in the position
shown, then if the lamps are identical, the reading The total p.d. across the components in a series
at P would be 0.2 A, and so would the reading at Q, circuit is equal to the sum of the individual p.d.s
giving a total of 0.4 A. Whether the current splits across each component. In Figure 4.3.4
equally or not depends on the lamps; for example, V = V1 + V2 + V3
if the lamps are not identical, the current might
where V1 is the p.d. across L1, V2 is the p.d. across
divide so that 0.3 A goes one way and 0.1 A by the
L2 and V3 is the p.d. across L3.
other branch.

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 4.3.2 Series and parallel circuits

4.5 V

X Y
L1 L2 L3

▲ Figure 4.3.4 p.d. in a series circuit

For example, if V1 = 1.4 V, V2 = 1.5 V and

V3 = 1.6 V, then V will be (1.4 + 1.5 + 1.6) V = 4.5 V.

Potential difference in a parallel

circuit ▲ Figure 4.3.6 Compact batteries
In the circuit of Figure 4.3.5
The cells in Figure 4.3.7b are in opposition and the
V1 = V2 e.m.f. at X, Y is zero.
The p.d. across devices in parallel in a circuit are If two 1.5 V cells are connected in parallel, as in
equal. Figure 4.3.7c, the e.m.f. at terminals P, Q is still 1.5 V
but the arrangement behaves like a larger cell and
1.5 V
will last longer.
V1 a
1.5 V 1.5 V

A B
L1
L2 b

X Y
V2
1.5 V 1.5 V

▲ Figure 4.3.5 p.d.s in a parallel circuit c

1.5 V
The p.d. across an arrangement of parallel resistance
is the same as the p.d. across one branch.
Practical work associated with voltage in series
and parallel circuits can be found in Topic 4.2.3.
1.5 V

Cells, batteries and e.m.f.

A battery (Figure 4.3.6) consists of two or more
electric cells. Greater e.m.f.s are obtained when
cells are joined in series, i.e. + of one to − of next;
the e.m.f.s of each are added together to give the
P Q
combined e.m.f. In Figure 4.3.7a the two 1.5 V cells
give an e.m.f. of 3 V at the terminals A, B. ▲ Figure 4.3.7

The p.d. at the terminals of a battery decreases

slightly when current is drawn from it. This effect is
due to the internal resistance of the battery which
causes heating as current flows through it.

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 4.3 Electric circuits

When no current is drawn from a battery it is said Worked example

to be an ‘open circuit’ and its terminal p.d. is a
maximum and equal to the e.m.f. of the battery. A 4.5 V battery is connected across three resistors of values
3 Ω, 4 Ω and 5 Ω connected in series.
a Calculate the current flowing through the resistors.
Test yourself Combined resistance of resistors in series
1 If the lamps are both the same in Figure 4.3.8 and if R = R1 + R2 + R3 = 3 Ω + 4 Ω + 5 Ω = 12 Ω
ammeter A1 reads 0.50 A, what do ammeters A 2, A 3,
A 4 and A5 read? Rearrange equation V = IR to give I = V/R then the current
flowing through the three resistors
A1 4.5 V
I = = 0.38 A
12 Ω
A2 A4
b Calculate the p.d. across the 4 Ω resistor.
p.d. across R2 is given by
V2 = IR2 = 0.38 A × 4 Ω = 1.5 V

Now put this into practice

A3 A5
1 Three resistors of value 4 Ω, 6 Ω and 8 Ω are connected in
series. Calculate their combined resistance.
2 A 4.5 V battery is connected across two resistors of value
▲ Figure 4.3.8
3 Ω + 6 Ω. Calculate
2 Three 2 V cells are connected in series and used as a the current flowing through the resistors
the supply for a circuit. b the p.d. across each.
What is the p.d. at the terminals of the supply?
3 How many joules of energy does 1 C gain on passing
through
a a 2 V cell Resistors in parallel
b three 2 V cells connected in series? The resistors in Figure 4.3.10 are in parallel.
The voltage V between the ends of each is the same
and the total current I equals the sum of the
Resistors in series currents in the separate branches, i.e.
The resistors in Figure 4.3.9 are in series. The same
I = I1 + I2 + I3
current I flows through each and the total voltage V
R1
across all three is the sum of the separate voltages I1
across them, i.e.
V = V1 + V2 + V3
V R2
I I2 I
R1 R2 R3
I I

R3
I3
V1 V2 V3

▲ Figure 4.3.9 Resistors in series

But V1 = IR1, V2 = IR2 and V3 = IR3. Also, if R is the V

combined resistance, V = IR, and so
▲ Figure 4.3.10 Resistors in parallel
IR = IR1 + IR2 + IR3
But I1 = V/R1, I2 = V/R2 and I3 = V/R3.
Dividing both sides by I,
R = R1 + R2 + R3 Also, if R is the combined resistance, I = V/R,

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 4.3.2 Series and parallel circuits

V = V +V +V (ii) the combined resistance, R, of two resistors in

R R1 R2 R3 parallel is less than that of either resistor R1 or
R2 alone and is calculated from
Dividing both sides by V,
1 = 1 + 1
1 = 1 + 1 + 1 R R1 R2
R R1 R2 R3 You can check these statements are true in the
For the simpler case of two resistors in parallel Worked example below.
Lamps are connected in parallel (Figure 4.3.5)
1 = 1 + 1 = R2 + R1 rather than in series in a lighting circuit.
R R1 R2 R1 R2 R1 R2 The advantages are as follows:
(i) The p.d. across each lamp is fixed (at the
R + R1
∴1 = 2 supply p.d.), so the lamp shines with the same
R R1 R2 brightness irrespective of how many other lamps
Inverting both sides, are switched on.
(ii) Each lamp can be turned on and off
RR product of resistances
R= 1 2 = independently; if one lamp fails, the others can
R1 + R2 sum of resistances still be operated.
Practical work associated with measuring resistance
Properties of parallel circuits can be found in Topic 4.2.4.
We can summarise the results for parallel circuits
as follows:
(i) the sum of the currents in the branches of a
parallel circuit equals the current entering or
leaving the parallel section

Worked example
A p.d. of 24 V from a battery is applied to the network of b What is the current in the 8 Ω resistor?
resistors in Figure 4.3.11a. Let R = total resistance of circuit = 4 Ω + 8 Ω, that is,
a What is the combined resistance of the 6 Ω and 12 Ω R = 12 Ω. The equivalent circuit is shown in Figure 4.3.11b,
resistors in parallel? and if I is the current in it then, since V = 24 V
Let R1 = resistance of 6 Ω and 12 Ω in parallel.
Then V 24 V
I= = = 2A
R 12 Ω
1 = 1+ 1 = 2 + 1 = 3 ∴ current in 8 Ω resistor = 2A
R1 6 12 12 12 12
24 V
12
∴ R1 = = 4Ω
3
24 V

I I

4Ω 8Ω
6Ω

8Ω
▲ Figure 4.3.11b
12 Ω

▲ Figure 4.3.11a

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 4.3 Electric circuits

c What is the voltage across the parallel network? Now put this into practice
Let V1 = voltage across parallel network in
Figure 4.3.11a. Then 1 a Calculate the combined resistance R of a 1 Ω, 2 Ω and
3 Ω resistor connected in series.
V1 = I × R1 = 2 A × 4 Ω = 8 V b A 12 V battery is connected across the resistors.
d What is the current in the 6 Ω resistor? Calculate the current I flowing through each resistor.
Let I1 = current in 6 Ω resistor, then since V1 = 8 V c What is the p.d. across each resistor?
2 a Calculate the combined resistance Ra of 2 Ω and 3 Ω
V1 8V 4 resistors connected in parallel.
I1 = = = A b A 12 V battery is connected across the resistors.
6Ω 6Ω 3
What is the p.d. across each resistor?
c Calculate the current I flowing through
i the 2 Ω resistor
ii the 3 Ω resistor.

Going further
Resistor colour code 1st 2nd number of
Figure Colour

Resistors have colour-coded bands as shown in figure figure noughts 0 black

tolerance
Figure 4.3.12. In the orientation shown the first two (accuracy)
1 brown
bands on the left give digits 2 and 7; the third band 2 red
gives the number of noughts (3) and the fourth band 3 orange
gives the resistor’s ‘tolerance’ (or accuracy, here ±10%). 4 yellow
So the resistor has a value of 27 000 Ω (±10%).
silver 5 green

red violet orange 10% 6 blue

2 7 000 7 violet
8 grey
resistor value 27 000 W ( 10%) 9 white
27 k W ( 10%)
Tolerance
5% gold
10% silver
20% no band

▲ Figure 4.3.12 Colour code for resistors

Test yourself
4 a Write down the equation for calculating the 5 a Write down the equation for calculating the
combined resistance R of resistors R1, R2 and R3 combined resistance R of resistors R1 and R2
connected in series. connected in parallel.
b Is the current in R1 larger, the same or smaller b Is the current in R1 larger, the same or smaller
than in R3? than in R2 if R1 is smaller than R2?

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 4.3.3 Action and use of circuit components

4.3.3 Action and use of circuit components

FOCUS POINTS
★ Describe how a variable potential divider works and use the correct equation for two resistors used as a
potential divider.
★ Describe how thermistors and LDRs can be used as input sensors.

The action of potential dividers and a range of other components, including thermistors, LDRs,
relays, light-emitting diodes and semiconductor diodes, will be considered in this section.
These components are widely used in electrical circuits in applications ranging from intruder
and temperature alarms to indicator lamps and switching circuits.

Variable potential divider Potential divider

The resistance of materials other than metals In the circuit shown in Figure 4.3.14, two resistors
does not necessarily rise when their temperature R1 and R2 are in series with a supply of voltage V.
increases. For example, in a semiconductor The current in the circuit is
thermistor, the resistance decreases when its
supply voltage V
temperature increases. I= =
If a thermistor is part of a potential divider total resistance ( R1 + R2 )
circuit (see Figure 4.3.13) then its resistance So the voltage across R1 is
decreases when the external temperature rises.
The combined resistance of the two resistors V × R1 R1
V1 = I × R1 = =V ×
then decreases, so if the supply voltage remains (R1 + R2) (R1 + R2)
constant, the current in the circuit will increase.
This means that the p.d. across the fixed resistor and the voltage across R2 is
increases relative to that across the thermistor.
V × R2 R2
The p.d. across the fixed resistor could then be V2 = I × R2 = =V ×
used to monitor temperature. (R1 + R2 ) (R1 + R2 )
Also the ratio of the voltages across the two
resistors is
V1 R1
=
V2 R2
I

R1 V1

V
thermistor
▲ Figure 4.3.13 Potential divider circuit for monitoring R2 V2
temperature

A variable resistor can also be used as a potential

divider (see Figure 4.2.26b, p. 199). Moving the I

contact on the resistor changes the output p.d. ▲ Figure 4.3.14 Potential divider circuit

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 4.3 Electric circuits

b LDR
Worked example a

Resistors R1 = 80 Ω and R2 = 40 Ω are connected in series and

used as a potential divider.
a Calculate the ratio of the p.d.s across the resistors. 6V
From the potential divider equation d.c.

V1/V2 = R1/R2 = 80 Ω /40 Ω = 2

Ratio of voltages is 2:1
b If the supply voltage is 24 V, what is the p.d. across each 6 V 0.06 A
resistor?
Dividing the supply voltage in the ratio 2:1 gives
24 V c •
V1 = 2 × = 16 V
3
and
24 V R relay
V2 = 1 × = 8V
3 +
6V
Now put this into practice d.c.
•

1 Write down the equation relating p.d.s and resistances in

a potential divider circuit. bell
2 Resistors R1 = 9 Ω and R2 = 6 Ω are connected in series LDR
and used as a potential divider.
a Calculate the ratio of the p.d.s across the resistors.
b If the supply voltage is 30 V, what is the p.d. across ▲ Figure 4.3.15 a LDR; b LDR demonstration circuit;
each resistor? c light-operated intruder alarm

Figure 4.3.15c shows how an LDR can be used to

switch a relay (Topic 4.5.3). The LDR forms part of
Input sensors a potential divider across the 6 V supply. When light
Thermistors and light-dependent resistors can be falls on the LDR, the resistance of the LDR, and
used as input sensors in a circuit to detect changes hence the voltage across it, decreases. There is a
in the environment. corresponding increase in the voltage across resistor
R and the relay; when the voltage across the relay
Light-dependent resistor (LDR) coil reaches a high enough p.d. (its operating p.d.)
The action of an LDR depends on the fact that the it acts as a switch and the normally open contacts
resistance of the semiconductor cadmium sulfide close, allowing current to flow to the bell, which
decreases as the intensity of the light falling on rings. If the light is removed, the p.d. across
it increases. resistor R and the relay drops below the operating
An LDR and a circuit showing its action are p.d. of the relay so that the relay contacts open
shown in Figures 4.3.15a and b. Note the circuit again; power to the bell is cut and it stops ringing.
symbol for an LDR, sometimes seen with a circle.
When light from a lamp falls on the window of the Thermistor
LDR, its resistance decreases and the increased A negative temperature coefficient (NTC) thermistor
current lights the lamp. contains semiconducting metallic oxides whose
LDRs are used in photographic exposure meters resistance decreases markedly when the temperature
and in series with a resistor to provide an input rises. The temperature may rise either because the
signal in switching circuits such as a light-operated thermistor is directly heated or because a current
intruder alarm. is in it.

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 4.3.3 Action and use of circuit components

Figure 4.3.16a shows one type of thermistor. buzzer as in a temperature-operated switch or other
Figure 4.3.16b shows the symbol for a thermistor in device. Relays controlled by a switching circuit
a circuit to demonstrate how the thermistor works. can also be used to switch on the mains supply for
When the thermistor is heated with a match, the electrical appliances in the home. In Figure 4.3.17
lamp lights. if the output of the switching circuit is ‘high’
A thermistor in series with a meter marked in (5 V), a small current flows to the relay which
°C can measure temperatures. Used in series with closes the mains switch; the relay also isolates the
a resistor it can also provide an input signal to low voltage circuit from the high voltage mains
switching circuits. supply.
a b 0 or 5 V
thermistor

output of
switching relay
circuit
6V
d.c.
mains
0V ~ supply

6 V 0.06 A
   appliance
c
•

R relay
▲ Figure 4.3.17 Use of a relay to switch mains supply
+
6V
d.c
•
Light-emitting diode (LED)
thermistor An LED, shown in Figure 4.3.18a, is a diode made
bell
from the semiconductor gallium arsenide phosphide.
When forward biased (with the cathode C connected
to the negative terminal of the voltage supply, as
▲ Figure 4.3.16 a Thermistor; b thermistor demonstration shown in Figure 4.3.18b), the current in it makes it
circuit; c high-temperature alarm emit red, yellow or green light. No light is emitted
Figure 4.3.16c shows how a thermistor can be used on reverse bias (when the anode A is connected
to switch a relay. The thermistor forms part of a to the negative terminal of the voltage supply).
potential divider across the d.c. source. When the If the reverse bias voltage exceeds 5 V, it may
temperature rises, the resistance of the thermistor cause damage.
falls, and so does the p.d. across it. The voltage In use, an LED must have a suitable resistor R
across resistor R and the relay increases. When the in series with it (e.g. 300 Ω on a 5 V supply) to limit
voltage across the relay reaches its operating p.d. the current (typically 10 mA). Figure 4.3.18b shows
the normally open contacts close, so that the circuit the symbol for an LED in a demonstration circuit.
to the bell is completed and it rings. If a variable a b
resistor is used in the circuit, the temperature at coloured translucent
R
which the alarm sounds can be varied. plastic case

Relays ‘flat’
5V
A
LED
A switching circuit cannot supply much power to an C
cathode C anode A
appliance so a relay is often included; this allows
the small current provided by the switching circuit
to control the larger current needed to operate a ▲ Figure 4.3.18 a LED and b demonstration circuit

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 4.3 Electric circuits

LEDs are used as indicator lamps on computers, way around, it does not conduct; its resistance is
radios and other electronic equipment. Many large and it is reverse-biased (Figure 4.3.21b).
clocks, calculators, video recorders and measuring The lamp in the circuit shows when the diode
instruments have seven-segment red or green is conducting, as the lamp lights up. It also acts
numerical displays (Figure 4.3.19a). Each segment is as a resistor to limit the current when the diode is
an LED and, depending on which have a voltage across forward-biased. Otherwise the diode might overheat
them, the display lights up the numbers 0 to 9, as in and be damaged.
Figure 4.3.19b. a
LEDs are small, reliable and have a long life;
their operating speed is high and their current
requirements are very low. 1N4001
Diode lasers operate in a similar way to LEDs but
emit coherent laser light; they are used in optical
fibre communications as transmitters. 1.5 V
1.25V
a b 0.25A

LED current passes

segment
b

▲ Figure 4.3.19 LED numerical display

Semiconductor diode
A diode is a device that lets current pass in one
direction only. One is shown in Figure 4.3.20 with its
symbol. (You will also come across the symbol with
an outer circle.) The wire nearest the band is the no current
cathode and the one at the other end is the anode. ▲ Figure 4.3.21 Demonstrating the action of a diode

cathode A diode is a non-ohmic conductor. It is useful as

a rectifier for changing alternating current (a.c.)
to direct current (d.c.). Figure 4.3.22 shows the
rectified output voltage obtained from a diode when
it is connected to an a.c. supply.
V rectified output voltage from diode
anode

▲ Figure 4.3.20 A diode and its symbol

The typical I–V graph is shown in Figure 4.2.29b t

(Topic 4.2.4). The diode conducts when the anode
goes to the + terminal of the voltage supply and
the cathode to the − terminal (Figure 4.3.21a).
It is then forward-biased; its resistance is small and
a.c. input voltage
conventional current passes in the direction of the
arrow on its symbol. If the connections are the other ▲ Figure 4.3.22 Rectification by a diode

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 4.3.3 Action and use of circuit components

Test yourself
6 Resistors R1 = 12 Ω and R2 = 36 Ω are connected 8 Identify the following components from their
in series and used as a potential divider. symbols:
a Draw a potential divider circuit containing
a battery and resistors R1 and R2 in series.
b Calculate the ratio of the p.d.s across the
resistors. A B
c If the supply voltage is 20 V, what is the p.d.
across each resistor?
7 Identify the following components from their
symbols:
C D
▲ Figure 4.3.24
A B C
9 A circuit is required to demonstrate that the
resistance of a thermistor decreases when its
temperature rises. Draw a circuit diagram that
D E could be used containing a battery, a lamp and a
▲ Figure 4.3.23 thermistor.

Revision checklist
After studying Topic 4.3 you should know and After studying Topic 4.3 you should be able to:
understand: ✔ use the equations for resistors in series, and for
✔ how to connect simple series and parallel circuits two resistors in parallel
✔ that the current in a series circuit is the same ✔ calculate current, p.d. and resistance in series and
everywhere in the circuit and that for a parallel parallel circuits
circuit, the sum of the currents into a junction is ✔ calculate p.d. in potential divider circuits
equal to the sum of the currents that leave the ✔ recognise and draw symbols for a variety of
junction components in electric circuits and be able to draw
✔ the effect on p.d. of a change in the resistance of a and interpret circuit diagrams incorporating those
conductor components, and explain their behaviours in a
✔ the advantages of having lamps connected in circuit.
parallel in lighting circuits.

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 4.3 Electric circuits

Exam-style questions
1 Three voltmeters are connected as in 3 a Calculate the effective resistance between
Figure 4.3.25. A and B in Figure 4.3.27. [4]
4Ω

V1

A 4Ω B
V

V2 ▲ Figure 4.3.27

b Figure 4.3.28 shows three resistors.

Calculate their combined resistance in ohms.
▲ Figure 4.3.25  [6]
What are the voltmeter readings x, y and z in 6Ω
the table below (which were obtained with three
different batteries)? 6Ω

V/V V1/V V2 /V 2Ω

x 12 6
6 4 y ▲ Figure 4.3.28

12 z 4 [Total: 10]
x [2] 4 a Resistors of value 6 Ω, 7 Ω and 8 Ω are
connected in series.
y [2]
i Calculate the combined resistance
z [2] of the resistors. [2]
[Total: 6] ii The resistance of one of the resistors
2 The resistors R1, R2, R3 and R4 in Figure 4.3.26 increases. If the current through the
are all equal in value. combination must remain unchanged
What would you expect each of the voltmeters does the supply voltage need to be
A, B and C to read, assuming that the connecting increased or decreased? [1]
wires in the circuit have negligible resistance? b Give two advantages of connecting lamps
A [4] in parallel.[4]
B [2] c Two resistors of the same size are connected
in parallel. Is the resistance of the
C [2]
combination greater or less than that of
A B C one of the resistors? [1]
[Total: 8]
5 What are the readings V1 and V2 on the
high-resistance voltmeters in the potential
R1 R2 R3 R4 divider circuit of Figure 4.3.29 if
a R1 = R2 = 10 kΩ [2]
12 V b R1 = 10 kΩ, R2 = 50 kΩ [4]
▲ Figure 4.3.26 c R1 = 20 kΩ, R2 = 10 kΩ? [4]
[Total: 8]

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 Exam-style questions

R1 R2 7 Figure 4.3.30a shows a lamp, a semiconductor diode

and a cell connected in series. The lamp lights when
the diode is connected in this direction. Say what
V1 V2 happens to each of the lamps in b, c and d. Give
reasons for your answers.
6V
b  [3]
▲ Figure 4.3.29 c  [4]
[Total: 10] d  [3]
6 A battery of 12 V is connected across a b
a light-dependent resistor (LDR) in series
with a resistor R. D D1 L2
a Draw the circuit diagram. [2] L
b The value of the resistor R is 20 Ω L1 D2
and the resistance of the LDR is 28 Ω.
Calculate
c d
i the value of the current in the circuit [2]
ii the p.d. across the resistor [2] E1 D L1 E1 L1
D1
iii the p.d. across the LDR. [2]
c The intensity of the light falling on the E2 L2 E2 D2 L2
LDR increases. State what happens to
i the resistance of the LDR [1]
ii the current in the circuit [1] ▲ Figure 4.3.30
iii the p.d. across R.[1] [Total: 10]
[Total: 11]

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 4.4 Practical electricity
FOCUS POINTS
★ State some common uses of electricity, from heating and lighting to battery charging, powering motors
and electronic systems.
★ State various potential hazards when using a mains supply.
★ Know the three wires that make up a mains circuit and where switches should be placed to enable the
mains supply to be switched off safely.
★ Understand how trip switches and fuses work and choose appropriate settings and values for each.
★ Know that electrical appliances are made safer by having the outer casing non-conducting or earthed.

In the twenty-first century we would be lost without all the benefits electricity supplies bring us.
Because electric circuits transfer substantial amounts of energy, use of the mains supply requires
caution and electrical safety is important. You will learn that overheated wires and damaged
insulation pose fire risks. Damp or wet conditions increase the risk of electric shock from faulty
wiring in appliances since water reduces the electrical resistance of a person’s skin. If too many
appliances are connected to a circuit, the current flowing in the circuit increases and can cause
cables to overheat. To prevent problems, devices such as fuses and trip switches (circuit breakers)
are installed to break the circuit before the safe current level is exceeded. Safety features
incorporated into appliances include double insulation and earthing of metal casing via the mains
plug.

a
Electric lighting
electrodes b

LED lights
LEDs (Topic 4.3) are increasingly being used in mercury glass fluorescent
the lighting of our homes. These semiconductor vapour tube powder
devices are 40–50% efficient in transferring the
energy carried by an electrical current to light. ▲ Figure 4.4.1 Fluorescent lamps
The efficiency of the filament lamps used in the
past was only about 10%.
Electric heating
Fluorescent lamps
Fluorescent strip lamps (Figure 4.4.1a) are long Heating elements
lasting and efficient. When one is switched on, the In domestic appliances such as electric fires, cookers,
mercury vapour emits invisible ultraviolet radiation kettles and irons the ‘elements’ (Figure 4.4.2) are
which makes the powder on the inside of the made from Nichrome wire. This is an alloy of nickel
tube fluoresce (glow), i.e. visible light is emitted. and chromium which does not oxidise (and so become
Different powders give different colours. brittle) when the current makes it red hot.
Compact energy-saving fluorescent lamps (Figure The elements in radiant electric fires are at red
4.4.1b) are available to fit straight into normal light heat (about 900°C) and the radiation they emit
sockets. is directed into the room by polished reflectors.
In convector types the element is below red heat
(about 450°C) and is designed to warm air which

222
 Electronic systems

is drawn through the heater by natural or forced

convection. In storage heaters the elements heat Powering motors
fire-clay bricks during the night using ‘off-peak’ Electric motors are found in many electrical
electricity. On the following day these cool down, appliances, from sewing machines and vacuum
giving off the stored heat to warm element
the room. cleaners to electric cars and trains. An electric
motor transfers the energy carried by an electric
element
current to kinetic energy. The action of a d.c.
electric motor is explained fully in Topic 4.5.5. The
power (P) required by a motor is given by P = IV
and is measured in watts (W) (see Topic 4.2.5).
The power needed for the motor in an electric car
is around 100 kW; for a DVD player only about 20 W
cooker hob
are required.
radiant fire cooker hob
radiant fire
Electronic systems
The use of electronics in our homes, factories,
offices, banks and hospitals is growing all the time.
The development of semiconductor devices such
as integrated circuits has given us, among other
things, computers, programmable control devices,
robots, home entertainment systems, digital
iron cameras and heart pacemakers. Electric circuits
enable electrical signals to be processed.
iron
element

element
kettle

▲ Figure 4.4.2 Heating elements

kettle

Battery chargers
A battery charger transfers energy to a secondary
cell (or rechargeable battery) by forcing an electric
current to flow in the opposite direction to the
normal current flow from the cell.
Some rechargeable batteries, such as those used
for an electric car, require a fast rate of charging
(large current); others, such as the batteries used
for electric lawn mowers or mobile phones, use a
slower rate. A battery charger should be switched
▲ Figure 4.4.3 Heart pacemaker
off after charging batteries that can be damaged by
overcharging; the life of a battery can be prolonged An electronic system can be considered to consist of
if the correct charging method is used. three main parts: an input sensor, a processor and
As well as mains-operated battery chargers, the a device called an output transducer as shown in
p.d. from solar cells can be used directly to charge a Figure 4.4.4.
battery. A smart battery charger can adjust its rate
of charging according to the state of charge of the input output
processor
battery; this is useful for making cost-effective use sensor transducer
of energy supplies, for example from a rooftop solar
system. ▲ Figure 4.4.4 Electronic system

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 4.4 Practical electricity

The input sensor detects changes in the environment others. A current of 100 mA through the heart is
and transfers energy from its present form to an likely to be fatal.
electric current. Input sensors include LDRs (light- Damp conditions increase the severity of an
dependent resistors) and thermistors (see Topic electric shock because water lowers the resistance
4.3.3), and also microphones and pressure switches. of the path to earth; wearing shoes with insulating
The processor decides on what action to perform rubber soles or standing on a dry insulating floor
on the electrical signal it receives from the increases the resistance between a person and earth
input sensor. It may involve an operation such as and will reduce the severity of an electric shock.
counting, amplifying, timing or storing. To avoid the risk of getting an electric shock:
The output device transfers the energy carried (i) switch off the electrical supply to an appliance
by the electric current in the processor to the before starting repairs
environment. These devices include lamps, LEDs (ii) use plugs that have an earth pin and a cord grip;
(light-emitting diodes) loudspeakers, motors, a rubber or plastic case is preferred
heaters, relays and oscilloscopes. (iii) do not allow appliances or cables to come into
In a radio, the input sensor is the aerial that contact with water, for example holding a
sends an electrical signal to processors in the radio. hairdryer with wet hands in a bathroom can be
One of the functions of the processors is to amplify dangerous; keep electrical appliances well away
the signal so that a loudspeaker can produce sound from baths and swimming pools
waves. (iv) do not have long cables trailing across a room,
under a carpet that is walked over regularly or
Dangers of electricity in other situations where the insulation can
become damaged. Take particular care when using
There are a number of hazards associated with electrical cutting devices (such as hedge cutters)
using the mains electricity supply. not to cut the supply cable.
In case of an electric shock, take the following
Key definition actions.
Hazards associated with using mains electricity supply 1 Switch off the supply if the shocked person is still
include damaged insulation, overheated cables, damp touching the equipment.
conditions, excess current from overloaded plugs,
2 Send for qualified medical assistance.
extension leads, single and multiple sockets
3 If breathing or heartbeat has stopped, start CPR
(cardiopulmonary resuscitation) by applying
Electric shock chest compressions at the rate of about 100 a
Electric shock occurs if current flows from an minute until there are signs of chest movement
electric circuit through a person’s body to earth. or medical assistance arrives.
This can happen if there is damaged insulation or
faulty wiring. The typical resistance of dry skin Fire risks
is about 10 000 Ω, so if a person touches a wire If flammable material is placed too close to a
carrying electricity at 240 V, an estimate of the hot appliance such as an electric heater, it may
current flowing through them to earth would be catch fire. Similarly, if the electrical wiring in the
I = V/R = 240/10 000 = 0.024 A = 24 mA. walls of a house becomes overheated, a fire may
For wet skin, the resistance is lowered to about start. Wires become hot when they carry electrical
1000 Ω (since water is a good conductor of currents – the larger the current carried, the hotter
electricity) so the current would increase to a particular wire will become.
around 240 mA; a lethal current. To reduce the risk of fire through overheated
It is the size of the current (not the voltage) and cables, the maximum current in a circuit should be
the length of time for which it acts which determine limited by taking the following precautions.
the strength of an electric shock. The path the (i) Use the correct fuse in an appliance or plug
current takes influences the effect of the shock; (see p. 226).
some parts of the body are more vulnerable than

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 House circuits

(ii) Do not attach too many appliances to a circuit via and the neutral (N). The neutral is earthed at the
extension leads or single and multiple sockets. local sub-station and so there is no p.d. between it
(iii)Do not overload circuits by using too many adapters. and earth. A third wire, the earth (E) also connects
(iv) Appliances such as heaters use large amounts of the top socket on the power points in the home to
power (and hence current), so do not connect earth. The supply in many countries is a.c. (Topic
them to a lighting circuit designed for low 4.2) and the live wire is alternately positive and
current use. (Thick wires have a lower resistance negative. Study the typical house circuits shown
than thin wires so are used in circuits expected in Figure 4.4.5.
to carry high currents.)
Damaged insulation or faulty wiring which leads to Circuits in parallel
a large current flowing to earth through flammable Every circuit is connected in parallel with the supply,
material can also start a fire. i.e. across the live and neutral, and receives the full
The factors leading to fire or electric shock can mains p.d. (for example 230 V).
be summarised as follows: The advantages of having appliances connected
in parallel, rather than in series, can be seen by
damaged insulation → electric shock and fire risk
studying the lighting circuit in Figure 4.4.5.
overheated cables → fire risk (i) The p.d. across each lamp is fixed (at the
damp conditions → increased severity of electric shocks mains p.d.), so the lamp shines with the same
overloading – → fire risk and electric shock brightness irrespective of how many other lamps
plugs, extension are switched on.
leads or sockets (ii) Each lamp can be turned on and off
independently; if one lamp fails, the others can
still be operated.
House circuits In a staircase circuit, the light is controlled from
Electricity usually comes to our homes by an two places by the two two-way switches.
underground cable containing two wires, the live (L)

supply CONSUMER UNIT

company’s
main meter
fuse

to
5A 15 A 30 A 30 A
N earth
L

N L N L
supply
cable main immersion
cooker
switch heater
N
E
N L

L
N
LIGHTING CIRCUIT RING MAIN
L E
CIRCUIT L
L
two-way N
L
switches E
L N

E
▲ Figure 4.4.5 Electric circuits in a house

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 4.4 Practical electricity

Switches a b

Switches and fuses are always in the live wire.

If they were in the neutral, light switches and power fuse
wire
sockets would be ‘live’ when switches were ‘off’ or
fuses ‘blown’ or melted (see below). A fatal shock cartridge
could then be obtained by, for example, touching fuse
the element of an electric fire when it was switched
off.
insulating
holder
Ring main circuit ▲ Figure 4.4.6 a Two types of fuse; b the circuit symbol
The live and neutral wires each run in two complete for a fuse
rings round the house and the power sockets, each
rated at 13 A, are tapped off from them. Thinner Typical power ratings for various appliances are shown
wires can be used since the current to each socket in Table 4.2.1, p. 204. Calculation of the current in
flows by two paths, i.e. from both directions in the a device allows the correct size of fuse to be chosen.
ring. The ring has a 30 A fuse and if it has, say, ten
sockets, then all can be used so long as the total
current does not exceed 30 A, otherwise the wires
Trip switches (circuit
overheat. A house may have several ring circuits, breakers)
each serving a different area. Trip switches (also known as circuit breakers)
(Figure 4.4.7) are now used instead of fuses in
Fuses consumer units. They contain an electromagnet
A fuse protects a circuit; it is always placed in the (Topic 4.1) which, when the current exceeds the rated
live wire. It is a short length of wire of material value of the circuit breaker, becomes strong enough
with a low melting temperature, often ‘tinned to separate a pair of contacts and break the circuit
copper’, which melts and breaks the circuit when the Like fuses, circuit breakers are always placed in the
current in it exceeds a certain value. Two reasons live wire.
for excessive currents are ‘short circuits’ due to In the design shown in Figure 4.4.7, when the
worn insulation on connecting wires and overloaded current is large enough in an electromagnet, an
circuits. Without a fuse the wiring would become adjacent iron bolt is attracted far enough for a
hot in these cases and could cause a fire. A fuse plunger to be released, which allows a push switch
should ensure that the current-carrying capacity of to open and contact to the rest of the circuit to be
the wiring is not exceeded. In general, the thicker a broken.
cable is, the more current it can carry, but each size Circuit breakers operate much faster than fuses
has a limit. and have the advantage that they can be reset by
Two types of fuse are shown in Figure 4.4.6. Always pressing a button. As for a fuse, the trip switch
switch off before replacing a fuse, and always replace setting should be chosen to be a little higher
with one of the same value as recommended by the than the value of the current in the device being
manufacturer of the appliance. A 3 A (red) fuse will protected.
be needed for appliances with powers up to 720 W, or
13 A (brown) for those between 720 W and 3 kW.

▲ Figure 4.4.7 Circuit breakers

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 Double insulation

The residual current circuit breaker (RCCB), also called

a residual current device (RCD), is an adapted circuit Earthing
breaker which is used when the resistance of the A ring main has a third wire which goes to the top
earth path between the consumer and the substation socket on all power points and is earthed by being
is not small enough for a fault-current to blow the connected either to a metal water pipe entering the
fuse or trip the circuit breaker. It works by detecting house or to an earth connection on the supply cable.
any difference between the currents in the live and This third wire is a safety precaution to prevent
neutral wires; when these become unequal due to an electric shock should an appliance develop a fault.
earth fault (i.e. some of the current returns to the The earth pin on a three-pin plug is connected to
substation via the case of the appliance and earth) the metal case of the appliance which is thus joined
it breaks the circuit before there is any danger. to earth by a path of almost zero resistance. If then,
They have high sensitivity and a quick response. for example, the element of an electric fire breaks or
An RCD should be plugged into a socket supplying sags and touches the case, a large current flows to
power to a portable appliance such as an electric earth and ‘blows’ the fuse. Otherwise the case would
lawnmower or hedge trimmer. In these cases, the become ‘live’ and anyone touching it would receive
risk of electrocution is greater because the user is a shock which might be fatal, especially if they were
generally making a good earth connection through ‘earthed’ by, say, standing in a damp environment,
their feet. such as on a wet concrete floor.

Worked example Double insulation

Appliances such as vacuum cleaners, hairdryers and
An electric heater has a power rating of 2 kW. food mixers are usually double insulated. Connection
a If the supply voltage is 240 V, calculate the current in the
to the supply is by a two-core insulated cable, with
heater.
Power P = IV no earth wire, and the appliance is enclosed in a
Rearrange the equation to give non-conducting plastic case. Any metal attachments
P 2000 W that the user might touch are fitted into this case
I= = = 8.3A
V 240 V so that they do not make a direct connection with
b Should a 3 A or 13 A fuse or trip switch setting be chosen the internal electrical parts, such as a motor. There
to protect the heater? is then no risk of a shock should a fault develop.
The fuse/trip switch setting should have a higher rating
than the current in the heater, so a 13 A fuse/trip switch
setting should be chosen. Test yourself
Now put this into practice 1 The largest number of 100 W lamps connected
1 An electric heater has a power rating of 1.5 kW. in parallel which can safely be run from a 230 V
a If the supply voltage is 240 V, calculate the current in supply with a 5 A fuse is
the heater. A 2    B 5    C 11    D 12
b Should a 3 A, 13 A or 30 A fuse be used to protect the 2 What is the maximum power in kilowatts of the
heater? appliance(s) that can be connected safely to a 13 A
2 A television has a power rating of 100 W. 230 V mains socket?
a If the supply voltage is 240 V, calculate the current in 3 a To what part of an appliance is the earth pin on
the television. a three-pin plug attached?
b Should a 3 A, 13 A or 30 A fuse be chosen to protect the b How can a two-pin appliance be designed to
television? reduce the risk of the user receiving an electric
3 An electric cooker has a power rating of 6.4 kW. shock if a fault develops?
a If the supply voltage is 240 V, calculate the current in
the cooker.
b Should a 3 A, 13 A or 30 A trip switch setting be chosen
to protect the oven?

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 4.4 Practical electricity

Revision checklist
After studying Topic 4.4 you should know and After studying Topic 4.4 you should be able to:
understand ✔ recall the hazards of damaged insulation, damp
✔ why switches, fuses and circuit breakers are wired conditions, overheated cables and excess current
into the live wire in house circuits from overloaded circuits
✔ the benefits of earthing metal cases and double ✔ state the function of a fuse and choose the
insulation. appropriate fuse rating for an appliance; explain
the use, choice and operation of a trip switch.

Exam-style questions
1 There are hazards in using the mains electricity 3 a A child whose hands are damp touches a wire
supply. carrying electricity at 240 V. The resistance
a Identify two factors which can increase the of the child’s skin between hand and earth is
risk of fire in circuits connected to the mains 800 Ω.
supply.[2] i Calculate the current which would flow
b Identify two factors which can increase the through the child. [2]
risk of electric shock. [2] ii State whether the current you
c Describe the steps you would take before calculated in i is likely to be lethal. [1]
replacing a blown fuse in an appliance. [3] iii State how the current could be
d Explain why an electrical appliance is double reduced.[2]
insulated or the outer casing is earthed. [3] b Work out the size of fuse (3 A or 13 A) which
[Total: 10] should be used in the following appliances if
2 Fuses are widely used in electrical circuits the supply is 230 V:
connected to the mains supply. i a 150 W television [2]
a Explain the function of a fuse in a circuit. [2] ii a 900 W iron [2]
b The circuits of Figures 4.4.8a and b show iii a 2 kW kettle. [2]
‘short circuits’ between the live (L) and [Total: 11]
neutral (N) wires. In both, the fuse has blown
but whereas circuit a is now safe, b is still
dangerous even though the lamp is out which
suggests the circuit is safe. Explain. [4]
a b
fuse
L L

fuse
N N

short circuit short circuit

▲ Figure 4.4.8 [Total: 6]

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 4.5 Electromagnetic effects
4.5.1 Electromagnetic induction
FOCUS POINTS
★ Know that an electromotive force (e.m.f.) is induced in a conductor when it moves across a magnetic field
or a changing magnetic field links with the conductor.
★ Describe how electromagnetic induction can be demonstrated and state the factors which affect the size of
an induced e.m.f.
★ Know that the direction of an induced e.m.f. is such as to oppose the change causing it.
★ Determine the relative directions of force, field and induced current.

Electricity and magnetism are closely linked. You will learn that an electrical conductor moving
through a magnetic field can induce a current. Similarly, an electrical conductor in a changing
magnetic field acquires an electromotive force (e.m.f.). You will find out about the factors which
determine the size of the induced e.m.f. Electromagnetic induction plays an important role in many
electrical applications from induction cookers and motors to electricity generators.

The effect of producing electricity from magnetism

magnet
was discovered in 1831 by Faraday and is called
electromagnetic induction. It led to the
construction of generators for producing electrical 1
energy in power stations. N 3
5
wire
Electromagnetic induction 6
4 S
experiments
2

Two ways of investigating electromagnetic induction

follow.
Straight wire and U-shaped magnet
First the wire is held at rest between the poles of
the magnet. It is then moved in each of the six
directions shown in Figure 4.5.1 and the meter
sensitive
observed. Only when it is moving upwards (direction centre-zero meter
1) or downwards (direction 2) is there a deflection
on the meter, indicating an induced current in the ▲ Figure 4.5.1 A current is induced in the wire when it is
wire. The deflection is in opposite directions in moved up or down between the magnet poles.
these two cases and only lasts while the wire is in
motion. is induced in the coil in one direction as the
magnet is moved in and in the opposite direction
Bar magnet and coil as it is moved out. There is no deflection when
The magnet is pushed into the coil, one pole first the magnet is at rest. The results are the same if
(Figure 4.5.2 overleaf), then held still inside it. the coil is moved instead of the magnet, i.e. only
It is then withdrawn. The meter shows that current relative motion is needed.

229
 4.5 Electromagnetic effects

These facts led him to state that:

The size of the induced e.m.f. is directly proportional
to the rate at which the conductor cuts magnetic
field lines.
sensitive
centre-zero coil (600 turns) Key definition
meter
Magnitude of an induced e.m.f. e.m.f. increases with
bar magnet increases of:
(i) the rate of change of the magnetic field or the rate of
▲ Figure 4.5.2 A current is induced in the coil when the cutting of magnetic field lines
magnet is moved in or out. (ii) the number of turns on the coil

This experiment indicates that an e.m.f. is induced in

a conductor when it is linked by a changing magnetic Direction of induced e.m.f.
field or when it moves across a magnetic field.
The direction of an induced e.m.f. opposes the
change causing it.
Practical work
In Figure 4.5.3a the magnet approaches the coil,
Induced currents north pole first. According to Lenz’s law, the
induced e.m.f. and resulting current flow should
Connect a sensitive centre-zero meter to a be in a direction that makes the coil behave like a
600 turn coil as shown in Figure 4.5.2. magnet with its top a north pole. The downward
Record the values and the direction of the motion of the magnet will then be opposed since
current detected by the meter when you move like poles repel.
the magnet first towards the coil and then
away from the coil. Try moving the magnet Key definition
faster; record your results again. Repeat the Lenz’s law the effect of the current produced by an
induced e.m.f. is to oppose the change producing it
procedure by moving the coil instead of the
magnet. When the magnet is withdrawn, the top of the coil
1 When is a current produced in the circuit? should become a south pole (Figure 4.5.3b) and
2 How is the induced e.m.f. related to the attract the north pole of the magnet, so hindering
current in the circuit? its removal. The induced e.m.f. and current are thus
in the opposite direction to that when the magnet
approaches.
Factors affecting the size of an a b

induced e.m.f.
To explain electromagnetic induction Faraday
N N
suggested that an e.m.f. is induced in a conductor
whenever it ‘cuts’ magnetic field lines, i.e. moves
N S
across them, but not when it moves along them or
is at rest. If the conductor forms part of a complete 0 0

circuit, an induced current is also produced.

Faraday identified three factors affecting the
magnitude of an induced e.m.f. and it can be ▲ Figure 4.5.3 The induced current opposes the motion of
shown with apparatus like that in Figure 4.5.2, that the magnet.
the induced e.m.f. increases with increases of
(i) the speed of motion of the magnet or coil This behaviour is an example of the principle of
(ii) the number of turns on the coil conservation of energy. If the currents produced a
(iii) the strength of the magnet. magnetic field of opposite polarity to those shown

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 4.5.2 The a.c. generator

in Figure 4.5.3 in each coil, energy would be created

from nothing. As it is, work is done, by whoever Test yourself
moves the magnet, to overcome the forces that 1 A magnet is pushed, N pole first, into a coil
arise. as in Figure 4.5.5. Which one of the following
statements A to D is not true?
A An e.m.f. is induced in the coil and causes
Going further a current through the sensitive centre-zero
meter.
For a straight wire moving at right angles to a
B The induced e.m.f. increases if the magnet
magnetic field, the direction of the induced current
is pushed in faster and/or the coil has more
can be found from Fleming’s right-hand rule (the
turns.
‘dynamo rule’) (Figure 4.5.4).
C Energy is transferred by an electric current.
Hold the thumb and first two fingers of the right hand
D The effect produced is called electrostatic
at right angles to each other with the First finger
induction.
pointing in the direction of the Field and the thuMb in
the direction of Motion of the wire, then the seCond
finger points in the direction of the induced Current. S N X coil
Note that the direction of motion represents the
direction in which the force acts on the conductor. magnet
Motion thuMb
First 0
Field finger

centre-zero meter
▲ Figure 4.5.5
induced
Current seCond 2 A straight wire moves vertically upwards at right
finger angles to a magnetic field acting horizontally
from right to left. Make a sketch to represent the
▲ Figure 4.5.4 Fleming’s right-hand (dynamo) rule
directions of the magnetic field, the motion of the
wire and the induced current in the wire if it is
Key definition connected to a complete circuit.
Fleming’s right-hand (dynamo) rule used to show
the relative directions of force, field and induced
current. When the thumb and first two fingers of
the right hand are held at right angles to each other
with the first finger pointing in the direction of the
magnetic field and the thumb in the direction of the
motion of the wire, then the second finger points in
the direction of the induced current.

4.5.2 The a.c. generator

FOCUS POINTS
★ Describe the construction and action of a simple a.c. generator.
★ Sketch and interpret a graph of e.m.f against time for an a.c. generator.

When a coil is rotated between the poles of a magnet, the conductor cuts the magnetic field lines
and an e.m.f. is induced. The size of the e.m.f. generated changes with the orientation of the
coil and alternates in sign during the course of each rotation. This process is used in the large
generators in power stations to produce an alternating (a.c.) electricity supply.

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 4.5 Electromagnetic effects

Simple a.c. generator An alternating e.m.f. is generated which acts first in

one direction and then the other; it causes a.c. to flow
The simplest alternating current (a.c.) generator in a circuit connected to the brushes. The frequency
(alternator) consists of a rectangular coil between of an a.c. is the number of complete cycles it makes
the poles of a C-shaped magnet (Figure 4.5.6a). each second and is measured in hertz (Hz), i.e. 1 cycle
The ends of the coil are joined to two slip rings per second = 1 Hz. If the coil rotates twice per second,
on the axle and against which carbon brushes press. the a.c. has frequency 2 Hz. The mains supply is a.c. of
When the coil is rotated it cuts the field lines frequency 50 Hz.
and an e.m.f. is induced in it. Figure 4.5.6b shows
how the e.m.f. varies over one complete rotation.
As the coil moves through the vertical position Going further
with ab uppermost, ab and cd are moving along
the lines (bc and da do so always) and no cutting Practical generators
occurs. The induced e.m.f. is zero. In power stations several coils are wound in
evenly spaced slots in a soft iron cylinder and
a coil rotation electromagnets usually replace permanent magnets.
The electromagnets rotate (the rotor, Figure 4.5.7a)
b c while the coils and their iron core are at rest (the
stator, Figure 4.5.7b). The large e.m.f. and currents
(e.g. 25 kV at several thousand amps) induced in
N S the stator are led away through stationary cables,
a d
otherwise they would quickly destroy the slip rings by
sparking. Instead the relatively small power required
by the rotor is fed via the slip rings from a small
alternating e.m.f. generator (the exciter) which is driven by the same
slip rings turbine as the rotor.
(rotate
a
with coil)
brushes (fixed)

b
1 cycle
e.m.f.

0
¹⁄₄ ¹⁄₂ ³⁄₄ 1
no. of
rotations

a d a
d a a d field lines
coil
vertical d a d
b
coil horizontal

▲ Figure 4.5.6 A simple a.c. generator and its output

During the first quarter rotation the e.m.f. increases

to a maximum when the coil is horizontal. Sides ab
and dc are then cutting the lines at the greatest
rate.
In the second quarter rotation the e.m.f.
decreases again and is zero when the coil is vertical
with dc uppermost. After this, the direction of
the e.m.f. reverses because, during the next half
▲ Figure 4.5.7 The rotor and stator of a power station
rotation, the motion of ab is directed upwards and alternator
dc downwards.

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 4.5.3 Magnetic effect of a current

In a thermal power station (Topic 1.7), the turbine is Test yourself

rotated by high-pressure steam obtained by heating
water in a coal- or oil-fired boiler or in a nuclear 3 Which feature of the rotating coil of an a.c.
reactor (or by hot gas in a gas-fired power station). generator allows the induced e.m.f. to be
A block diagram of a thermal power station is shown connected to fixed contacts?
in Figure 4.5.8. The Sankey diagram showing energy 4 a Sketch the output of an a.c. generator against
transfer was given in Figure 1.7.5, p. 62. time.
b At what position of the coil in an a.c. generator
stator a.c. output is the output
steam i a maximum
ii zero?

boiler turbine rotor exciter

water
stator a.c. output

▲ Figure 4.5.8 Block diagram of a thermal power

station

4.5.3 Magnetic effect of a current

FOCUS POINTS
★ Describe the pattern and direction of the magnetic field around a current-carrying straight wire and a
solenoid.
★ Use the examples of relays and loudspeakers to describe the application of the magnetic effect of a current.
★ Describe the variation of the magnetic field strength around a current-carrying straight wire and a
solenoid and recall the effect on the magnetic field of changing the current’s direction and size.

A further link between electricity and magnetism comes from the presence of a magnetic field
around a conductor carrying a current. In this topic you will learn that the magnetic field can be
concentrated by the geometry of the conductor. A long cylindrical coil (a solenoid) will act like a
bar magnet when current is switched on. As you have seen in Topic 4.1, electromagnets have many
applications. In this topic you can discover how they are also used in switches, relays, bells and
loudspeakers.
Magnetic field lines are used to represent the variation in magnetic field strength around a current-
carrying conductor and its dependence on the size and direction of the current.

Oersted’s discovery Evidently around a wire carrying a current there

is a magnetic field. As with the field due to a
In 1819 Hans Oersted accidentally discovered the permanent magnet, we represent the field due to
magnetic effect of an electric current. His experiment a current by field lines or lines of force. Arrows on
can be repeated by holding a wire over and parallel the lines show the direction of the field, i.e. the
to a compass needle that is pointing N and S direction in which a N pole points.
(Figure 4.5.9). The needle moves when the current Different field patterns are given by differently
is switched on. Reversing the current causes the shaped conductors.
needle to move in the opposite direction.

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 4.5 Electromagnetic effects

current direction If the current direction is known, the direction of

the field can be predicted by the right-hand screw
rule:
S
compass needle If a right-handed screw moves forwards in the direction
N movement
of needle of the current (conventional), the direction of rotation
of the screw gives the direction of the magnetic field.

Field due to a circular coil

The field pattern is shown in Figure 4.5.11. At the
centre of the coil the field lines are straight and at
right angles to the plane of the coil. The right-hand
screw rule again gives the direction of the field at
any point.
low-voltage high-current supply circular coil

▲ Figure 4.5.9 An electric current produces a magnetic effect. field

line

Field due to a straight wire current

direction
If a straight vertical wire passes through the centre
of a piece of card held horizontally and there is ▲ Figure 4.5.11 Field due to a circular coil
a current in the wire (Figure 4.5.10), iron filings
sprinkled on the card settle in concentric circles Field due to a solenoid
when the card is gently tapped. A solenoid is a long cylindrical coil. It produces
a field similar to that of a bar magnet; in Figure
4.5.12a, end A behaves like a N pole and end B like
right-handed a S pole. The polarity can be found as before by
screw shows field applying the right-hand screw rule to a short length
plotting direction
compass
of one turn of the solenoid. Alternatively, the right-
hand grip rule can be used. This states that if the
fingers of the right hand grip the solenoid in the
field lines direction of the current (conventional), the thumb
shown by iron
filings
points to the N pole (Figure 4.5.12b). Figure 4.5.12c
card shows how to link the end-on view of the current
direction in the solenoid to the polarity. A compass
could be used to plot the magnetic field lines
straight
around the solenoid (see Topic 4.1).
current
wire direction solenoid field line

▲ Figure 4.5.10 Field due to a straight wire

Plotting compasses placed on the card settle along A B

the field lines and show the direction of the field
at different points. When the current direction
is reversed, the compasses point in the opposite
current direction
direction showing that the direction of the field
reverses when the current reverses. ▲ Figure 4.5.12a Field due to a solenoid

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 4.5.3 Magnetic effect of a current

N
right
hand

(i) View from A (ii) View from B

▲ Figure 4.5.12b The right-hand grip rule ▲ Figure 4.5.12c End-on views

Variation of magnetic field strength Test yourself

There is variation of magnetic field strength
5 The vertical wire in Figure 4.5.13 is at right
around a current-carrying straight wire (Figure
angles to the card. In what direction will a
4.5.10) – it becomes less as the distance from the plotting compass at A point when
wire increases. This is shown by the magnetic field a there is no current in the wire
lines becoming further apart. When the current b the current direction is upwards?
through the wire is increased, the strength of card
the magnetic field around the wire increases and
the field lines become closer together. When the N

direction of the current changes, the magnetic field A

acts in the opposite direction.
Inside the solenoid in Figure 4.5.12a, the field wire
lines are closer together than they are outside the
▲ Figure 4.5.13
solenoid. This indicates that the magnetic field is
stronger inside a solenoid than outside it. When the 6 Figure 4.5.14 shows a solenoid wound on a core
of soft iron. Will the end A be a N pole or S pole
direction of the current changes in the solenoid, when the current is in the direction shown?
the magnetic field acts in the opposite direction.
A
The field inside a solenoid can be made very strong
if it has a large number of turns or a large current.
Permanent magnets can be made by allowing molten
▲ Figure 4.5.14
ferromagnetic metal to solidify in such fields.
7 a State where the magnetic field is strongest in
Key definition a current-carrying solenoid.
Variation of magnetic field strength the magnetic field b Name two factors which affect the strength
decreases with distance from a current-carrying wire and of a magnetic field around a current-carrying
varies around a solenoid solenoid.

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 4.5 Electromagnetic effects

Applications of the magnetic effect Loudspeaker

of a current Varying currents from a radio, CD player, etc. pass
through a short cylindrical coil whose turns are
Relay at right angles to the magnetic field of a magnet
A relay is a switch based on the principle of an with a central pole and a surrounding ring pole
electromagnet. It is useful if we want one circuit to (Figure 4.5.17a).
control another, especially if the current and power The magnetic fields around the coil and the
are larger in the second circuit. Figure 4.5.15 shows magnet interact and the coil vibrates with the
a typical relay. When a current is in the coil from same frequency as the a.c. of the electrical signal
the circuit connected to AB, the soft iron core is it receives. A paper cone attached to the coil
magnetised and attracts the L-shaped iron armature. moves with it and sets up sound waves in the
This rocks on its pivot and closes the contacts at surrounding air (Figure 4.5.17b).
C in the circuit connected to DE. The relay is then a End -on view b
‘energised’ or ‘on’. casing ring central
pole pole

insulator springy metal

D
C N N
pivot
E
N S N S
coil
iron armature
on
N N
tube
A
paper
B cone

coil soft iron core

▲ Figure 4.5.17 Moving-coil loudspeaker
▲ Figure 4.5.15 Relay

The current needed to operate a relay is called

the pull-on current and the drop-off current is the Test yourself
smaller current in the coil when the relay just stops 8 Explain when a relay would be used in a circuit.
working. 9 The resistance, R, of the coil in a relay is 300 Ω and
If the coil resistance, R, of a relay is 185 Ω and its operating p.d. V is 15 V. Calculate the pull-on
its operating p.d. V is 12 V, then the pull-on current current.
10 The pull-on current in a relay is 60 mA and it
I = V/R = 12/185 = 0.065 A = 65 mA. The symbols operates at 12  V. Calculate the resistance of the
for relays with normally open and normally closed coil.
contacts are given in Figure 4.5.16. 11 Explain how an a.c. signal is converted into sound
a b by a loudspeaker.

▲ Figure 4.5.16 Symbols for a relay: a open; b closed

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 4.5.4 Force on a current-carrying conductor

Going further
bell push
Electric bell
When the circuit in Figure 4.5.18 is completed, by
someone pressing the bell push, current flows in the
coils of the electromagnet which becomes magnetised
and attracts the soft iron bar (the armature).
The hammer hits the gong but the circuit is now broken
at the point C of the contact screw. springy
metal
The electromagnet loses its magnetism (becomes strip
demagnetised) and no longer attracts the armature.
The springy metal strip is then able to pull the armature
back, remaking contact at C and so completing the soft iron
circuit again. This cycle is repeated so long as the bell armature
push is depressed, and continuous ringing occurs.

contact screw

electromagnet

hammer
gong

▲ Figure 4.5.18 Electric bell

4.5.4 Force on a current-carrying conductor

FOCUS POINTS
★ Describe an experiment that demonstrates that a force acts on a conductor in a magnetic field when it
carries a current.
★ Know how the directions of force, magnetic field and current relate to each other.
★ Describe the magnetic field pattern and the resultant force between two parallel current-carrying
conductors.

Electric motors form the heart of many electrical devices ranging from domestic appliances such as
vacuum cleaners and washing machines to electric trains and lifts. In a car, the windscreen wipers
are usually driven by one and the engine is started by another. All these devices rely on the fact that
a current flowing in a magnetic field experiences a force. The force will cause a current-carrying
conductor to move or be deflected, and cause two parallel current-carrying wires to be attracted or
repelled.

The motor effect Demonstration

A wire carrying a current in a magnetic field In Figure 4.5.19, the flexible wire is loosely
experiences a force. If the wire can move, it supported in the strong magnetic field of a
does so. C-shaped magnet (permanent or electromagnet).
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 4.5 Electromagnetic effects

When the switch is closed, current flows in the force on wire

wire, which jumps upwards as shown. If either the
direction of the current or the direction of the field
is reversed, the wire moves downwards. The force
increases if the strength of the field increases and if
the current increases.
N S

motion

N wire

S ▲ Figure 4.5.20b

Fleming’s left-hand rule

The direction of the force or thrust on the wire can
flexible
wire be found by Fleming’s left-hand rule, which is also
to low-voltage called the motor rule (Figure 4.5.21).
high-current supply Hold the thumb and first two fingers of the left
hand at right angles to each other with the First
finger pointing in the direction of the Field and the
seCond finger in the direction of the Current, then
▲ Figure 4.5.19 A wire carrying a current in a magnetic field
experiences a force.
the Thumb points in the direction of the Thrust (or
force).
Explanation If the wire is not at right angles to the field, the
Figure 4.5.20a is a side view of the magnetic field force is smaller and is zero if the wire is parallel to
lines due to the wire and the magnet. Those due the field.
to the wire are circles and we will assume their Thumb
Thrust
direction is as shown. The dotted lines represent
the field lines of the magnet and their direction is
towards the right. First finger
The resultant field obtained by combining both
fields is shown in Figure 4.5.20b. There are more Current Field
lines below than above the wire since both fields seCond finger
act in the same direction below but they are in ▲ Figure 4.5.21 Fleming’s left-hand (motor) rule
opposition above. If we suppose the lines are like
stretched elastic, those below will try to straighten
out and in so doing will exert an upward force on
Force on beams of charged
the wire. particles in a magnetic field
In Figure 4.5.22 the evenly spaced crosses represent
a uniform magnetic field (i.e. one of the same
strength throughout the area shown) acting into
N S and perpendicular to the paper. A beam of electrons
entering the field at right angles to the field
experiences a force due to the motor effect whose
direction is given by Fleming’s left-hand rule. This
wire
indicates that the force acts at right angles to the
direction of the beam and makes it follow a circular
▲ Figure 4.5.20a path as shown. The beam of negatively charged
electrons is treated as being in the opposite direction
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 4.5.4 Force on a current-carrying conductor

to conventional current. A beam of positively charged

particles would be deflected in the opposite direction Test yourself
to that shown (see Topic 5.2, p. 267). 12 The current direction in a wire running between
the N and S poles of a magnet lying horizontally is
shown in Figure 4.5.23. The force on the wire due
to the magnet is directed
A from N to S
B from S to N
C opposite to the current direction
D vertically upwards.
magnetic field current
electron (into paper)
beam
S
force on
electron
N
circular path electron

▲ Figure 4.5.23
13 An electron beam follows a circular path in a
perpendicular magnetic field. Will the radius of
the path increase or decrease if the strength of the
▲ Figure 4.5.22 Path of an electron beam at right angles to magnetic field increases? Why?
a magnetic field

Magnetic field between two As a result the wires experience equal and opposite
forces towards each other. When the currents in
parallel current-carrying wires the parallel wires are in opposite directions, their
When two long parallel wires are near each other magnetic fields interact to give the resultant field
and carry currents in the same direction, their pattern shown in Figure 4.5.24b; the density of
magnetic fields interact to give the resultant field field lines is now greatest between the wires and a
pattern shown in cross-section in Figure 4.5.24a; repulsive force between the wires results. Current
there are fewer lines between the wires (where direction into the page is represented by + and out
the fields are in opposite directions) than on their of the page by •.
outer sides (where they are in the same direction.)
a like currents attract b unlike currents repel

force on force on force on

wire wire wire

▲ Figure 4.5.24 Magnetic field between two parallel current-carrying wires

The direction of the force experienced by one right-hand screw rule to find the direction of the
wire due to the current in the other can be found field around each wire.
from Fleming’s left-hand rule, after using the In summary: like currents attract, unlike currents
repel.
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 4.5 Electromagnetic effects

4.5.5 The d.c. motor

FOCUS POINTS
★ Know the factors that may increase the turning effect on a current-carrying coil in a magnetic field.
★ Describe how an electric motor works.

In the previous topic you learnt that a current flowing in a magnetic field experiences a force. The
force may lead to a turning effect on a current-carrying coil in a magnetic field because of the forces
acting on the two sides of the coil. The magnitude of the turning effect is increased by increasing the
number of turns on the coil, increasing the current or increasing the strength of the magnetic field.
This turning effect is the basis of all electric motors from electric toothbrushes to ship propulsion.

The motor effect shows that a straight current- an upward force and side cd a downward force. (No
carrying wire in a magnetic field experiences a forces act on ad and bc since they are parallel to the
force. If the wire is wound into a coil, forces act on field.) These two forces rotate the coil in a clockwise
both sides of the coil and a turning effect results direction until it is vertical.
when the coil carries current in a magnetic field.
coil

Turning effect on a coil b

c
A rectangular coil of wire mounted on an axle which
can rotate between the poles of a magnet may
experience a turning effect when a direct current
(d.c.) is passed through it. N S
The turning effect increases if: a d
(i) the number of turns on the coil increases
(ii) the current flowing in the coil increases
(iii) the strength of the magnetic field increases.
brush
The larger the turning effect on the coil, the faster brush
(fixed)
(fixed)
it will turn.
commutator
Simple d.c. electric motor (rotates with coil)

A simple motor to work from direct current (d.c.)

▲ Figure 4.5.25 Simple d.c. motor
consists of a rectangular coil of wire mounted on
an axle which can rotate between the poles of a The brushes are then in line with the gaps in the
C-shaped magnet (Figure 4.5.25). commutator and the current stops. However, because
Each end of the coil is connected to half of a of its inertia, the coil overshoots the vertical and
split ring of copper, called a split-ring commutator, the commutator halves change contact from one
which rotates with the coil. Two carbon blocks, the brush to the other. This reverses the current through
brushes, are pressed lightly against the commutator the coil and so also the directions of the forces
by springs. The brushes are connected to an on its sides. Side ab is on the right now, acted on
electrical supply. by a downward force, while cd is on the left with
If Fleming’s left-hand rule is applied to the coil in an upward force. The coil thus carries on rotating
the position shown, we find that side ab experiences clockwise.

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 4.5.5 The d.c. motor

Practical motors
Practical motors have the following features:
(i) A coil of many turns wound on a soft iron cylinder
or core which rotates with the coil. This makes
it more powerful. The coil and core together are
called the armature.
(ii) Several coils each in a slot in the core and each
having a pair of commutator segments. This gives
increased power and smoother running. The motor
of an electric drill is shown in Figure 4.5.26.
(iii) An electromagnet (usually) to produce the field in
which the armature rotates.
Most electric motors used in industry are induction
motors. They work off a.c. (alternating current) on a
different principle from the d.c. motor. ▲ Figure 4.5.26 Motor inside an electric drill

Practical work

A model motor g Slide the base into the magnet with opposite
The motor shown in Figure 4.5.27 is made from a poles facing. Connect to a 3 V battery (or other
kit. low-voltage d.c. supply) and a slight push of
a Wrap Sellotape round one end of the metal the coil should set it spinning at high speed.
tube which passes through the wooden block. 3 List the variables in the construction of a
b Cut two rings off a piece of narrow rubber simple d.c. motor.
tubing; slip them on to the taped end of the 4 How would the motion of the coil change if you
metal tube. reversed the current direction?
c Remove the insulation from one end of a
Sellotape brushes
1.5-metre length of SWG 26 PVC-covered
copper wire and fix it under both rubber rings
bare ends
so that it is held tight against the Sellotape. of coil
This forms one end of the coil.
d Wind 10 turns of the wire in the slot in the wooden block

wooden block and finish off the second end of axle

the coil by removing the PVC and fixing this rubber

rings
too under the rings but on the opposite side of split pin
metal
the tube from the first end. The bare ends act tube base
as the commutator.
e Push the axle through the metal tube of the magnet
wooden base so that the block spins freely.
f Arrange two 0.5 metre lengths of wire to act rivet yoke
to battery
as brushes and leads to the supply, as shown.
Adjust the brushes so that they are vertical
coil in slot
and each touches one bare end of the coil
when the plane of the coil is horizontal. The ▲ Figure 4.5.27 A model motor
motor will not work if this is not so.

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 4.5 Electromagnetic effects

Going further
b view from above
Moving-coil galvanometer
radial field
A galvanometer detects small currents or small p.d.s,
often of the order of milliamperes (mA) or millivolts (mV).
In the moving-coil pointer-type meter, a coil is pivoted
between the poles of a permanent magnet (Figure
4.5.28a). Current enters and leaves the coil by hair
springs above and below it. When there is a current, a
pair of forces act on the sides of the coil (as in an electric
motor), causing it to rotate until stopped by the springs.
The greater the current, the greater the deflection which
is shown by a pointer attached to the coil.
a
5 10
15

pointer
soft iron coil
20

cylinder
coil
N ▲ Figure 4.5.28 Moving-coil pointer-type galvanometer
concave
pole S
terminals The soft iron cylinder at the centre of the coil is fixed
soft iron and along with the concave poles of the magnet it
cylinder produces a radial field (Figure 4.5.28b), i.e. the field
hair lines are directed to and from the centre of the cylinder.
spring The scale on the meter is then even or linear, i.e. all
divisions are the same size.

Test yourself
14 How would the turning effect on a current-carrying
coil in a magnetic field change if
N

a the size of the magnetic field is increased

b the direction of the magnetic field is reversed?
S

15 In the simple d.c. electric motor of Figure 4.5.29, the

coil rotates anticlockwise as seen by the eye from X
the position X when current flows in the coil. Is the
current flowing clockwise or anticlockwise around ▲ Figure 4.5.29
the coil when viewed from above?
16 Explain the function of the split-ring commutator
and brushes in a d.c. motor.

4.5.6 The transformer

FOCUS POINTS
★ Describe the construction of a simple transformer.
★ Explain how a simple iron-cored transformer works.
★ Understand the terms primary, secondary, step-up and step-down and correctly use the transformer equation.
★ Describe how high-voltage transformers are used in the transmission of electricity and why high voltages
are preferred.

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 4.5.6 The transformer

Many household devices such as electronic keyboards, toys, lights and telephones require a
lower voltage than is provided by the mains supply and a transformer is needed to reduce the
mains voltage. When two coils lie in a magnetic field, variations in the current in one coil induce a
current change in the other. In this section you will learn that this effect is used in a transformer to
raise or lower alternating voltages. The voltage transformation depends on the ratio of the number
of turns of wire in each coil. Alternating current generated in a power station is transformed into
a very high voltage for long-distance electrical transmission. This reduces the size of the current
flowing in the transmission cables and minimises the energy lost to thermal energy due to the
resistance of the cables.

Transformers Mutual induction

A transformer transforms (changes) an alternating When the current in a coil is switched on or off
voltage from one value to another of greater or or changed in a simple iron-cored transformer,
smaller value. It has a primary coil and a secondary a voltage is induced in a neighbouring coil.
coil consisting of insulation-coated wires wound on The effect, called mutual induction, is an example
a complete soft iron core, either one on top of the of electromagnetic induction and can be shown
other (Figure 4.5.30a) or on separate limbs of the with the arrangement of Figure 4.5.31. Coil A is the
core (Figure 4.5.30b). primary and coil B the secondary.
a to 6 V d.c.
soft iron

rheostat sensitive
centre-zero
meter

coil A coil B
(600 turns) (600 turns)
tapping key

primary secondary ▲ Figure 4.5.31 A changing current in a primary coil (A)

induces a current in a secondary coil (B).
b
soft iron Switching on the current in the primary sets up a
magnetic field and as its field lines grow outwards
from the primary, they cut the secondary. A p.d. is
induced in the secondary until the current in the
primary reaches its steady value. When the current
is switched off in the primary, the magnetic field
dies away and we can imagine the field lines cutting
the secondary as they collapse, again inducing a
p.d. in it. Changing the primary current by quickly
altering the rheostat has the same effect.
The induced p.d. is increased by having a soft iron
rod in the coils or, better still, by using coils wound
primary secondary
on a complete iron ring. More field lines then cut the
▲ Figure 4.5.30 Primary and secondary coils of a secondary due to the magnetisation of the iron.
transformer

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 4.5 Electromagnetic effects

Practical work
Transformer equation
An alternating voltage applied to the primary
induces an alternating voltage in the secondary.
Mutual induction with a.c. The value of the secondary voltage can be shown,
An a.c. is changing all the time and if it flows for a transformer in which all the field lines cut the
in a primary coil, an alternating voltage and secondary, to be given by
current are induced in a secondary coil. primary voltage primary turns
=
Connect the circuit of Figure 4.5.32. All wires secondary voltage secondary turns
used should be insulated. The 1 V high current
In symbols
power unit supplies a.c. to the primary and the
lamp detects the secondary current. Insulated VP NP
wires should be used for the primary and =
VS NS
secondary coils.
Find the effect on the brightness of the lamp of A step-up transformer has more turns on the
secondary than the primary and VS is greater than
(i) pulling the C-cores apart slightly VP (Figure 4.5.33a). For example, if the secondary
(ii) increasing the secondary turns to 15 has twice as many turns as the primary, VS is about
(iii) decreasing the secondary turns to 5. twice VP. In a step-down transformer there are fewer
high current
turns on the secondary than the primary and VS is
iron C-cores
power unit less than VP (Figure 4.5.33b).
a b

lamp (2.5 V 0.3 A)

VP VS VP VS

1 V a.c. ▲ Figure 4.5.33 Symbols for a transformer:

a step-up (VS > VP); b step-down (VP > VS)

spare
wire Test yourself
primary secondary
17 The main function of a step-down transformer
(10 turns) (10 turns) is to
A decrease current
▲ Figure 4.5.32 B decrease voltage
C change a.c. to d.c.
5 In the circuit of Figure 4.5.32, if a d.c. supply D change d.c. to a.c.
were used instead of an a.c. supply, would 18 A transformer has 1000 turns on the primary coil.
The voltage applied to the primary coil is 230  V a.c.
you expect the lamp to light? Explain your
How many turns are on the secondary coil if the
answer. output voltage is 46  V a.c.?
6 In the circuit of Figure 4.5.33 would you A 20
expect the brightness of the lamp to C 2000
increase or decrease if you lowered the B 200
voltage to the primary coil? D 4000

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 4.5.6 The transformer

Going further Worked example

Energy losses in a transformer A transformer steps down the mains supply from 230 V to
10 V to operate an answering machine.
If the p.d. is stepped up in a transformer, the current
is stepped down in proportion. This must be so, if a What is the turns ratio, N P , of the transformer windings?
we assume that all the energy transferred by the NS
current to the primary appears in the secondary, i.e. primary voltage, VP = 230 V
that energy is conserved and the transformer is 100%
secondary voltage, VS = 10 V
efficient or ‘ideal’ (many approach this efficiency).
Then N V 230 V 23
turns ratio = P = P = =
power in primary = power in secondary N S VS 10 V 1
b How many turns are on the primary if the secondary has
IPVP = ISVS 100 turns?
where IP and IS are the primary and secondary currents, secondary turns, NS = 100
respectively. From a,
I V N P 23
∴ S = P =
I P VS NS 1
So, for the ideal transformer, if the p.d. is doubled the ∴ NP = 23 × NS = 23 × 100
current is halved. In practice, it is more than halved, = 2300 turns
because of small energy losses in the transformer
arising from the following causes. Now put this into practice
1 A transformer steps down the mains supply from 240 V to
Resistance of windings 12 V to operate a doorbell.
The windings of copper wire have some resistance N
a What is the turns ratio P of the transformer
and heat is produced by the current in them. Large NS
windings?
transformers like those in Figure 4.5.34 have to be
b How many turns are on the primary if the secondary
oil-cooled to prevent overheating.
has 80 turns?
2 A transformer steps up an a.c. voltage of 240 V to 960 V.
a Calculate the turns ratio of the transformer windings.
b How many turns are on the secondary if the primary
has 500 turns?

▲ Figure 4.5.34 Step-up transformers at a power

station

Eddy currents
The iron core is in the changing magnetic field of
the primary and currents, called eddy currents, are
induced in it which cause heating. These are reduced
by using a laminated core made of sheets, insulated
from one another to have a high resistance.

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 4.5 Electromagnetic effects

Transmission of electrical power Power cables have resistance and so the electric
current causes heating of the cable during the
Grid system transmission of electricity from the power station
to the user. In order to reduce energy losses, the
The National Grid is a network of cables, mostly
current in the cables should be kept low.
supported on pylons, that connects all the power
Higher voltages are used in the transmission of
stations in a country to consumers. In the largest
electric power so that smaller currents can be used
modern stations, electricity is generated at
to transfer the energy. Advantages of high-voltage
25 000 V (25 kilovolts = 25 kV) and stepped up in a
transmission of electricity include:
transformer to a higher p.d. to be sent over long
(i) reducing the amount of energy lost as thermal
distances. Later, the p.d. is reduced by substation
energy in the transmission cables
transformers for distribution to local users
(ii) allowing wires with small cross-sectional areas to
(Figure 4.5.35).
be used; these are cheaper and easier to handle
At the National Control Centre, engineers
than the thicker wires required to carry large
direct the flow of electricity and re-route it when
currents.
breakdown occurs. This makes the supply more
reliable and cuts costs by enabling smaller, less High p.d.s require good insulation but are readily
efficient stations to be shut down at off-peak produced by a.c. generators.
periods.
Key definition
Advantages of high-voltage transmission Advantages of high-voltage transmission of electricity
The efficiency with which transformers step (i) lower power loss in transmission cables
alternating p.d.s up and down accounts for the use (ii) lower currents in cables so thinner/cheaper cables
can be used
of a.c. rather than d.c. in power transmission.

275 kV or 400 kV

132 kV

25 kV

power station transformer Supergrid transformer grid

towns
heavy
light industry
farms villages industry

415 V or 230 V 11 kV 33 kV

transformer transformer transformer

▲ Figure 4.5.35 The National Grid transmission system in Britain

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 Exam-style questions

Revision checklist
After studying Topic 4.5 you should know and After studying Topic 4.5 you should be able to:
understand: ✔ describe experiments to show electromagnetic
✔ Faraday’s explanation of electromagnetic induction induction
✔ the right-hand screw and right-hand grip rules ✔ predict the direction of induced e.m.f.s and
for relating current direction and magnetic field currents and describe and explain the operation of
direction a simple a.c. generator
✔ the action and applications of a relay and a ✔ draw sketches to identify the pattern of magnetic
loudspeaker field lines arising from currents in straight wires
✔ that a rectangular current-carrying coil and solenoids
experiences a turning effect in a magnetic field ✔ identify regions of different magnetic field strength
and that the effect is increased by increasing the around a solenoid and straight wire and describe
number of turns on the coil, the current in the coil the effect on their magnetic fields of changing the
or the strength of the magnetic field magnitude and direction of the current
✔ how to use Fleming’s left-hand rule for relating ✔ describe an experiment that demonstrates a force
directions of force, field and current acts on a current-carrying conductor in a magnetic
✔ the terms primary, secondary, step-up and step- field, and recall the factors which influence the
down in relation to a transformer size and direction of the force
✔ the use of transformers in the high voltage ✔ describe how the magnetic field patterns due to
transmission of electrical power the current in two parallel wires causes the wires
✔ the reasons why greater voltage a.c. is preferred to be attracted or repelled
✔ explain the action of a simple d.c. electric
motor
✔ describe the construction of a transformer and
use the transformer equation VS/VP = NS/NP
✔ explain the action of a transformer.

Exam-style questions
1 a Describe an experiment to demonstrate
Y
electromagnetic induction. [4] G N
b State the factors affecting the magnitude S
of an induced e.m.f. [3]
[Total: 7] X

2 a Describe the deflections observed on the

sensitive, centre-zero meter G (Figure 4.5.36) ▲ Figure 4.5.36
when the copper rod XY is connected to its [Total: 6]
terminals and is made to vibrate up and down
3 A simple a.c. generator is shown in Figure 4.5.37.
(as shown by the arrows), between the poles
a Identify A and B and describe their purpose.[3]
of a U-shaped magnet, at right angles to the
b Describe changes that could be made to
magnetic field. [2]
increase the e.m.f. generated. [3]
b Explain the behaviour of the meter
c Sketch a graph of e.m.f. against time for
in part a.  [4]
the generator and relate the position of
the generator coil to the peaks, troughs
and zeros of the e.m.f. [4]

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 4.5 Electromagnetic effects

b A current-carrying coil experiences a turning

effect in a magnetic field. State the effect
N
axis of on the magnitude of the turning effect of:
rotation i increasing the current in the coil [1]
ii reducing the number of turns on
A
the coil [1]
iii increasing the strength of the magnetic
S field.[1]
[Total: 8]
B
8 An electric motor is used to raise a weight
▲ Figure 4.5.37 attached to a string. Select which of the
[Total: 10] following is used to transfer energy in the
4 a Sketch the magnetic field lines (including process.
their direction) around a current-carrying A Mechanical working
solenoid.[4] B Heating
b What happens if the direction of the C Electrical working
current in the wire is reversed? [1] D Electromagnetic waves
[Total: 5] [Total: 1]
5 Part of the electrical system of a car is shown 9 a Draw a labelled diagram of the essential
in Figure 4.5.38. Explain why components of a simple d.c. motor. [3]
a connections are made to the car body [2] b Explain how continuous rotation is
b there are two circuits in parallel with produced in a d.c. motor and show how
the battery[2] the direction of rotation is related to
c wire A is thicker than wire B [1] the direction of the current. [4]
d a relay is used. [2] c State what would happen to the
direction of rotation of the motor you
contacts
A have described if
i the current direction was reversed [1]
B starter coil
switch
ii the magnetic field was reversed [1]
starter iii both current and field were
motor
reversed simultaneously.[1]
relay
[Total: 10]
10 a Describe the construction of a simple
transformer with a soft iron core. [4]
connections b Explain the function of a step-up
to car body
transformer.[2]
▲ Figure 4.5.38
c A step-up transformer is used to obtain a
[Total: 7] p.d. of 720 V from a mains supply of 240 V.
6 Explain how a loudspeaker works. Calculate the number of turns that will
[Total: 6] be needed on the secondary if there are
7 a Describe an experiment to show that a 120 turns on the primary. [4]
force acts on a current-carrying conductor [Total: 10]
in a magnetic field, including the effect
of reversing the current or the direction of
the magnetic field. [5]

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 Exam-style questions

11 a Explain what is meant by the following terms b What changes would you expect if a
in connection with a transformer: bundle of soft iron wires was placed through
i primary the centre of the coils? Give a reason for your
ii secondary answer. [3]
iii step-up c What would happen if more turns of wire
iv step-down. [4] were wound on the coil B? [1]
b Calculate the number of turns on the
secondary of a step-down transformer A B
which would enable a 12 V lamp to be used
with a 230 V a.c. mains power, if there are
460 turns on the primary. [4]
[Total: 8]
12 Two coils of wire, A and B, are placed near one G
another (Figure 4.5.39). Coil A is connected to ▲ Figure 4.5.39
a switch and battery. Coil B is connected to a
centre-reading meter, G. [Total: 11]
a If the switch connected to coil A were
13 a Explain the use of transformers in the
closed for a few seconds and then opened,
transmission of electrical power. [3]
the meter connected to coil B would be
b Give two reasons for the use of high
affected. Explain and describe,
voltages in the transmission of
step by step, what would actually
electricity.[2]
happen.[7]
[Total: 5]

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 4.6 Uses of an oscilloscope
FOCUS POINTS
★ Explain how an oscilloscope can be used to display waveforms and measure p.d. and intervals of time.

The discovery of the electron led to great technological advances in electronics. Electrons moving
at high speed in a vacuum are called cathode rays, and twentieth century televisions and computer
screens all contained a cathode ray tube. The cathode ray oscilloscope (CRO) is an important
scientific instrument that works in a similar way. The oscilloscope allows rapidly changing electrical
signals to be analysed by plotting a voltage–time graph on a screen. When a microphone is used
to convert a sound wave into an electrical signal, the waveform can be viewed directly on the
oscilloscope screen. An oscilloscope can be used as a voltmeter, to measure varying p.d.s, and also
to measure intervals of time, enabling the frequency of a signal to be found.

Oscilloscope settings measured is connected to the Y-input terminal of the

A small cathode ray oscilloscope (CRO) is shown in oscilloscope. The Y-gain control amplifies the input
Figure 4.6.1a. The circuit symbol for an oscilloscope p.d. to make it large enough to appear a suitable
is shown in Figure 4.6.1b. size on the screen. The Y-gain setting in volts per
division or V/div allows the size of the input p.d. to
a
be measured.
The timebase controls how fast the bright spot
(the input signal) moves from left to right. The
distance moved by the spot is directly proportional
to time and so the horizontal axis becomes a time
axis. The timebase setting in milliseconds per
division or ms/div allows time intervals in a varying
p.d. to be measured.
When preparing the oscilloscope for use, set the
X-shift and Y-shift controls (which allow the spot to
be moved ‘manually’ over the screen in the X and Y
b directions, respectively) to their mid-positions.
The timebase and Y-gain controls can then be
adjusted to suit the input.
▲ Figure 4.6.1 a Oscilloscope; b circuit symbol for an
oscilloscope
Key definitions
Y-gain controls the amplification of the input p.d.
The vertical axis on an oscilloscope screen provides
a measurement of p.d. and the horizontal axis is Timebase controls the time interval displayed on the
a measure of time. The signal to be displayed or horizontal axis of the screen

250
 Uses of an oscilloscope

With the timebase switched on, Figure 4.6.2

shows the display on an oscilloscope screen (called Uses of an oscilloscope
traces) for three different input p.d.s. In Figure
4.6.2a, the p.d. applied to the Y-input is zero, and Measuring p.d.s
there is a straight line across the centre of the An oscilloscope can be used as a d.c./a.c. voltmeter
screen. In Figure 4.6.2b, the Y-input is a constant by connecting the p.d. to be measured to the
d.c. signal and the trace is a horizontal line Y-input terminals; the displacement of the trace in
displaced upwards by an amount determined by the the vertical direction is proportional to the p.d.
Y-gain setting. In Figure 4.6.2c, the Y-input is an For example, if the Y-amp gain control is set on
a.c. signal, so the p.d. is alternately positive and 1 V/div, a vertical displacement of one whole division
negative. on the screen would be given by a 1 V d.c. input.
A vertical line one division long (timebase off)
a b c
would be produced by an a.c. input of 1 V peak to
trough (i.e. amplitude 0.5 V).
The vertical displacement can be measured with
the timebase either on or off. To find the value of a
d.c voltage, count the number of whole divisions the
▲ Figure 4.6.2 Oscilloscope traces with timebase on trace (horizontal line or spot) is displaced vertically
and multiply that number by the V/div setting.
When the timebase is switched off, the trace is For an a.c. input, count the number of divisions
concentrated to a spot that does not move from occupied by the vertical line (timebase off) or
left to right. Figure 4.6.3 shows how the display vertical peak-to-trough distance (timebase on).
appears for different inputs. In Figure 4.6.3a, The amplitude of the a.c. voltage can then be found
the input p.d. is zero and the spot remains at by multiplying the V/div setting by half the number
the centre of the screen. In Figure 4.6.3b, the of vertical divisions counted.
input p.d. is a constant d.c. signal and the spot is
displaced upwards.In Figure 4.6.3c, the Y-input is Displaying waveforms
an a.c. signal, so the p.d. is alternately positive When the timebase is on, the oscilloscope acts
and negative and the trace appears as a continuous as a ‘graph-plotter’ to show the waveform, i.e.
vertical line whose length increases when the the variation with time, of the p.d. applied to
Y-gain is increased. its Y-input. The displays in Figure 4.6.4 are of
alternating p.d.s with sine waveforms. For the trace
a b c
in Figure 4.6.4a, the timebase frequency equals that
of the input and one complete wave is obtained.
For the trace in Figure 4.6.4b, it is half that of the
input and two waves are formed. If the traces are
obtained with the Y-amp gain control on, say, 0.5 V/
▲ Figure 4.6.3 Oscilloscope traces with timebase off div, the vertical peak-to-trough voltage of the
a.c. = 3.0 divs × 0.5 V/div, that is, 1.5 V, and the
A concentrated spot can damage the screen so the amplitude of the signal = 0.75 V.
timebase should be set to produce an extended line Sound waveforms can be displayed if a
when possible. microphone is connected to the Y-input terminals
(see Topic 3.4).

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 4.6 Uses of an oscilloscope

a b
Test yourself
1 An oscilloscope is used to measure a d.c. voltage.
Calculate the value of the voltage if the trace on
the oscilloscope is displaced (from zero)
a by 3.0 divisions when the Y-gain setting is
▲ Figure 4.6.4 Alternating p.d. waveforms on the CRO 0.5 V/div
b by 4.2 divisions when the Y-gain setting is
2.0 V/div.
Measuring time intervals and 2 An oscilloscope is used to display an a.c. signal.
frequency Calculate the amplitude of the a.c. signal if the
length of the vertical line obtained on the display
These can be measured if the oscilloscope has a when the timebase is turned off is 8.6 divisions
calibrated timebase. For example, when the timebase and the Y-gain setting is 1.0 V/div.
is set on 10 ms/div, the spot takes 10 milliseconds 3 One wavelength of an input signal occupies
to move one division horizontally across the screen. 4.0 horizontal divisions on the screen of an
oscilloscope. If the timebase setting is 1 ms/div,
If this is the timebase setting for the waveform calculate the frequency of the signal.
in Figure 4.6.4b then, since one complete wave
occupies two horizontal divisions, we can say

time for one complete wave = 2.0 divs × 10 ms/div Revision checklist
= 20 ms After studying Topic 4.6 you should be able to:
✔ describe how an oscilloscope can be used to
=
20 = 1 s display waveforms
1000 50 ✔ understand the function of the Y-gain and
∴ number of complete waves per second = 50 timebase controls on an oscilloscope when
∴ frequency of a.c. applied to Y-input = 50 Hz measuring p.d. and short time intervals.

Exam-style questions
1 a Describe the function on an oscilloscope of c An oscilloscope is used to measure a d.c.
i the timebase control voltage. Calculate the value of the voltage
ii the Y-gain control. if the trace on the oscilloscope is displaced
[4] (from zero) by 2.8 divisions when the Y-gain is
b You are asked to use an oscilloscope to set at 0.1 V/div.
display a waveform. If you want to make two [2]
wavelengths occupy the screen rather than one [Total: 7]
wavelength, which setting would you change
on the oscilloscope?
[1]

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