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SINGAPORE-CAMBRIDGE GCE O-LEVEL
PHYSICS OUTLINE
SYLLABUS 5059
UPDATED 20 JAN 2014
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Overview
Themes
Chapters Count
I. Measurement
1
1
II. Newtonian Mechanics
2-7
6
III. Thermal Physics
8-11
4
IV. Waves
12-15
4
V. Electricity & Magnetism
16-22
7
1. Physical Quantities, Units and Measurement ............................................................................ 12
2. Kinematics ................................................................................................................................ 17
3. Dynamics .................................................................................................................................. 20
4. Mass, Weight and Density......................................................................................................... 23
5. Turning Effect of Forces ............................................................................................................ 25
6. Pressure ................................................................................................................................... 27
7. Energy, Work and Power .......................................................................................................... 29
8. Kinetic Model of Matter ............................................................................................................. 32
9. Transfer of Thermal Energy ...................................................................................................... 34
10. Temperature ........................................................................................................................... 36
11. Thermal Properties of Matter................................................................................................... 37
12. General Wave Properties ........................................................................................................ 41
13. Light ........................................................................................................................................ 44
14. Electromagnetic Spectrum ...................................................................................................... 49
15. Sound ..................................................................................................................................... 51
16. Static Electricity....................................................................................................................... 54
17. Current of Electricity ................................................................................................................ 58
18. D.C. Circuits ............................................................................................................................ 63
19. Practical Electricity .................................................................................................................. 65
20. Magnetism .............................................................................................................................. 69
21. Electromagnetism ................................................................................................................... 71
22. Electromagnetic Induction ....................................................................................................... 77
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Contents
1. Physical Quantities, Units and Measurement ....................................................................... 12
(a) show understanding that all physical quantities consist of a numerical magnitude and a unit12
(b) recall the following base quantities and their units: mass (kg), length (m), time (s), current (A),
temperature (K), amount of substance (mol) ............................................................................. 12
(c) use the following prefixes and their symbols to indicate decimal sub-multiples and multiples of
the SI units: nano (n), micro (μ), milli (m), centi (c), deci (d), kilo (k), mega (M), giga (G) ........... 12
(d) show an understanding of the orders of magnitude of the sizes of common objects ranging
from a typical atom to the Earth ................................................................................................. 12
(e) state what is meant by scalar and vector quantities and give common examples of each .... 13
(f) add two vectors to determine a resultant by a graphical method ........................................... 13
(g) describe how to measure a variety of lengths with appropriate accuracy by means of tapes,
rules, micrometers and calipers, using a vernier scale as necessary ......................................... 14
(h) describe how to measure a short interval of time including the period of a simple pendulum
with appropriate accuracy using stopwatches or appropriate instruments.................................. 15
2. Kinematics............................................................................................................................... 17
(a) state what is meant by speed and velocity ........................................................................... 17
(b) calculate average speed using distance travelled / time taken ............................................. 17
(c) state what is meant by uniform acceleration and calculate the value of an acceleration using
change in velocity / time taken................................................................................................... 17
(d) interpret given examples of non-uniform acceleration .......................................................... 18
(e) plot and interpret a displacement-time graph and a velocity-time graph ............................... 18
(f) deduce from the shape of a displacement-time graph when a body is: (i) at rest (ii) moving
with uniform velocity (iii) moving with non-uniform velocity ........................................................ 18
(g) deduce from the shape of a velocity-time graph when a body is: (i) at rest (ii) moving with
uniform velocity (iii) moving with uniform acceleration (iv) moving with non-uniform acceleration
.................................................................................................................................................. 18
(h) calculate the area under a velocity-time graph to determine the displacement travelled for
motion with uniform velocity or uniform acceleration .................................................................. 19
(i) state that the acceleration of free fall for a body near to the Earth is constant and is
approximately 10 m/s2 ............................................................................................................... 19
(j) describe the motion of bodies with constant weight falling with or without air resistance,
including reference to terminal velocity ...................................................................................... 19
3. Dynamics ................................................................................................................................. 20
(a) apply Newton's Laws to: (i) describe the effect of balanced and unbalanced forces on a body
(ii) describe the ways in which a force may change the motion of a body (iii) identify actionreaction pairs acting on two interacting bodies (stating of Newton's Laws is not required) ......... 20
(b) identify forces acting on an object and draw free body diagram(s) representing the forces
acting on the object (for cases involving forces acting in at most 2 dimensions) ........................ 21
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(c) solve problems for a static point mass under the action of 3 forces for 2-dimensional cases (a
graphical method would suffice) ................................................................................................ 21
(d) recall and apply the relationship resultant force = mass × acceleration to new situations or to
solve related problems .............................................................................................................. 22
(e) explain the effects of friction on the motion of a body ........................................................... 22
4. Mass, Weight and Density ...................................................................................................... 23
(a) state that mass is a measure of the amount of substance in a body (b) state that mass of a
body resists a change in the state of rest or motion of the body (inertia).................................... 23
(c) state that a gravitational field is a region in which a mass experiences a force due to
gravitational attraction ............................................................................................................... 23
(d) define gravitational field strength, g, as gravitational force per unit mass ............................. 23
(e) recall and apply the relationship weight = mass × gravitational field strength to new situations
or to solve related problems ...................................................................................................... 23
(f) distinguish between mass and weight ................................................................................... 24
(g) recall and apply the relationship density = mass / volume to new situations or to solve related
problems ................................................................................................................................... 24
5. Turning Effect of Forces ......................................................................................................... 25
(a) describe the moment of a force in terms of its turning effect and relate this to everyday
examples (b) recall and apply the relationship moment of a force (or torque) = force ×
perpendicular distance from the pivot to new situations or to solve related problems ................ 25
(c) state the principle of moments for a body in equilibrium (d) apply the principle of moments to
new situations or to solve related problems ............................................................................... 25
(e) show understanding that the weight of a body may be taken as acting at a single point known
as its centre of gravity................................................................................................................ 25
(f) describe qualitatively the effect of the position of the centre of gravity on the stability of objects
.................................................................................................................................................. 26
6. Pressure .................................................................................................................................. 27
(a) define the term pressure in terms of force and area (b) recall and apply the relationship
pressure = force / area to new situations or to solve related problems....................................... 27
(c) describe and explain the transmission of pressure in hydraulic systems with particular
reference to the hydraulic press ................................................................................................ 27
(d) recall and apply the relationship pressure due to a liquid column = height of column × density
of the liquid × gravitational field strength to new situations or to solve related problems ............ 28
(e) describe how the height of a liquid column may be used to measure the atmospheric
pressure .................................................................................................................................... 28
(f) describe the use of a manometer in the measurement of pressure difference ....................... 28
7. Energy, Work and Power ........................................................................................................ 29
(a) show understanding that kinetic energy, potential energy (chemical, gravitational, elastic),
light energy, thermal energy, electrical energy and nuclear energy are examples of different
forms of energy ......................................................................................................................... 29
(b) state the principle of the conservation of energy and apply the principle to new situations or to
solve related problems .............................................................................................................. 29
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(c) calculate the efficiency of an energy conversion using the formula efficiency = energy
converted to useful output / total energy input ........................................................................... 29
(d) state that kinetic energy Ek = ½ mv2 and gravitational potential energy Ep = mgh (for potential
energy changes near the Earth’s surface) (e) apply the relationships for kinetic energy and
potential energy to new situations or to solve related problems ................................................. 30
(f) recall and apply the relationship work done = force × distance moved in the direction of the
force to new situations or to solve related problems .................................................................. 30
(g) recall and apply the relationship power = work done / time taken to new situations or to solve
related problems........................................................................................................................ 30
8. Kinetic Model of Matter ........................................................................................................... 32
(a) compare the properties of solids, liquids and gases ............................................................. 32
(b) describe qualitatively the molecular structure of solids, liquids and gases, relating their
properties to the forces and distances between molecules and to the motion of the molecules . 32
(c) infer from Brownian motion experiment the evidence for the movement of molecules .......... 32
(d) describe the relationship between the motion of molecules and temperature ....................... 33
(e) explain the pressure of a gas in terms of the motion of its molecules ................................... 33
(f) recall and explain the following relationships using the kinetic model (stating of the
corresponding gas laws is not required): (i) a change in pressure of a fixed mass of gas at
constant volume is caused by a change in temperature of the gas (ii) a change in volume
occupied by a fixed mass of gas at constant pressure is caused by a change in temperature of
the gas (iii) a change in pressure of a fixed mass of gas at constant temperature is caused by a
change in volume of the gas ...................................................................................................... 33
(g) use the relationships in (f) in related situations and to solve problems (a qualitative treatment
would suffice) ............................................................................................................................ 33
9. Transfer of Thermal Energy ................................................................................................... 34
(a) show understanding that thermal energy is transferred from a region of higher temperature to
a region of lower temperature .................................................................................................... 34
(b) describe, in molecular terms, how energy transfer occurs in solids ...................................... 34
(c) describe, in terms of density changes, convection in fluids ................................................... 34
(d) explain that energy transfer of a body by radiation does not require a material medium and
the rate of energy transfer is affected by: (i) colour and texture of the surface (ii) surface
temperature (iii) surface area..................................................................................................... 34
(e) apply the concept of thermal energy transfer to everyday applications ................................. 35
10. Temperature .......................................................................................................................... 36
(a) explain how a physical property which varies with temperature, such as volume of liquid
column, resistance of metal wire and electromotive force (e.m.f.) produced by junctions formed
with wires of two different metals, may be used to define temperature scales ........................... 36
(b) describe the process of calibration of a liquid-in-glass thermometer, including the need for
fixed points such as the ice point and steam point ..................................................................... 36
11. Thermal Properties of Matter ............................................................................................... 37
(a) describe a rise in temperature of a body in terms of an increase in its internal energy (random
thermal energy) ......................................................................................................................... 37
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(b) define the terms heat capacity and specific heat capacity .................................................... 37
(c) recall and apply the relationship thermal energy = mass × specific heat capacity × change in
temperature to new situations or to solve related problems ....................................................... 37
(d) describe melting/solidification and boiling/condensation as processes of energy transfer
without a change in temperature ............................................................................................... 38
(e) explain the difference between boiling and evaporation ....................................................... 38
(f) define the terms latent heat and specific latent heat .............................................................. 38
(g) recall and apply the relationship thermal energy = mass × specific latent heat to new
situations or to solve related problems ...................................................................................... 38
(h) explain latent heat in terms of molecular behaviour .............................................................. 39
(i) sketch and interpret a cooling curve ...................................................................................... 39
12. General Wave Properties ...................................................................................................... 41
(a) describe what is meant by wave motion as illustrated by vibrations in ropes and springs and
by waves in a ripple tank ........................................................................................................... 41
(b) show understanding that waves transfer energy without transferring matter......................... 42
(c) define speed, frequency, wavelength, period and amplitude ................................................ 42
(d) state what is meant by the term wavefront ........................................................................... 43
(e) recall and apply the relationship velocity = frequency × wavelength to new situations or to
solve related problems .............................................................................................................. 43
(f) compare transverse and longitudinal waves and give suitable examples of each .................. 43
13. Light ....................................................................................................................................... 44
(a) recall and use the terms for reflection, including normal, angle of incidence and angle of
reflection.................................................................................................................................... 44
(b) state that, for reflection, the angle of incidence is equal to the angle of reflection and use this
principle in constructions, measurements and calculations ........................................................ 44
(c) recall and use the terms for refraction, including normal, angle of incidence and angle of
refraction ................................................................................................................................... 45
(d) recall and apply the relationship sin i / sin r = constant to new situations or to solve related
problems (e) define refractive index of a medium in terms of the ratio of speed of light in vacuum
and in the medium ..................................................................................................................... 45
(f) explain the terms critical angle and total internal reflection .................................................... 46
(g) identify the main ideas in total internal reflection and apply them to the use of optical fibres in
telecommunication and state the advantages of their use ......................................................... 46
(h) describe the action of a thin lens (both converging and diverging) on a beam of light .......... 47
(i) define the term focal length for a converging lens ................................................................. 47
(j) draw ray diagrams to illustrate the formation of real and virtual images of an object by a thin
converging lens ......................................................................................................................... 48
14. Electromagnetic Spectrum ................................................................................................... 49
(a) state that all electromagnetic waves are transverse waves that travel with the same speed in
vacuum and state the magnitude of this speed .......................................................................... 49
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(b) describe the main components of the electromagnetic spectrum (c) state examples of the use
of the following components: (i) radiowaves (e.g. radio and television communication) (ii)
microwaves (e.g. microwave oven and satellite television) (iii) infra-red (e.g. infra-red remote
controllers and intruder alarms) (iv) light (e.g. optical fibres for medical uses and
telecommunications) (v) ultra-violet (e.g. sunbeds and sterilisation) (vi) X-rays (e.g. radiological
and engineering applications) (vii) gamma rays (e.g. medical treatment)................................... 50
(d) describe the effects of absorbing electromagnetic waves, e.g. heating, ionisation and damage
to living cells and tissue ............................................................................................................. 50
15. Sound..................................................................................................................................... 51
(a) describe the production of sound by vibrating sources (b) describe the longitudinal nature of
sound waves in terms of the processes of compression and rarefaction ................................... 51
(c) explain that a medium is required in order to transmit sound waves and the speed of sound
differs in air, liquids and solids ................................................................................................... 51
(d) describe a direct method for the determination of the speed of sound in air and make the
necessary calculation ................................................................................................................ 51
(e) relate loudness of a sound wave to its amplitude and pitch to its frequency ......................... 52
(f) describe how the reflection of sound may produce an echo, and how this may be used for
measuring distances ................................................................................................................. 52
(g) define ultrasound and describe one use of ultrasound, e.g. quality control and pre-natal
scanning .................................................................................................................................... 52
16. Static Electricity .................................................................................................................... 54
(a) state that there are positive and negative charges and that charge is measured in coulombs
.................................................................................................................................................. 54
(b) state that unlike charges attract and like charges repel ........................................................ 54
(c) describe an electric field as a region in which an electric charge experiences a force (d) draw
the electric field of an isolated point charge and recall that the direction of the field lines gives the
direction of the force acting on a positive test charge ................................................................ 54
(e) draw the electric field pattern between two isolated point charges ....................................... 55
(f) show understanding that electrostatic charging by rubbing involves a transfer of electrons... 55
(g) describe experiments to show electrostatic charging by induction ........................................ 56
(h) describe examples where electrostatic charging may be a potential hazard ......................... 56
(i) describe the use of electrostatic charging in a photocopier, and apply the use of electrostatic
charging to new situations ......................................................................................................... 57
17. Current of Electricity............................................................................................................. 58
(a) state that current is a rate of flow of charge and that it is measured in amperes ................... 58
(b) distinguish between conventional current and electron flow ................................................. 58
(c) recall and apply the relationship charge = current × time to new situations or to solve related
problems ................................................................................................................................... 58
(d) define electromotive force (e.m.f.) as the work done by a source in driving unit charge around
a complete circuit ...................................................................................................................... 59
(e) calculate the total e.m.f. where several sources are arranged in series ................................ 59
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(f) state that the e.m.f. of a source and the potential difference (p.d.) across a circuit component
is measured in volts (g) define the p.d. across a component in a circuit as the work done to drive
unit charge through the component ........................................................................................... 59
(h) state the definition that resistance = p.d. / current (i) apply the relationship R = V/I to new
situations or to solve related problems ...................................................................................... 59
(j) describe an experiment to determine the resistance of a metallic conductor using a voltmeter
and an ammeter, and make the necessary calculations ............................................................ 60
(k) recall and apply the formulae for the effective resistance of a number of resistors in series
and in parallel to new situations or to solve related problems .................................................... 60
(l) recall and apply the relationship of the proportionality between resistance and the length and
cross-sectional area of a wire to new situations or to solve related problems ............................ 61
(m) state Ohm’s Law ................................................................................................................. 61
(n) describe the effect of temperature increase on the resistance of a metallic conductor ......... 61
(o) sketch and interpret the I/V characteristic graphs for a metallic conductor at constant
temperature, for a filament lamp and for a semiconductor diode ............................................... 62
18. D.C. Circuits .......................................................................................................................... 63
(a) draw circuit diagrams with power sources (cell, battery, d.c. supply or a.c. supply), switches,
lamps, resistors (fixed and variable), variable potential divider (potentiometer), fuses, ammeters
and voltmeters, bells, light-dependent resistors, thermistors and light-emitting diodes .............. 63
(b) state that the current at every point in a series circuit is the same and apply the principle to
new situations or to solve related problems (c) state that the sum of the potential differences in a
series circuit is equal to the potential difference across the whole circuit and apply the principle
to new situations or to solve related problems (d) state that the current from the source is the
sum of the currents in the separate branches of a parallel circuit and apply the principle to new
situations or to solve related problems (e) state that the potential difference across the separate
branches of a parallel circuit is the same and apply the principle to new situations or to solve
related problems........................................................................................................................ 64
(f) recall and apply the relevant relationships, including R = V/I and those for current, potential
differences and resistors in series and in parallel circuits, in calculations involving a whole circuit
.................................................................................................................................................. 64
(g) describe the action of a variable potential divider (potentiometer) ........................................ 64
(h) describe the action of thermistors and light-dependent resistors and explain their use as input
transducers in potential dividers (i) solve simple circuit problems involving thermistors and lightdependent resistors ................................................................................................................... 64
19. Practical Electricity ............................................................................................................... 65
(a) describe the use of the heating effect of electricity in appliances such as electric kettles,
ovens and heaters ..................................................................................................................... 65
(b) recall and apply the relationships P = VI and E = VIt to new situations or to solve related
problems ................................................................................................................................... 65
(c) calculate the cost of using electrical appliances where the energy unit is the kW h .............. 65
(d) compare the use of non-renewable and renewable energy sources such as fossil fuels,
nuclear energy, solar energy, wind energy and hydroelectric generation to generate electricity in
terms of energy conversion efficiency, cost per kW h produced and environmental impact ....... 66
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(e) state the hazards of using electricity in the following situations: (i) damaged insulation (ii)
overheating of cables (iii) damp conditions ................................................................................ 67
(f) explain the use of fuses and circuit breakers in electrical circuits and of fuse ratings ............ 67
(g) explain the need for earthing metal cases and for double insulation ..................................... 67
(h) state the meaning of the terms live, neutral and earth .......................................................... 67
(i) describe the wiring in a mains plug........................................................................................ 68
(j) explain why switches, fuses, and circuit breakers are wired into the live conductor ............... 68
20. Magnetism ............................................................................................................................. 69
(a) state the properties of magnets ............................................................................................ 69
(b) describe induced magnetism ................................................................................................ 69
(c) describe electrical methods of magnetisation and demagnetisation ..................................... 69
(d) draw the magnetic field pattern around a bar magnet and between the poles of two bar
magnets (e) describe the plotting of magnetic field lines with a compass .................................. 70
(f) distinguish between the properties and uses of temporary magnets (e.g. iron) and permanent
magnets (e.g. steel) ................................................................................................................... 70
21. Electromagnetism ................................................................................................................. 71
(a) draw the pattern of the magnetic field due to currents in straight wires and in solenoids and
state the effect on the magnetic field of changing the magnitude and/or direction of the current 71
(b) describe the application of the magnetic effect of a current in a circuit breaker .................... 72
(c) describe experiments to show the force on a current-carrying conductor, and on a beam of
charged particles, in a magnetic field, including the effect of reversing (i) the current (ii) the
direction of the field ................................................................................................................... 73
(d) deduce the relative directions of force, field and current when any two of these quantities are
at right angles to each other using Fleming’s left-hand rule ....................................................... 74
(e) describe the field patterns between currents in parallel conductors and relate these to the
forces which exist between the conductors (excluding the Earth’s field) .................................... 74
(f) explain how a current-carrying coil in a magnetic field experiences a turning effect and that
the effect is increased by increasing (i) the number of turns on the coil (ii) the current .............. 75
(g) discuss how this turning effect is used in the action of an electric motor .............................. 75
(h) describe the action of a split-ring commutator in a two-pole, single-coil motor and the effect of
winding the coil on to a soft-iron cylinder ................................................................................... 76
22. Electromagnetic Induction ................................................................................................... 77
(a) deduce from Faraday’s experiments on electromagnetic induction or other appropriate
experiments: (i) that a changing magnetic field can induce an e.m.f. in a circuit (ii) that the
direction of the induced e.m.f. opposes the change producing it ................................................ 77
(iii) the factors affecting the magnitude of the induced e.m.f. ..................................................... 78
(b) describe a simple form of a.c. generator (rotating coil or rotating magnet) and the use of slip
rings (where needed) (c) sketch a graph of voltage output against time for a simple a.c.
generator ................................................................................................................................... 79
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(d) describe the use of a cathode-ray oscilloscope (c.r.o.) to display waveforms and to measure
potential differences and short intervals of time (detailed circuits, structure and operation of the
c.r.o. are not required) ............................................................................................................... 80
(e) interpret c.r.o. displays of waveforms, potential differences and time intervals to solve related
problems ................................................................................................................................... 81
(f) describe the structure and principle of operation of a simple iron-cored transformer as used
for voltage transformations ........................................................................................................ 82
(g) recall and apply the equations VP / VS = NP / NS and VPIP = VSIS to new situations or to solve
related problems (for an ideal transformer) ................................................................................ 82
(h) describe the energy loss in cables and deduce the advantages of high voltage transmission
.................................................................................................................................................. 82
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SECTION I: MEASUREMENT
Overview
In order to gain a better understanding of the physical world, scientists use a process of
investigation that follows a general cycle of observation, hypothesis, deduction, test and revision,
sometimes referred to as the scientific method. Galileo Galilei, one of the earliest architects of this
method, believed that the study of science had a strong logical basis that involved precise
definitions of terms and physical quantities, and a mathematical structure to express relationships
between these physical quantities.
In this section, we study a set of base physical quantities and units that can be used to derive all
other physical quantities. These precisely defined quantities and units, with accompanying orderof-ten prefixes (e.g. milli, centi and kilo) can then be used to describe the interactions between
objects in systems that range from celestial objects in space to sub-atomic particles.
Extracted from PHYSICS GCE ORDINARY LEVEL (2014) Syllabus Document
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1. Physical Quantities, Units and Measurement
Content





Physical quantities
SI units
Prefixes
Scalars and vectors
Measurement of length and time
Learning Outcomes
Candidates should be able to:
(a) show understanding that all physical quantities consist of a numerical magnitude and a
unit
Term
Definition
Constituents
Physical quantity
Quantity that can be measured
[no need to remember this definition]
 A numerical magnitude
 A unit
(b) recall the following base quantities and their units: mass (kg), length (m), time (s),
current (A), temperature (K), amount of substance (mol)
Term
Base quantity (Derived quantities, e.g. area, are derived from base quantities, e.g. length)
Type
Mass
Length
Time
Current
Temperature
Amount of substance
SI unit
kilograms
metres
seconds
amperes
Kelvin
mole
Unit symbol
kg
m
s
A
K
mol
(c) use the following prefixes and their symbols to indicate decimal sub-multiples and
multiples of the SI units: nano (n), micro (μ), milli (m), centi (c), deci (d), kilo (k), mega (M),
giga (G)
Magnitude
+ve sign prefix (symbol)
−ve sign prefix (symbol)
Examples (where 1 ≤ y < 10)
×10±1
deca- (da)
deci- (d)
×10±2
hexa- (h)
centi- (c)
×10±3
kilo- (k)
milli- (m)
×10±6
mega- (M)
micro- (µ)
×10±9
giga- (G)
nano- (n)







y kg = y ×103 g
y cm = y ×10−2 m
y cm2 = y ×10−4 m2
y cm3 = y ×10−6 m3
y m = y ×102 cm
y m2 = y ×104 cm2
y m3 = y ×106 cm3
(d) show an understanding of the orders of magnitude of the sizes of common objects
ranging from a typical atom to the Earth
Object
H atom
Chopsticks length
Football field length
Mount Everest’s height
Earth’s radius
Magnitude
110−15 m
210−1 m
1102 m
8.848103 m
6.378106 m
Note: There is no need to remember these magnitudes, an appreciation will do
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(e) state what is meant by scalar and vector quantities and give common examples of each
Term
Definition
Scalar quantity
Physical quantities that have magnitude only
Vector quantity
Physical quantities that possess both magnitude and direction
Examples
Scalar
Vector
Distance
Displacement
Speed
Velocity
Energy
Force
Mass
Weight
(f) add two vectors to determine a resultant by a graphical method
Determination of resultant force
Case 1:
Parallel vectors
Case 2: Non-parallel vectors
Case 2a: Same origin
Case 2b: Tip-to-tail
Step 1: Write down the scale using
1 cm : ? N (scale must
allow diagram drawn to be
more than half of the space
given in question)
Step 2: Draw the 2 forces with
single arrows according to
the scale
Step 3: Finish the parallelogram
with dotted lines using set
square
Step 4: Draw resultant force from
the origin with a double
arrow
Step 5: Measure length of resultant
force
Step 6: Calculate resultant force
Step 1: Write down the scale using
1 cm : ? N (scale must
allow diagram drawn to be
more than half of the space
given in question)
Step 2: Draw the 2 forces with
single arrows according to
the scale
Step 3: Draw resultant force from
the start to end of the 2
forces with a double arrow
Step 4: Measure length of resultant
force
Step 5: Calculate resultant force
Scale: 1 cm : 0.5 N
Scale: 1 cm : 0.5 N
Case
Step 1: Calculate
resultant
force
Steps
3N
Example
5N
Resultant force
= 5N − 3N
= 2N in the forward
direction
5N
7N
3N
5N
4.4 N
40o
20o 76o
3N
40o
18o
20o
Resultant force
= 3.5 ÷ 0.5
= 7 N, acting 18o to the horizontal
13
Resultant force
= 3.5 ÷ 0.5
= 7 N, acting o to the horizontal
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(g) describe how to measure a variety of lengths with appropriate accuracy by means of
tapes, rules, micrometers and calipers, using a vernier scale as necessary
Purpose
Method of measurement
Possible
error
#
Instrument
Precision
1
Tape
10−1 cm
To measure
widths (e.g.
long distances)
Position eye directly above the markings on
the tape when making measurement to avoid
parallax error
Parallax
error
2
Metre rule
10−1 cm
To measure
depths (e.g. of
ponds)
 Measure from a randomly chosen point
instead of the ends to avoid zero error (from
wear and tear)
 Substract the reading at the start of the
object from the reading at the end of the
object
Parallax
error
3
Caliper
10−1 cm
 To measure
circular
objects
 To measure
cylinders
Circular objects
 Use jaws of the external calipers to grip the
widest part of the circular object
 Distance between jaws is measured with a
metre rule
Cylinders
 Invert the jaws to use the internal calipers
 Use jaws of the internal calipers to measure
the inner diameter of the cylinder
 Distance between jaws is measured with a
metre rule
Parallax
error
4
Vernier
caliper
10−2 cm
 To measure
the internal
and external
diameters of
an object
 Consists of a
main scale
and a sliding
vernier scale
 Grip the object using the correct pair of jaws
 Read the main scale directly opposite the
zero mark on the vernier scale (e.g. 2.4 cm)
 Read the vernier mark that coincides with a
marking on the main scale (e.g. +0.03 cm)
 Close the vernier caliper to check for zero
error to be corrected (e.g. +0.02 cm)
 Calculate the final reading by adding the
vernier reading and substracting the zero
error [e.g. 2.4 + (+0.03) − (+0.02) = 2.41 cm]
Zero
error
5
Micrometer
screw
gauge
10−3 cm
To measure the
external
diameter of
small precision
(e.g. wires, ball
bearings)
 Turn the thimble such that the object is
gripped gently
 Turn the ratchet until it starts to click
 Read the main scale reading at the edge of
the thimble (e.g. 6.5 mm)
 Read the thimble scale reading (reading 35
indicates 0.35 mm)
 Close the micrometer screw guage to check
for zero error to be corrected (e.g. +0.02
mm)
 Calculate the final reading by adding the
vernier reading and substracting the zero
error [e.g. 6.5 + (+0.35) − (+0.02) = 6.65 cm]
Zero
error
Note: This is mainly important for practical sessions
14
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(h) describe how to measure a short interval of time including the period of a simple
pendulum with appropriate accuracy using stopwatches or appropriate instruments
Term
Meaning as for a pendulum
Oscillation
Each complete to-and-fro motion of the pendulum bob
Period
Time taken for one complete oscillation
Instrument
Precision
Stopwatch
10−2 s
Method of measurement of
pendulum period
Factors affecting period
of the pendulum
Possible
error
 Measure the time taken for the
pendulum to make 20 oscillations
 Find the period accurately by
dividing the total time by 20
 Length of string affects
the period
 Mass of bob does not
affect the period
Human
reaction time
(about 0.3 to
0.5 s)
Note: This is mainly important for practical sessions
15
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SECTION II: NEWTONIAN MECHANICS
Overview
Mechanics is the branch of physics that deals with the study of motion and its causes. Through a
careful process of observation and experimentation, Galileo Galilei used experiments to overturn
Aristotle’s ideas of the motion of objects, for example the flawed idea that heavy objects fall faster
than lighter ones, which dominated physics for about 2,000 years.
The greatest contribution to the development of mechanics is by one of the greatest physicists of
all time, Isaac Newton. By extending Galileo’s methods and understanding of motion and
gravitation, Newton developed the three laws of motion and his law of universal gravitation, and
successfully applied them to both terrestrial and celestial systems to predict and explain
phenomena. He showed that nature is governed by a few special rules or laws that can be
expressed in mathematical formulae. Newton’s combination of logical experimentation and
mathematical analysis shaped the way science has been done ever since.
In this section, we begin by examining kinematics, which is a study of motion without regard for the
cause. After which, we study the conditions required for an object to be accelerated and introduce
the concept of forces through Newton’s Laws. Subsequently, concepts of moments and pressure
are introduced as consequences of a force. Finally, this section rounds up by leading the
discussion from force to work and energy, and the use of the principle of conservation of energy to
explain interactions between bodies.
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2. Kinematics
Content




Speed, velocity and acceleration
Graphical analysis of motion
Free-fall
Effect of air resistance
Learning Outcomes
Candidates should be able to:
(a) state what is meant by speed and velocity
Term
Definition
Average speed
Total distance travelled per unit time
Velocity
Change in displacement per unit time
(b) calculate average speed using distance travelled / time taken
Term
Formula
Average speed
Average speed 
Distance
Time taken
(c) state what is meant by uniform acceleration and calculate the value of an acceleration
using change in velocity / time taken
Common
legend
Key
t
a
u
v
s
Term
Time taken
Acceleration
Initial velocity
Final velocity
Displacement
Term
Acceleration
Definition
Formulae
Change in velocity per unit time
 Acceleration 
 a
Uniform acceleration
Constant change in velocity per unit time
Change in velocity
Time taken
v u
t
N.A.
Related formulae to find acceleration
Given
Formula to use
Time taken & Final velocity
v  u  at
Time taken & Displacement
s  ut  21 at 2
Final velocity & Displacement
v 2  u 2  2as
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(d) interpret given examples of non-uniform acceleration
Non-uniform acceleration
Uniform acceleration
Increasing acceleration
Pushing on the pedal
Decreasing acceleration
Releasing force on the pedal
No change in force exerted on the pedal
(e.g. pushing the pedal all the way)
(e) plot and interpret a displacement-time graph and a velocity-time graph
Differences
Displacement-time graph
Velocity-time graph
Label of y-axis
Displacement / m
Velocity / m s-1
Label of x-axis
Time / s
Time / s
Area below graph
N.A.
Total displacement / m
Gradient of graph
Velocity / m s-1
Acceleration / m s-2
(f) deduce from the shape of a displacement-time graph when a body is: (i) at rest (ii)
moving with uniform velocity (iii) moving with non-uniform velocity
Displacement-time graph
Scenarios
Displacement
Gradient
At rest
Zero displacement
N.A.
Moving with uniform velocity
Increasing displacement
Constant gradient
Moving with non-uniform velocity
Varying displacement
Varying gradient
(g) deduce from the shape of a velocity-time graph when a body is: (i) at rest (ii) moving
with uniform velocity (iii) moving with uniform acceleration (iv) moving with non-uniform
acceleration
Velocity-time graph
Scenarios
Velocity
Gradient
At rest
Zero velocity
N.A.
Moving with uniform velocity
Constant velocity
Zero gradient
Moving with uniform acceleration
Increasing velocity
Constant gradient
Moving with non-uniform acceleration
Varying velocity
Varying gradient
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(h) calculate the area under a velocity-time graph to determine the displacement travelled
for motion with uniform velocity or uniform acceleration
Term
Formulae
Displacement
Displacement  Area under velocity-time graph
Area of square  Velocity  Time taken
Area of triangle 
Term
1
2
 Velocity  Time taken
Formulae in symbols
v  u  t 
Displacement
s
Average velocity
Average velocity 
1
2
1
2
v  u 
(i) state that the acceleration of free fall for a body near to the Earth is constant and is
approximately 10 m/s2
Relationship between force and acceleration
 When a force is exerted on an object, the object will experience constant acceleration in the direction of
the force if there is no other force acting against it (i.e. constant resultant force)
 Any free falling object near to the Earth will experience constant acceleration of approximately 10 m/s2 due
to gravity as there is no air resistance acting against it
 Acceleration will only decrease when the object enters Earth as it will then experience air resistance
(j) describe the motion of bodies with constant weight falling with or without air resistance,
including reference to terminal velocity
Differences
With air resistance
Without air resistance
Description
of motion of
bodies with
constant
weight
 As an object falls in air,
 it increases its speed with an initial acceleration of 10ms-2
 Air resistance opposing weight increases as speed
increases,
 causing resultant force and hence acceleration to decrease
 When air resistance is equal to the weight of the body,
 the forces balance out to zero resultant force causing zero
acceleration and the object travels at constant terminal
velocity
 As an object falls in a
vacuum,
 it increases its speed with
an uniform acceleration of
10ms-2
 This is because there is no
air resistance present,
 thus resultant force is
constant
Graph of
velocity
against time
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3. Dynamics
Content



Balanced and unbalanced forces
Free-body diagram
Friction
Learning Outcomes
Candidates should be able to:
(a) apply Newton's Laws to: (i) describe the effect of balanced and unbalanced forces on a
body (ii) describe the ways in which a force may change the motion of a body (iii) identify
action-reaction pairs acting on two interacting bodies (stating of Newton's Laws is not
required)
Scenarios
Description
Possible effects
Condition
Balanced
forces on a
body
Resultant
force is
equal to 0 N
Object at rest
Object initially at rest
Object travels at constant
speed in a straight line
Object initally in motion
Unbalanced
forces on a
body
Resultant
force is more
than 0 N
Object accelerates
 Object is initially at rest
 or Force in same direction as object’s motion
Object decelerates
Force in opposite direction to object’s motion
Object changes direction
Force acts at an angle to object’s motion
Illustrations of unbalanced forces
Object accelerates
Term
Object decelerates
Meaning
Example
Action
force
The force a body (body 1)
exerts on another body
(body 2)
Feet of a swimmer
pushing against the
swimming pool wall
Reaction
force
The subsequent force body
2 exerts on body 1 in
reaction to the action force
Force that propels in
swimmer forward in
reaction
20
Object changes direction
Relationship
 Forces always occur in pairs, each made
up of a action force and a reaction force
 Action and reaction forces are equal in
magnitude,
 act in opposite directions and
 on 2 different bodies
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(b) identify forces acting on an object and draw free body diagram(s) representing the
forces acting on the object (for cases involving forces acting in at most 2 dimensions)
Legend
Key
Term
Explanation
T
Thrust
N.A.
W
Weight of object
Due to gravity
F
Force
N.A.
+
Contact force
Reaction force due to weight of object
*
Friction
Between object and ground
R
Air resistance
Friction between object and air molecules
F
f
Air resistance applicable
Object thrust upwards 
Object released high up 
Without air resistance
With air resistance
Air resistance not applicable
Object on the ground
Object pushed on the ground 
(c) solve problems for a static point mass under the action of 3 forces for 2-dimensional
cases (a graphical method would suffice)
References
Refer to Learning Outcome 1(f) on Page 13
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(d) recall and apply the relationship resultant force = mass × acceleration to new situations
or to solve related problems
Term
Formula
SI units
Resultant
force
 Resultant force  Mass  Acceleration
 F  ma
Interpretation
F
m
a
N
kg
m s-2
A resultant force of 2 N exerted on
a body of mass 0.5 kg causes the
body to accelerate at 4 m s-2
(e) explain the effects of friction on the motion of a body
Scenario
Possible motions
Explanation
Box rests on a flat
horizontal floor
Box remains at rest
 There is no frictional force acting on the box
 Contact force of the ground is equal to the weight of the
box due to gravity
Box slides along a
rough table
Decelerates and
eventually stops
 Frictional force opposes the force of the motion
 Kinetic energy is converted to heat energy
Box rests on a slope
Box remains at rest
 Downward force of attraction acting on the box due to
gravity is equal to the upward frictional force
 Resultant force is zero
Box accelerates down
the slope
 Downward force of attraction acting on the box due to
gravity is more than the upward frictional force
 Resultant force is more than zero
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4. Mass, Weight and Density
Content



Mass and weight
Gravitational field and field strength
Density
Learning Outcomes
Candidates should be able to:
(a) state that mass is a measure of the amount of substance in a body (b) state that mass of
a body resists a change in the state of rest or motion of the body (inertia)
Term
Definition
Mass
Measure of the amount of substance in a body which resists a change in the state of rest or motion
of the body
Inertia
The resistance of a body with mass to start moving if it is stationary or stop moving if it is in motion
in its first instance
(c) state that a gravitational field is a region in which a mass experiences a force due to
gravitational attraction
Term
Definition
Gravitational field
A region in which a mass experiences a force due to gravitational attraction
(d) define gravitational field strength, g, as gravitational force per unit mass
Term
Definition
Gravitational field strength
 Gravitational force acting per unit mass on an object
 The gravitational field strength on Earth is about 10 N kg-1
(e) recall and apply the relationship weight = mass × gravitational field strength to new
situations or to solve related problems
Term
Definition
Weight
The force of
attraction on
an object
due to
gravity
Formula
SI units
 Weight
W
m
g
 Mass  Gravitational field strength
 W  mg
 g on Earth is about 10 N kg-1
kg
N
N kg-1
23
Interpretation
A 2 kg mass has a
weight of 20 N due to
Earth’s gravitational pull
of 10 N kg-1
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(f) distinguish between mass and weight
Differences
Mass
Weight
Meaning
Amount of matter in a body
Due to pull of gravity on a body
Scalar or vector
Scalar; has only magnitude
Vector; has both magnitude and direction
Unit
Measured in kg (kilograms)
Measures in N (newtons)
Variations
Constant regardless of gravitational field
strength
Varies according to gravitational field
strength
(g) recall and apply the relationship density = mass / volume to new situations or to solve
related problems
Term
Definition
Density
Mass per unit volume
Formula
 Density 
SI units
Mass
Interpretation

m
V
kg m-3
kg
m3
Volume
m
 
V
24
An object with mass of 4 kg
and volume of 2 m3 has a
density of 2 kg m-3
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5. Turning Effect of Forces
Content



Moments
Centre of gravity
Stability
Learning Outcomes
Candidates should be able to:
(a) describe the moment of a force in terms of its turning effect and relate this to everyday
examples (b) recall and apply the relationship moment of a force (or torque) = force ×
perpendicular distance from the pivot to new situations or to solve related problems
Term
Definition
Turning effect
 The turning of an object about a pivot
 The greater the moment, the greater the object turns about the pivot
Term
Definition
Formula
Moment
of a
force
The product of the
force and the
perpendicular
distance between
the line of action of
the force and a
pivot, and resulting
in a turning effect
 Moment
 Force  Perpendicular distance
SI units
Interpretation
Moment
F
pd
Nm
N
m
 Moment  F  pd
A force of 2 N
acting with a
perpendicular
distance of
2 m produces
a moment of 4
Nm
(c) state the principle of moments for a body in equilibrium (d) apply the principle of
moments to new situations or to solve related problems
Term
Principle of
moments
Definition
Formula
When an object is in equilibrium, the sum of clockwise
moments about a pivot is equal to sum of anticlockwise
moments about the same pivot
Sum of clockwise moments
 Sum of anti-clockwise moments
(e) show understanding that the weight of a body may be taken as acting at a single point
known as its centre of gravity
Term
Centre of gravity
of an object
Definition
Alternative definition
Point of application of the resultant force on
an object exerted by gravity for any
orientation of the object
25
Point through which the whole weight of
an object appears to act for any
orientation of the object
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(f) describe qualitatively the effect of the position of the centre of gravity on the stability of
objects
Scenario
Effect on stability
Measure to increase stability
Higher centre of gravity
 Lower stability of the object
 Toppling will occur at
smaller angles of tilt
Decrease the centre of gravity by adding
more mass below the current centre of
gravity to the object
Object is tilted such that centre
of gravity is still vertically above
the base of object
Object will not topple
Increase the size of base
Object is tilted such that centre
of gravity is no longer vertically
above the base of object
Object will topple
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6. Pressure
Content



Pressure
Pressure differences
Pressure measurement
Learning Outcomes
Candidates should be able to:
(a) define the term pressure in terms of force and area (b) recall and apply the relationship
pressure = force / area to new situations or to solve related problems
Term
Definition
Formula
Pressure
Average force per
unit area
 Pressure 
 p=
SI units
p
F
A
Pa or N m-2
N
m2
Force
Area
F
Interpretation
A force of 4 N acting on
an area of 2 m2 results in
a pressure of 2 Pa
A
(c) describe and explain the transmission of pressure in hydraulic systems with particular
reference to the hydraulic press
Transmission of pressure in hydraulic systems
Description




Oil is the incompressible, high density liquid used in the transmission of pressure
Effort piston has a smaller cross sectional area than that of the piston below the load
Since liquid pressure at both pistons are equal when they are at the same level,
A small force exerted on the effort piston will create a much bigger force on the load piston in comparison
Diagram
Calculations
 Since water level at X is the
same as the water level at Y,
 Pressure at X  Pressure at Y
F
F
 X  Y
AX AY
oil
F 
 FX  AX  Y 
 AY 
27
 Since AX  AY
 FX  FY
 If the load is at Y and FY
represents the weight of the
load, use of the hydraulic
press will require a smaller
force of FX instead of FY to
lift the load upwards
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(d) recall and apply the relationship pressure due to a liquid column = height of column ×
density of the liquid × gravitational field strength to new situations or to solve related
problems
Term
Formula
Pressure
due to
liquid
column
SI units
 Pressure due to liquid
 Height of column  Density of liquid  Gravitational field strength
 p  h g
Example of diagram of manometer
p
h

g
N m-2
m
kg m-3
N kg-1
Calculations
gas  Water level at A is the same as the water level at B
 Gas pressure at A  Pressure at B
 Atmospheric pressure  h g at B
 1.01 105 Pa  h g at B
(e) describe how the height of a liquid column may be used to measure the atmospheric
pressure
Diagram of barometer
Description of measurement of atmospheric pressure
 Set up a barometer using high density mercury of 13.6 kg m -3
 Atmospheric pressure  Pressure from mercury in glass tube
 h g

  0.760 13.6  9.8  103

 1.013  105 Pa
(f) describe the use of a manometer in the measurement of pressure difference
Redirect instructions
Refer to Learning Outcome 6(f) above
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7. Energy, Work and Power
Content



Energy conversion and conservation
Work
Power
Learning Outcomes
Candidates should be able to:
(a) show understanding that kinetic energy, potential energy (chemical, gravitational,
elastic), light energy, thermal energy, electrical energy and nuclear energy are examples of
different forms of energy
Examples of forms of energy
Kinetic
Movement
Potential
Thermal
Stored energy
Chemical
Food or
batteries
Light
Electrical
Nuclear
Heat
Gravitational
Raised above
ground
Elastic
Compression or
stretching of elastic
objects like springs
(b) state the principle of the conservation of energy and apply the principle to new
situations or to solve related problems
Term
Definition
Principle of
conservation of energy
Energy can neither be created nor destroyed but can only be transferred from one
body to another or from one form to another while total energy remains the same
(c) calculate the efficiency of an energy conversion using the formula efficiency = energy
converted to useful output / total energy input
Term
Formula
Energy input
Energy input  Useful energy output  Wasted energy output
Efficiency
Efficiency 
Useful energy output
 100%
Energy input
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(d) state that kinetic energy Ek = ½ mv2 and gravitational potential energy Ep = mgh (for
potential energy changes near the Earth’s surface) (e) apply the relationships for kinetic
energy and potential energy to new situations or to solve related problems
Term
Formula
Kinetic energy
of an object
Potential energy
of an object
SI units
 Kinetic energy  21  Mass   Speed
Ek
m
v
 Ek  21 mv 2
J
kg
m s-1
 Gravitational potential energy
Ep
m
g
h
J
kg
N kg-1
m
2
 Mass  Gravitational field strength  Height
 Ep  mgh
(f) recall and apply the relationship work done = force × distance moved in the direction of
the force to new situations or to solve related problems
Term
Formula
SI units
Work done
of an object
 Work done  Force  Distance travelled
 W  Fd
W
F
d
J
N
m
(g) recall and apply the relationship power = work done / time taken to new situations or to
solve related problems
Term
Power of
an object
Formula
 Power 
 P=
W
t
=
Work done
Time taken
E

SI units
Energy converted
P
W
E
t
W or J s-1
J
J
s
Time taken
t
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SECTION III: THERMAL PHYSICS
Overview
Amongst the early scientists, heat was thought as some kind of invisible, massless fluid called
‘caloric’. Certain objects that released heat upon combustion were thought to be able to ‘store’ the
fluid. However, this explanation failed to explain why friction was able to produce heat. In the
1840s, James Prescott Joule used a falling weight to drive an electrical generator that heated a
wire immersed in water. This experiment demonstrated that work done by a falling object could be
converted to heat.
In the previous section, we studied about energy and its conversion. Many energy conversion
processes which involve friction will have heat as a product. This section begins with the
introduction of the kinetic model of matter. This model is then used to explain and predict the
physical properties and changes of matter at the molecular level in relation to heat or thermal
energy transfer.
Extracted from PHYSICS GCE ORDINARY LEVEL (2014) Syllabus Document
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8. Kinetic Model of Matter
Content



States of matter
Brownian motion
Kinetic model
Learning Outcomes
Candidates should be able to:
(a) compare the properties of solids, liquids and gases
Properties
Solids
Liquids
Gases
Volume
Fixed
Fixed
Not fixed
Shape
Fixed
Not fixed
Not fixed
Compressibility
No
No
Yes
Density
High
High
Low
Others
Usually hard and rigid
Tend to form droplets
N.A.
(b) describe qualitatively the molecular structure of solids, liquids and gases, relating their
properties to the forces and distances between molecules and to the motion of the
molecules
Molecular structure
Solids
Liquids
Gases
Forces of attraction
between particles
Particles held by very
strong forces of attraction
Particles held by strong
forces of attraction
Particles held by weak
forces of attraction
Distance between
particles
Packed very closely
together with more particles
per unit volume
Packed close to one
another
Spread far apart from one
another
Motion of particles
Vibrate about fixed
positions
Slide and move past
one another randomly
Move in a constant,
random and erratic manner
(c) infer from Brownian motion experiment the evidence for the movement of molecules
Brownian motion experiment
Term
Definition
Setup
Brownian
motion
Small particles suspended
in a liquid or gas tend to
move in random paths
through the fluid even if it is
calm
Place smoke
particles in a
container of air,
suspending
them in air
32
Observations
Smoke particles are being
continuously bombarded by
air molecules and move
irregularly by Brownian
motion
Inferences
This shows
that the fluids
have an ability
to flow or
move freely
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(d) describe the relationship between the motion of molecules and temperature
Relationship between motion of molecules and temperature
 When solid or fluid (liquid / gas) is at a higher temperature, the particles vibrate or move faster respectively
 The average kinetic energy of the particles is the measure of temperature or degree of hotness
(e) explain the pressure of a gas in terms of the motion of its molecules
Explanation of pressure of a gas
Effect of increasing temperature on pressure
 Molecules present in a fluid collide with the walls of the
container at a constant rate
 Each collision exerts a force on the walls of the
container
 As the force is acted on a particular quantity of surface
area of walls, the gas exerts pressure on the walls
 When temperature is increased, molecules
move faster and collide with the walls of the
container more frequently
 Average force on the walls of the container
increases over the same surface area of
walls, thus gas pressure increases
(f) recall and explain the following relationships using the kinetic model (stating of the
corresponding gas laws is not required): (i) a change in pressure of a fixed mass of gas at
constant volume is caused by a change in temperature of the gas (ii) a change in volume
occupied by a fixed mass of gas at constant pressure is caused by a change in temperature
of the gas (iii) a change in pressure of a fixed mass of gas at constant temperature is
caused by a change in volume of the gas
Gas
equation
p1V1 p2V2

, where p : Pressure, V : Volume, T : Temperature, only for gases
T1
T2
Cause
Temperature of gas increases
Effect
Volume increases
Pressure unchanged
Pressure increases
Pressure increases
Condition
Only if container
can expand further
Only if container can
expand further
Only if container
cannot expand
Under all cases
Explanation
 Molecules gain
kinetic energy and
move faster
 Gas molecules hit
the container
walls with higher
speed
 Frequency of
collisions of the
gas molecules
with the walls
increases
 Greater force is
exerted on walls,
gas expands
since container
can expand
 Gas expands in
volume since the
container can expand,
decreasing the
number of gas
particles per unit
volume and increasing
surface area of walls
 Number of gas
particles hitting the
walls per unit area
decreases
 Average force exerted
per unit area remains
unchanged, hence a
constant pressure is
maintained
 Molecules gain
kinetic energy
and move faster
 Gas molecules hit
the container
walls with higher
speed
 Frequency of
collisions of the
gas molecules
with the walls
increases
 Average force
exerted per unit
area on the
container walls
increases
 Gas is
compressed at
constant
temperature and
number of gas
particles per unit
volume increases
 Frequency of
collisions of
molecules with
container walls
increases
 Force exerted per
unit area on the
container
increases, thus
pressure increases
Volume decreases
(g) use the relationships in (f) in related situations and to solve problems (a qualitative
treatment would suffice)
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9. Transfer of Thermal Energy
Content



Conduction
Convection
Radiation
Learning Outcomes
Candidates should be able to:
(a) show understanding that thermal energy is transferred from a region of higher
temperature to a region of lower temperature
Thermal energy transfer
Thermal energy is transferred from a region of higher temperature to a region of lower temperature
(b) describe, in molecular terms, how energy transfer occurs in solids
Energy transfer occurs in solids
In comparison with fluids
 When one region of a solid is heated, the molecules
there gain kinetic energy and vibrate faster
 They collide with the slower neighbouring particles and
transfer energy to them
 In fluids, the particles are further apart from
each another than in liquids or gases
 Therefore kinetic energy is transferred more
slowly
(c) describe, in terms of density changes, convection in fluids
Convection in fluids
In comparison with solids
 Hot fluid expands and has lower density than cold
fluid, causing it to rise
 Cold fluid contracts and has higher density than
hot fluids, sinking to replace the hot fluid
 Convection current is set up when the cycle
repeats
 Convection involves the bulk movement of fluids
which carry heat with them
 Solids cannot cause convection as heat can only be
transferred from one molecule to another
 The molecules are unable to flow around
themselves
(d) explain that energy transfer of a body by radiation does not require a material medium
and the rate of energy transfer is affected by: (i) colour and texture of the surface (ii)
surface temperature (iii) surface area
Energy transfer of a body by radiation
 Infrared radiation is continuously emitted by all objects through their surfaces as radiation does not require
a material medium for thermal transfer to occur
 When these infrared waves reach another object, the waves are transformed into heat energy, which is
then absorbed by the object
 Higher surface areas, higher surface temperatures (relative to surroundings) and dull surfaces accelerate
radiation of heat
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(e) apply the concept of thermal energy transfer to everyday applications
Applications
Styrofoam
food
packages
Vacuum
flasks
Features
Advantages
Mostly made
of styrofoam
Conduction is
reduced
 This is due to the presence of many air pockets
 Air is a poor conductor of heat
Covered with
a lid
Convection is
reduced
Convection currents are unable to be set up due to the
presence of the lid compressing the contents into a closely
packed arrangement
Plastic
stopper
Conduction &
convection is
reduced
 Plastic is a poor conductor of heat
 With a stopper, a convection current is being prevented
from set up
Vacuum
between the
glass walls
Reasons
As vacuum is unable to conduct and cause convection of
heat, the amount of heat medium is decreased
Silvered
glass walls
Radiation is
reduced
 The shiny and smooth surface is a poor emitter and
absorber of heat
 It is able to reflect heat back to the container very well
Air trapped
above
contents
Conduction is
reduced
Air is a poor conductor of heat
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10. Temperature
Content

Principles of thermometry
Learning Outcomes
Candidates should be able to:
(a) explain how a physical property which varies with temperature, such as volume of liquid
column, resistance of metal wire and electromotive force (e.m.f.) produced by junctions
formed with wires of two different metals, may be used to define temperature scales
Differences
Mercury thermometer
Platinum wire
Thermocouple
Physical
property
Volume or height of
liquid column
Resistance
Electromotive force (e.m.f.) produced
by 2 junctions formed with wires of 2
different metals
Rationale
Mercury is sensitive to
changes in temperature
and expands when
temperature rises
 Resistance of the wire
rises when temperature
rises
Voltage
 Resistance 
Current
E.m.f. between two substances
increases when the temperature
difference between them rises
Apparatus
mV
Copper
Copper
Iron
0oC
Calculations
100o C,
then  o C
s
where X is the value of physical property used (can be  ve /  ve)
X  X0
 C 
 100,
X100  X 0
and  o C is the temperature of the substance measured
o
(b) describe the process of calibration of a liquid-in-glass thermometer, including the need
for fixed points such as the ice point and steam point
Calibration of liquid-in-glass thermometer
 Place thermometer in ice point (funnel containing pure melting ice),
then in steam point (above boiling water)
 Mark the level of mercury in both situations
 The difference in temperature of both points is 100oC
 Between the upper and lower fixed points markings, divide and mark
one hundred equal divisions
 Since an increase in the temperature will increase the volume of
mercury proportionately, each division is one degree Celsius
36
Need for fixed points
 Fixed points (ice and steam
points) are used for calibration
for all thermometers to agree
accurately on a same
temperature scale
 This is because fixed points are
reproducible and will produce
definite temperatures
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11. Thermal Properties of Matter
Content




Internal energy
Specific heat capacity
Melting, boiling and evaporation
Specific latent heat
Learning Outcomes
Candidates should be able to:
(a) describe a rise in temperature of a body in terms of an increase in its internal energy
(random thermal energy)
Term
Meaning
Internal
energy
Random thermal energy of a body resulting from the kinetic and potential energy of the particles by
their movement and arrangement
Description of rise in temperature of a body
When a body is heated, its internal energy (consisting of kinetic energy and potential energy) rises
Kinetic energy
Potential energy
Kinetic energy of particles
increases, causing particles
vibrate or move faster
 During melting and boiling, potential energy of the particles also increases
 This is since there is no rise in temperature, causing latent heat to be
taken in
(b) define the terms heat capacity and specific heat capacity
Term
Definition
Symbol
Heat capacity
Amount of heat energy required to raise the temperature of a body by 1 K or 1 °C
C
Specific heat
capacity
Amount of heat energy required to raise the temperature of 1 kg of a body by 1 K
or 1 °C
c
(c) recall and apply the relationship thermal energy = mass × specific heat capacity ×
change in temperature to new situations or to solve related problems
Term
Thermal energy
when there is a
temperature change
Formula
SI units
 Thermal energy
m
c

 Mass  Specific heat capacity  Change in temperature
 Heat  (m)(c )(  )
J kg-1 oC-1
or
J kg-1 K-1
oC
kg
37
or
K
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(d) describe melting/solidification and boiling/condensation as processes of energy transfer
without a change in temperature
Term
Meaning
Melting
Process of energy transfer from the surroundings to a solid to turn it to a liquid without a
change in temperature
Solidification
Process of energy transfer from a liquid to the surroundings to turn it to a solid without a
change in temperature
Boiling
Process of energy transfer from the surroundings to a liquid to turn it to a gas without a
change in temperature
Condensation
Process of energy transfer from a gas to the surroundings to turn it to a liquid without a
change in temperature
(e) explain the difference between boiling and evaporation
Description of evaporation
 At any temperature, the molecules of liquid are in continuous random motion with different speeds
 Some more energetic molecules near to the surface of the liquid have enough energy to overcome the
attractive forces of other molecules and escape
 They evaporate from the liquid to form a vapour
Differences
Boiling
Evaporation
Temperature
Occurs at a fixed temperature
Occurs at any temperature
Location
Occurs throughout the liquid
Occurs at the surface of the liquid
Heat source
Heat is supplied from an energy source
Heat is supplied by the surroundings
(f) define the terms latent heat and specific latent heat
Term
Latent heat
Definition
Heat energy released or absorbed during a change of state to make or break
intermolecular forces of attraction without any change in temperature
Latent heat of fusion
Heat energy required to change a solid to its liquid state or vice versa without any
change in temperature
Latent heat of
vapourisation
Heat energy required to change a liquid to its vapour state or vice versa without
any change in temperature
Specific latent heat
Heat energy required to change 1 kg of a substance from one state to another or
vice versa
(g) recall and apply the relationship thermal energy = mass × specific latent heat to new
situations or to solve related problems
Term
Formula
Thermal energy when there
is no temperature change
 Thermal energy  Mass  Specific latent heat
m
f
 Latent heat  (m)( f )
kg
J kg-1
38
SI units
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(h) explain latent heat in terms of molecular behaviour
Term
Latent heat
Definition
Heat energy released or absorbed during a change of state to make or break intermolecular
forces of attraction without any change in temperature
(i) sketch and interpret a cooling curve
Sketch of cooling curve of water
Interpretation of cooling curve
Description
condensation
Explanation
Decreases in
temperature during
gas, liquid and solid
state in the graph
This is because thermal energy is
being released with no change in
intermolecular forces of attraction
between the molecules
No change in
temperature during
condensation and
freezing until all the
water vapour has
condensed and all the
water has frozen
This is because thermal energy is
being released to form greater
intermolecular forces of attraction
between the molecules such that
there is a state change
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SECTION IV: WAVES
Overview
Waves are inherent in our everyday lives. Much of our understanding of wave phenomena has
been accumulated over the centuries through the study of light (optics) and sound (acoustics). The
nature of oscillations in light was only understood when James Clerk Maxwell, in his unification of
electricity, magnetism and electromagnetic waves, stated that all electromagnetic fields spread in
the form of waves.
Using a mathematical model (Maxwell’s equations), he calculated the speed of electromagnetic
waves and found it to be close to the speed of light, leading him to make a bold but correct
inference that light consists of propagating electromagnetic disturbances. This gave the very
nature of electromagnetic waves, and hence its name.
In this section, we examine the nature of waves in terms of the coordinated movement of particles.
The discussion moves on to wave propagation and its uses by studying the properties of light,
electromagnetic waves and sound, as well as their applications in wireless communication, home
appliances, medicine and industry.
Extracted from PHYSICS GCE ORDINARY LEVEL (2014) Syllabus Document
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12. General Wave Properties
Content



Describing wave motion
Wave terms
Longitudinal and transverse waves
Learning Outcomes
Candidates should be able to:
(a) describe what is meant by wave motion as illustrated by vibrations in ropes and springs
and by waves in a ripple tank
Term
Definition
Wave motion
Propagation of waves through a medium by the vibration of particles in the wave transmitting
energy
Illustrations
Transverse waves
Longitudinal waves
Rope
N.A.
Spring
Ripple tank
N.A.
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Comparison of waves in a ripple tank
Description
Waves of water undergo refraction when it travels from deeper water to shallower water or
vice versa
Differences
Deeper water
Shallower water
Wavelength
Increases
Decreases
Velocity
Increases
Decreases
Frequency
Remains the same
Remains the same
Direction
Away from the normal
Towards the normal
Wavefront
Perpendicular to
direction of wave
Perpendicular to
direction of wave
Illustrations
(b) show understanding that waves transfer energy without transferring matter
Waves
 A wave is the collective motion of many particles
 Occurs when particles of the medium move in a specific manner
What is transferred
What is not transferred
Energy
Medium
(c) define speed, frequency, wavelength, period and amplitude
Term
Definition
Formula
Frequency
The number of complete waves produced per second by a source
f 
1
T
Period
The time taken to produce one complete wave
T 
1
f
Wavelength
Shortest distance between any two points of a wave in phase
Represented by 
(Refer to diagram)
Speed
Distance travelled by a crest or rarefraction per unit time by a wave
v  f
Amplitude
Maximum displacement of crest or rarefaction from the rest position
Refer to diagram
Diagram
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(d) state what is meant by the term wavefront
Term
Definition
Wavefront
Imaginary line on a wave that joins all points that are in the same phase
(e) recall and apply the relationship velocity = frequency × wavelength to new situations or
to solve related problems
Term
Formula
SI units
Velocity of wave
 Velocity  Frequency  Wavelength
 v  f
v
f

m s-1
Hz
m
(f) compare transverse and longitudinal waves and give suitable examples of each
Term
Definition
Properties
Transverse
wave
Waves that travel in a direction perpendicular
to the direction of vibration of the particles
Crests and troughs represent amplitude and
minimum displacement respectively
Longitudinal
wave
Waves that travel in a direction parallel to the
direction of vibration of the particles
Rarefactions and compressions represent
amplitude and minimum displacement
respectively
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13. Light
Content



Reflection of light
Refraction of light
Thin lenses
Learning Outcomes
Candidates should be able to:
(a) recall and use the terms for reflection, including normal, angle of incidence and angle of
reflection
Ray diagram
Legend
mirror
 i represents the
angle of incidence
 r represents the
angle of reflection
(b) state that, for reflection, the angle of incidence is equal to the angle of reflection and use
this principle in constructions, measurements and calculations
Reflection laws
 Angle of incidence
is equal to angle of
reflection
 The normal,
incident ray and
reflected ray all lie
in the same plane
Features of a plane mirror image
Features





Acronym
Virtual
Image is the same size as the object (Size)
Image as far away from the mirror as the object is from the mirror (Far)
Laterally inverted
Upright
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(c) recall and use the terms for refraction, including normal, angle of incidence and angle of
refraction
Term
Meaning
Conditions
Refraction
 Refers to the change in direction or bending of light
when it passes from one medium to another medium
of different optical densities due to the change in
speed of light
 The light ray bends towards the normal when
travelling into a medium of higher optical density
 The light ray bends away from the normal when
travelling into a medium of lower optical density
 Angle of incidence
must not be 0o
 If ray travels from a
denser to less dense
medium, angle of
incidence must be
less than critical
angle
Ray diagram
Real and apparent depth
Remark
‘Density’ in
this case
represents
optical
density
Legend
 i represents the angle of
incidence
 r represents the angle of
refraction
(d) recall and apply the relationship sin i / sin r = constant to new situations or to solve
related problems (e) define refractive index of a medium in terms of the ratio of speed of
light in vacuum and in the medium
Term
Definition
Refractive
index of a
medium
The constant ratio of
the speed of light in
vacuum to the speed
of light in the medium
Formula
n



Speed of light in vacuum
Speed of light in medium
sin i
sin r
sin r
(from vacuum to medium)
Legend
 n represents refractive index
 i represents the angle of
incidence
 r represents the angle of
refraction
(from medium to vacuum)
sin i
Real depth
Apparent depth
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(f) explain the terms critical angle and total internal reflection
Term
Definition
Formula
Critical
angle
The angle of incidence of a ray in the optically denser
medium whereby the angle of refraction of it in the
optically less dense medium is 90o
Total
internal
reflection
Reflection of light rays within the optically denser medium
when the angle of incidence in the optically denser
medium is more than the critical angle
 1
c  sin-1   ,
n
n
sin 90
sin c

1
sin c
N.A.
Illustrative diagrams
Refraction
Critical angle
 i represents the angle of
incidence which is less than
critical angle
 r represents the angle of
refraction which is within the
optically less dense medium
and is less than 90o
Total internal reflection
 i represents the angle of
incidence which is equal to critical
angle
 r represents the angle of
refraction which is along the
boundary of the 2 mediums and
is equal to 90o
 i represents the angle of
incidence which is more than
critical angle
 r represents the angle of
reflection which is within the
optically denser medium and is
equal to 90o
(g) identify the main ideas in total internal reflection and apply them to the use of optical
fibres in telecommunication and state the advantages of their use
Main ideas in total internal reflection
 Light ray has to travel from denser medium towards the less dense medium
 Angle of incidence of light ray is more than critical angle
 The light ray will reflect internally by the laws of reflection within the denser medium
Optical fibres in telecommunications
Advantages
Diagram
 Light pulses carry
telecommunications data at a faster
rate
 Less data loss compared to use of
copper wires
 Optical fibres are generally cheaper
and lighter than copper wires
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(h) describe the action of a thin lens (both converging and diverging) on a beam of light
Differences
Lens type
Converging lens
Diverging lens
Convex lens
Concave lens
Light rays
Ray
diagram
optical center
principal focus
Description
of lens
action
 The lens is curved,
 thus the angles of incidence of parallel rays
of light differ,
 causing the rays to change direction
differently after passing through the lens
 The lens is curved,
 thus the angles of incidence of parallel
rays of light differ,
 causing the rays to change direction
differently after passing through the lens
 The front of the lens facing the incident light
rays curve outwards
 The light rays converge at a common focal
point
 The front of the lens facing the incident
light rays curve inwards
 The light rays diverge from one another
(i) define the term focal length for a converging lens
Term
Definition
Diagram
Focal length
of converging
lens
Distance between the optical center and the
principal focus, where parallel rays of light
converge after passing through the lens
focal length
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(j) draw ray diagrams to illustrate the formation of real and virtual images of an object by a
thin converging lens
#
Object location
Image location
Image properties
Acroynm
Uses
1
u
v f
Diminished, inverted, real
DIR
Telescope
2
u  2f
2f  v  f
Diminished, inverted, real
DIR
 Camera
 Eye
3
u  2f
v  2f
Same size, inverted, real
SIR
Photocopier
4
2f  u  f
v  2f
Magnified, inverted, real
MIR
Projector
5
uf
v 
Magnified, upright, virtual
MUV
Spotlight
6
uf
f  v  2f
Magnified, upright, virtual
MUV
 Magnifying glass
 Spectacles
Image formation based on object location
#
Object
location
1
2
u
u  2f
3
4
u  2f
2f  u  f
5
6
uf
uf
Ray
diagram
#
Object
location
Ray
diagram
#
Object
location
Ray
diagram
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14. Electromagnetic Spectrum
Content



Properties of electromagnetic waves
Applications of electromagnetic waves
Effects of electromagnetic waves on cells and tissue
Learning Outcomes
Candidates should be able to:
(a) state that all electromagnetic waves are transverse waves that travel with the same
speed in vacuum and state the magnitude of this speed
#
Point
Property of electromagnetic waves (EM waves)
1
Type
 Transverse waves
 Electric and magnetic fields oscillate 90o to each other
2
Laws
They obey the laws of reflection and refraction
3
Electric charge
No electric charge is carried through EM waves
4
Medium
No medium is required and the wave can travel through vacuum
5
Frequency
Remains the same all the time
6
Wavelength
Decreases from optically less dense to denser medium
7
Velocity
 3 x 108 ms-1 in vacuum, slows down in matter
 Decreases from optically less dense to denser medium
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(b) describe the main components of the electromagnetic spectrum (c) state examples of
the use of the following components: (i) radiowaves (e.g. radio and television
communication) (ii) microwaves (e.g. microwave oven and satellite television) (iii) infra-red
(e.g. infra-red remote controllers and intruder alarms) (iv) light (e.g. optical fibres for
medical uses and telecommunications) (v) ultra-violet (e.g. sunbeds and sterilisation) (vi) Xrays (e.g. radiological and engineering applications) (vii) gamma rays (e.g. medical
treatment)
Component
Frequency
Applications
Radio waves
1× 10^ 8 Hz
Radio and television
communications
Able to go around obstructions (due to longer
wavelengths)
Microwaves
1× 10^ 10 Hz
Microwave oven
Water molecules vibrate millions of times a
second to produce heat from friction
Satellite television
Can penetrate haze, light rain, snow, clouds and
smoke with proper alignment
Remote controllers

Intruder alarms
Alarm rings when it receives infra-red radiation an
intruding human gives out
Medical optical fibres

Telecommunications

Sunbeds
Artificial tanning (shorter frequency UVA)
Sterilisation
Germicidal lamps (longer frequency UVB/C)
Infra-red
Light
1× 10^ 12 Hz
(Red)
5× 10^ 14 Hz
(Violet)
Ultra-violet
3× 10^ 16 Hz
Description
X-rays
3× 10^ 18 Hz
 Diagnose fractures
 Airport scanners
Can penetrate through all materials other than
lead, thus may be applied using X-ray imagery
Gamma rays
3× 10^ 20 Hz
Cancer treatment
Kill cancer cells in cancerous tumours (high
energy waves)
Changes in the EM spectrum from radio to gamma waves
Frequency
Wavelength
Increases from radio waves to gamma rays
Decreases from radio waves to gamma rays
(d) describe the effects of absorbing electromagnetic waves, e.g. heating, ionisation and
damage to living cells and tissue
Effects of absorbing electromagnetic waves
Infrared
High energy EM waves
X-rays
 Human skin absorbs
infrared waves from BBQ
pits
 Human bodies will
receive the radiation and
be heated to feel warm
 EM waves of frequencies higher than light have
high energy causing ionisation
 Ionisation of living matter in human bodies
damages chromosomes, living cells and tissues
 Overexposure leads to premature ageing and
lifespan shortening
 Overexposure of
developing fetus to Xray imagery can cause
abnormal cell division
 A deformed baby and
leukemia may result
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15. Sound
Content




Sound waves
Speed of sound
Echo
Ultrasound
Learning Outcomes
Candidates should be able to:
(a) describe the production of sound by vibrating sources (b) describe the longitudinal
nature of sound waves in terms of the processes of compression and rarefaction
Production of sound in air
A vibrating source causes particles in air
to be displaced, moving away and from
the source continuously
Description of sound waves
 Air particles oscillate left and right to produce compressions at
high air pressure and rarefactions at low air pressure
 A longitudinal sound wave is produced
(c) explain that a medium is required in order to transmit sound waves and the speed of
sound differs in air, liquids and solids
Conditions for transmission of sound waves
 A vibrating source must be present
 The source must be placed in a medium
 Energy transmitted by sound waves depends
on its frequency and amplitude
 Speed of sound increases from gas to solid
Approximate speeds of sound
In gases
Air
330 m s-1
In liquids
Water
1500 m s-1
In solids
Iron
5000 m s-1
Steel
6000 m s-1
(d) describe a direct method for the determination of the speed of sound in air and make the
necessary calculation
Experiment to determine speed of sound in air
Method
Calculation
 Observers A and B are positioned at a far
distance apart, S, to minimise human reaction
error
 Observer A fires a pistol and Observer B starts
the stopwatch on seeing the flash of the pistol
 He stops the stopwatch when he hears the sound
 The time interval between the two actions, T, is
recorded
Speed of sound
is calculated by
the following
formula:
Speed 
51
S
T
Reliability
 For better accuracy, the
experiment is repeated and the
average speed of sound is
calculated
 The experiment is further
repeated by interchanging the
positions of Observers A and B
to minimise the effects of wind
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(e) relate loudness of a sound wave to its amplitude and pitch to its frequency
Cause
Effects on
Frequency increases
Amplitude increases
Pitch
Increases
Remains the same
Loudness
Remains the same
Increases
(f) describe how the reflection of sound may produce an echo, and how this may be used
for measuring distances
Experiment to measure distances using echoes
Theory
Method
Calculation
Reliability
 Sound waves follow the
laws of reflectlon
 The harder and larger the
surface is, the stronger the
echo
 When sound waves are
reflected after striking
objects, the reflected sound,
an echo, is produced
 When a source emits a sound and then
receives an echo, the sound must have
travelled a distance of 2D, where D is
the distance between the source and
the reflected surface
 The time interval between emission and
receiving of the sound is recorded as T
 The speed of sound in the medium is
labelled as V
Distance from
source and
reflected surface
is calculated by
the following
formula:
For better
accuracy,
the
experiment
is repeated
and the
average
distance is
calculated
D
TV
2
Example of measuring distances using echoes (depth of seabed)
Diagram
Calculation
Let 2d be the depth of the seabed,
T be the duration between sound emission and echo receival,
and V be the speed of sound in water, which is 1500 ms-1
 Total distance travelled by sound  2d  TV
 d
TV
2

1500T
2
 750T
(g) define ultrasound and describe one use of ultrasound, e.g. quality control and pre-natal
scanning
Term
Definition
Ultrasound
Sound with
waves above
20 kHz
frequency,
which is above
the upper limit
of the human
hearing range
(Humans can
only hear
sound of
frequencies
between 20 Hz
to 20 kHz)
Uses
Description
Mechanism
Quality
control
 Manufactures of
various concrete types
 check for cracks or
cavities in concrete
slabs with ultrasound
 to ensure that their
concrete are of the
highest quality
 Ultrasound is released from an
emitter at one end of the concrete
slab and
 a sensor is positioned at the other
end to detect the ultrasound
 If the speed of sound recorded is
lower than actual, this means parts
of the concrete contain air
Pre-natal
scanning
 Ultrasound can be
used to obtain images
of inside a body,
 thus is used to
examine development
of a foetus in a
pregnant woman
 Ultrasound pulses are sent into the
body using a trasmitter
 Echoes reflected from any surface
within the body are received
 The time interval is noted to
determine the depth of the
reflecting surface within the body
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SECTION V: ELECTRICITY AND MAGNETISM
Overview
For a long time, electricity and magnetism were seen as independent phenomena. Hans Christian
Oersted, in 1802, discovered that a current carrying conductor deflected a compass needle. This
discovery was overlooked by the scientific community until 18 years later. It may be a chance
discovery, but it takes an observant scientist to notice. The exact relationship between an electric
current and the magnetic field it produced was deduced mainly through the work of Andre Marie
Ampere. However, the major discoveries in electromagnetism were made by two of the greatest
names in physics, Michael Faraday and James Clerk Maxwell.
The section begins with a discussion of electric charges that are static, i.e. not moving. Next, we
study the phenomena associated with moving charges and the concepts of current, voltage and
resistance. We also study how these concepts are applied to simple circuits and household
electricity. Thereafter, we study the interaction of magnetic fields to pave the way for the study of
the interrelationship between electricity and magnetism. The phenomenon in which a current
interacts with a magnetic field is studied in electromagnetism, while the phenomenon in which a
current or electromotive force is induced in a moving conductor within a magnetic field is studied in
electromagnetic induction.
Extracted from CHEMISTRY GCE ORDINARY LEVEL (2014) Syllabus Document
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16. Static Electricity
Content




Laws of electrostatics
Principles of electrostatics
Electric field
Applications of electrostatics
Learning Outcomes
Candidates should be able to:
(a) state that there are positive and negative charges and that charge is measured in
coulombs
Charge
Types
Measurement
 Positive
 Negative
 Charge is measured in coulombs (C)
 For example, one negative electron has a charge of 1.6 x 10-19 C
(b) state that unlike charges attract and like charges repel
Interaction of charges
Combination of charges
Interaction
Unlike charges
Positive-negative
Attract
Like charges
Positive-positive
Repel
Negative-negative
(c) describe an electric field as a region in which an electric charge experiences a force (d)
draw the electric field of an isolated point charge and recall that the direction of the field
lines gives the direction of the force acting on a positive test charge
Term
Definition
Electric field
Region in which an electric charge experiences a force
Electric field lines
Gives direction of the electric field (i.e. direction of the force on a small positive charge)
Electric field of an isolated point charge
Positive charge
Negative charge
Diagram
Field lines
From charge
Towards charge
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(e) draw the electric field pattern between two isolated point charges
Electric field of an isolated point charge
Positive-negative
 Opposite charges attract,
 hence the two charges are linked by field lines
Positive-positive
Negative-negative
 Like charges repel,
 hence no field lines connect the two charges
Electric field of parallel charged plates
(f) show understanding that electrostatic charging by rubbing involves a transfer of
electrons
Experimental method of rubbing (to show electrostatic charging between 2 uncharged materials)
Action
Result
Rub two different
materials against
each other
 Some negatively charged electrons are transferred from one material to the other
 An object becomes negatively charged if it gains electrons and positively charged if it
loses electrons
Ease of loss of electrons between objects
Ease of loss of electrons generally decreases down the following list:
Electron loss
Easiest
Hardest
Object type
Examples
Electron transfer
Transparent object
Glass, Perspex
Smooth, high surface area object
Silk, Fur, Hair, Wool
Opaque object
Ebonite, Rubber, Polyethene
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(g) describe experiments to show electrostatic charging by induction
Experimental method of induction (to show electrostatic charging of a single metal conductor)
#
Action
Result
Diagram
1
To negatively
charge a neutral
conductor, bring a
positively charged
rod near it
 Like charges repel and unlike charges
attract each other
 Thus the positively charged rod leaves an
excess of negative charges at the side of
conductor nearest to the rod and positive
charges at the other side by induction
2
Earth the side of
the conductor with
the positive
charges
Electrons flow from Earth to the conductor to
neutralise the positive charges
3
Remove the Earth,
then the rod
Electron migration causes the rod to be
completely negatively charged
Experimental method of induction (to show electrostatic charging of 2 metal spheres)
#
Action
Result
1
 Let the two conductors (metal
spheres on insulating stands)
touch each other
 Bring a negatively charged rod
near the conductor on the left
 The negatively charged rod induces the charges in the two
conductors,
 repelling the negative charges to the furthest end of the conductor
on the right,
 leaving excess positive charges at the end of conductor on the left
nearest to the rod
2
 Separate the two conductors
far from each other
 Remove the rod


The conductor on the left will be positively charged
while the other on the right will be negatively charged
(h) describe examples where electrostatic charging may be a potential hazard
Potential hazards of electrostatic charging
Lightning
Electrostatic discharge
 Friction between water molecules in thunderclouds and
air molecules in the air cause the thunderclouds to be
charged
 Air is ionised when the charge on the thunderclouds
becomes large enough
 The ionised air provides a conducting path for the huge
quantity of electric charge on the thunderclouds to the
nearest object or sharpest object on the ground via
lightning strikes during a sudden discharge
 Electrostatic charging is thus a potential hazard for
people when they are out in an open field or under a tall
tree during a thunderstorm, especially in the absence of
a lightning conductor
56
Friction between objects may cause excessive
charges to build up in them:
 Friction between
tyres of a truck and
the road can result
in sudden
discharge
 Sparks and
subsequent ignition
of flammable items
on the truck may
occur when this
happens
 Friction between
electronic equipment
(e.g. computer
boards, hard drives)
and other objects can
result in electrostatic
discharges over time
 These electronic
equipment may be
damaged as this
happens
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(i) describe the use of electrostatic charging in a photocopier, and apply the use of
electrostatic charging to new situations
Components of the photocopier
Photoreceptor drum
Laser assembly
Toner
Fuser
 Metal drum roller
 Coated with a photoconductive layer
 Laser
 Movable mirror
 Lens
Fine negatively charged powder
Heat source
Electrostatic charging in a photocopier
#
Action
Result
1
A photoreceptor drum is rotated
near a highly positively charged
corona wire
The photoreceptor drum
becomes positively charged
2
The laser beam is cast over a
page of the original document
through a lens onto the
photoreceptor drum
 Areas of photoconductive
layer on the drum surface
that are exposed to the laser
is discharged
 Negatively charged toner is
then attracted to the
remaining positively charged
areas
3
 Toner on the drum is
transferred to the paper
 Paper is heated by the fuser
Toner power melts onto the
paper surface, affixing itself
permanently on the surface
Diagram
Note: A laser printer operates differently from a photocopier, although both rely on electrostatic charging
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17. Current of Electricity
Content




Conventional current and electron flow
Electromotive force
Potential difference
Resistance
Learning Outcomes
Candidates should be able to:
(a) state that current is a rate of flow of charge and that it is measured in amperes
Term
Definition
Measurement
Curren
t
A measure of the rate of flow
of electric charge through a
cross section of a conductor
 Ammeter
 Connected in series
Formula
 Current 
 I
SI units
Charge
I
Q
t
A
C
s
Time
Q
t
(b) distinguish between conventional current and electron flow
Conventional current flow
Flow of positive charges from a
positively charged end to a
negatively charged end (i.e. current)
Electron flow
Combined flow of charges
Flow of electrons from a
negatively charged end to a
positively charged end
(c) recall and apply the relationship charge = current × time to new situations or to solve
related problems
Term
Definition
Formula
Charge
 When an object is charged, it is electrified
 Equals to the product of current and time
 Charge  Current  Time
Q
I
t
 Q  It
C
A
s
58
SI units
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(d) define electromotive force (e.m.f.) as the work done by a source in driving unit charge
around a complete circuit
Term
Definition
Measurement
Formula
Electromotive
force
Work done by
an electrical
source in
driving a unit
charge round a
complete circuit
 Voltmeter
 Connected in parallel across
the positive and negative
ends of the electrical source
 E.m.f.
Electrical energy converted

Charge
  
SI units
W
Q

W
Q
V
J
C
(e) calculate the total e.m.f. where several sources are arranged in series
Example of circuit of 3 dry cells as sources
Diagram
Readings recorded
Total e.m.f.
Voltmeter
Dry cell e.m.f.
1
1.5 V
2
1.5 V
3
3V
Total e.m.f. of all dry cells
 Sum of all e.m.f. of each dry cell
 1.5  1.5  3
6V
(f) state that the e.m.f. of a source and the potential difference (p.d.) across a circuit
component is measured in volts (g) define the p.d. across a component in a circuit as the
work done to drive unit charge through the component
Term
Potential
difference
Definition
Measurement
Amount of energy
converted to other forms of
energy when one coulomb
of positive charge passes
between 2 reference points
 Voltmeter
 Connected in
parallel across
the 2 points
Formula
SI units
 Potential difference
Electrical energy converted

Charge
 V 
W
Q

Q
t
A
C
s
(h) state the definition that resistance = p.d. / current (i) apply the relationship R = V/I to new
situations or to solve related problems
Term
Definition
Factors
Resistance
Ratio of the
potential
difference across
a component to
the current flowing
through it
 Length
 Cross
sectional
area
 Type of
material
Formula 1
 Resistance 
V
 R
I
59
SI units
Potential difference
R
V
I
Ω or ohm
V
A
Current
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(j) describe an experiment to determine the resistance of a metallic conductor using a
voltmeter and an ammeter, and make the necessary calculations
Experiment to determine resistance of a metallic conductor
Method
Calculation
 Connect a dry cell, rheostat and ammeter in series to
the metallic conductor
 In the same circuit, connect a voltmeter in parallel to the
metallic conductor
 Vary the resistance of the rheostat and and note down
values of V (reading of voltmeter) and I (reading of
ammeter) for at least 5 sets of readings
By Ohm’s law, resistance R will be equivalent to
the voltage divided by current
R
V
I
Hence, plot a graph of V against I to find the
gradient of the graph, R
(k) recall and apply the formulae for the effective resistance of a number of resistors in
series and in parallel to new situations or to solve related problems
Differences
Resistors in series
Resistors in parallel
Circuit diagram
where R1 and R2 are
the resistances of the
resistors respectively
Formula for
effective resistance
for the circuit above
Reff  R1  R2
where R1 and R2 are
the resistances of the
resistors respectively

1
1
1


Reff R1 R2
 1
1 

 Reff  

 R1 R2 
Nature of
effective resistance
Reff  R1
Reff  R1
Reff  R2
Reff  R2
General formula for
effective resistance
Reff  R1  ...  Rn
Reff
1
 1
1 

 ... 

Rn 
 R1
60
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(l) recall and apply the relationship of the proportionality between resistance and the length
and cross-sectional area of a wire to new situations or to solve related problems
Differences
Resistance of material
Resistivity of material
Main formula
R
Unit
Ω
Ωm
Nature
 Resistance increases as length increases
 Resistance increases as cross-sectional area decreases
Independent of length & crosssectional area
V
I
Term

Formula 2
Resistance
 Resistance  Resistivity 
RA
l
SI units
Wire length
Relationships
R

l
A
Ω
Ωm
m
m2
Cross-sectional area
l
 R  
A
 Rl
1
 R
A
(m) state Ohm’s Law
Law
Ohm’s
Law
Definition
Relationship
Current passing through a metallic conductor is directly proportional to the
potential difference across its ends, provided the physical conditions are
constant
 I V
V
 R  constant

I
(n) describe the effect of temperature increase on the resistance of a metallic conductor
Effect of temperature increase on resistance
Resistance of metallic conductor increases
Explanation
 Particles in metallic conductor gain kinetic energy and
vibrate faster
 This causes electrons moving through the conductor to
slow down
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(o) sketch and interpret the I/V characteristic graphs for a metallic conductor at constant
temperature, for a filament lamp and for a semiconductor diode
Non-ohmic conductors (examples)
Differences
Ohmic conductors
Filament lamp
Purpose
Semiconductor diode
N.A.
Provides light indoors
and at night
Allows current to flow in only one direction
(i.e. forward direction) through the circuit
Ohmic conductors
follow Ohm’s law
The filament lamp is a
non-ohmic conductor
The semiconductor diode is another nonohmic conductor
Gradient V/I is
constant since I is
directly proportional
to V
 Gradient V/I
increases as V
increases across the
lamp
 This is because as
p.d. increases, the
current increases
less than
proportionately
 This indicates that
resistance of the
lamp increases as
p.d. increases
 Gradient V/I decreases as V increases
from zero
 This is because as p.d. increases, the
current increases more than
proportionately
 This indicates that resistance decreases
when p.d. in the forward direction
increases, allowing a relatively large
current, I, to flow through
I/V sketch
V/I sketch
(invert the I/V
sketch along
the line V=I)
Interpretation
62
 Gradient V/I is very large as V increases
to zero
 This indicates that resistance is very high
when p.d. in the reverse direction
increases
 Almost no current flows in this reverse
direction
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18. D.C. Circuits
Content




Current and potential difference in circuits
Series and parallel circuits
Potential divider circuit
Thermistor and light-dependent resistor
Learning Outcomes
Candidates should be able to:
(a) draw circuit diagrams with power sources (cell, battery, d.c. supply or a.c. supply),
switches, lamps, resistors (fixed and variable), variable potential divider (potentiometer),
fuses, ammeters and voltmeters, bells, light-dependent resistors, thermistors and lightemitting diodes
Symbols of power sources
Cell
Battery
D.C supply
Symbols of common components
A.C. supply
Lamp
Bell
Switch
Fuse
Symbols of resistors and diodes
Fixed resistor
Variable resistor
Symbols of measurement devices
Ammeter
Thermistor
Light-dependent resistor
Light-emitting diode
Symbols of other devices
Voltmeter
Potentiometer
Circuit diagram example
Experimental setup
Circuit diagram
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(b) state that the current at every point in a series circuit is the same and apply the principle
to new situations or to solve related problems (c) state that the sum of the potential
differences in a series circuit is equal to the potential difference across the whole circuit
and apply the principle to new situations or to solve related problems (d) state that the
current from the source is the sum of the currents in the separate branches of a parallel
circuit and apply the principle to new situations or to solve related problems (e) state that
the potential difference across the separate branches of a parallel circuit is the same and
apply the principle to new situations or to solve related problems
Circuit
Current in circuit
Potential difference across whole circuit
Series
Same at every point
Sum of potential differences in circuit
Parallel
Sum of currents in the separate branches
Same as across the separate branches
(f) recall and apply the relevant relationships, including R = V/I and those for current,
potential differences and resistors in series and in parallel circuits, in calculations involving
a whole circuit
Term
Resistance
Formula
 Resistance 
SI units
Remarks
R
V
I
Ω or ohm
V
A
Potential difference
Current
V
 R
I
When the circuit has resistors in
both the series and parallel
arrangement, calculate effective
resistance of the ones arranged
in parallel first
(g) describe the action of a variable potential divider (potentiometer)
Purpose of potentiometer
A potentiometer is able to
divide the supply voltage in
any ratio that is required by
varying resistance and
using the formula V  IR
Action of potentiometer
 The potentiometer is made of a conducting slider in contact with a resistor
with fixed cross-sectional area
 By sliding the slider along the resistor, the length of the resistance material
that the current of the circuit has to flow through can be varied
 Since R  l , resistance of the circuit increases when the length increases
 As V  IR , potential difference across the circuit can thus be adjusted
between zero and the maximum supply voltage
(h) describe the action of thermistors and light-dependent resistors and explain their use as
input transducers in potential dividers (i) solve simple circuit problems involving
thermistors and light-dependent resistors
Input tranducers
Transducers that convert non-electrical energy to electrical energy
Differences
Thermistor
Light-dependent resistor
Device
A device whose resistance decreases
when temperature increases
A device whose resistance decreases as the
amount of light shining on it increases
Applications
 Temperature control
 Temperature measurement in fire alarms
Under bright lighting, the LDR would have very
low resistance, and vice versa
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19. Practical Electricity
Content



Electric power and energy
Dangers of electricity
Safe use of electricity in the home
Learning Outcomes
Candidates should be able to:
(a) describe the use of the heating effect of electricity in appliances such as electric kettles,
ovens and heaters
Use of electricity
Description of use
 Heating effect
 Used in heating
appliances like
electric kettles,
ovens and
heaters
 Heating elements in heating appliances musthave high resistivity (high resistance
per unit length of material of constant cross-sectional area) and must be able to
withstand high temperatures
 When current passes through these elements (e.g. nichrome) in heating appliances
when, much heat is generated
 By varying current passing through, heat produced by Joule heating can be
effectively controlled
(b) recall and apply the relationships P = VI and E = VIt to new situations or to solve related
problems
Term
Formula
SI units
Electrical energy
 Energy  Current  Voltage  Time
 E  VIt
Electrical power
 Power  Current  Voltage
 P  VI
Derivation of formulae
E
V
I
t
J
V
A
s
P
V
I
W
V
A
P  VI is derived from:
Q
 I   Q  It
t
W
 V
 W  VQ  VIt
Q
W VQ VIt


 VI
 P
t
t
t
(c) calculate the cost of using electrical appliances where the energy unit is the kW h
Term
Electrical energy
Cost of using electrical appliances
Formula
 Energy  Power  Time
SI units
E
P
t
 E  Pt
kWh
kW
h
Cost  Energy  Rate
Cost
Energy
Rate
¢
kWh
¢ per kWh
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(d) compare the use of non-renewable and renewable energy sources such as fossil fuels,
nuclear energy, solar energy, wind energy and hydroelectric generation to generate
electricity in terms of energy conversion efficiency, cost per kW h produced and
environmental impact
Energy
source
Energy conversion
Renewability
Source
Efficiency
Reasons
Fossil fuels
Nonrenewable
Chemical
potential energy
30-40%
Good distribution system of electricity from
fossil fuels in many countries
Nuclear
energy
Nonrenewable
Nuclear energy
30-40%
Only a small amount of uranium is needed
to generate a large amount of energy
Solar energy
Renewable
Light energy
10-20%
Efficiency is high only when there is
daylight and minimal cloud cover
Wind energy
Renewable
Kinetic energy
30-40%
Wind direction and speed varies
Hydroelectric
generation
Renewable
Gravitational
potential energy
90%
Water flow
 is concentrated
 can be easily controlled
Non-renewable energy sources
Energy source
Cost per kWh produced
Environmental impact
Fossil fuels
High costs due to
 lower availability of fossils
 higher energy demand
Gases produced as a result of the combustion of fossil
fuels are usually pollutive (e.g. may combine with rain to
form acid rain)
Nuclear energy
Radioactivity, when leaked,
is very expensive to clean up
 Radioactivity, when leaked, is difficult and expensive to
clean up
 Threat to safety as it can cause mutations to humans
Non-renewable energy sources
Energy
source
Cost per kWh produced
Environmental impact
Cons
Pros
Cons
Pros
Solar energy
High costs involved in manufacturing
Cost of fuel (i.e.
sunlight) is free
Clean
energy
Large areas must be
cleared to make space
for the solar panels
Wind energy
Falling costs due to technological
improvements
Cost of fuel (i.e.
wind) is free
Clean
energy
Spinning turbines
cause noise pollution
Hydroelectric
generation
High costs involved in
 constructing the dam and power
plant together
 maintanence in clearing of slit
blocking water flow behind the dam
N.A.
Clean
energy
Dams built may
disrupt ecosystems
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(e) state the hazards of using electricity in the following situations: (i) damaged insulation (ii)
overheating of cables (iii) damp conditions
Hazards of using electricity
Damaged insulation
Overheating cables
Damp conditions
 If one touches the
exposed live wire,
electrons flow
through the body to
Earth
 May cause severe
electric shock, injury
and death
 Many electrical appliances used
concurrently
 Total power drawn from the mains
supply may be very large
 Wires not thick enough will produce
high resistance producing more heat
 Cable becomes overheated to result
in a fire
 Water is a good conductor of electricity
 Provides conducting path for large
current to flow
 Since the human body has very low
resistance
 Human body is electrocuted when
current of more than 50 mA flows
through
(f) explain the use of fuses and circuit breakers in electrical circuits and of fuse ratings
Safety devices
Use of fuses
Use of circuit breakers
 Internal wire melts when excessive current
flows through
 The fuse rating on a fuse indicates the
maximum current that can flow through it
before the fuse starts to melt
 Protects electrical appliances from damage
 Ensures safety of the user
 Switches off electrical supply in a circuit when there is
overflow of current
 The miniature circuit breaker trips when there is a fault in
the circuit
 The Earth leakage circuit breaker switches off all circuits
in the house when there is an Earth leakage of more than
25 mA from the live to earth wire
Must be replaced
May be reset after problem is resolved
(g) explain the need for earthing metal cases and for double insulation
Safety precautions
Need for earthing metal cases
Need for double insulation
 In case the live wire comes into contact with the metal casing
by accident, someone who touches the casing will be
electrocuted
 To ensure the safety of the user, the metal casing is earthed
 An earth wire is connected to casing to conduct current away
to the earth directly instead of going through the human body
 Appliances with plugs of two pins have
no earth wire
 Double insulation insulates electric
cable from internal components and
insulates the internal components from
external casing of these appliances
(h) state the meaning of the terms live, neutral and earth
Term
Meaning
Live
Wire which delivers electrical energy to appliance at high voltage, allowing the appliance to
function
Neutral
Wire kept at zero volts which forms a current flow path back to the supply to complete the circuit
Earth
Low resistance wire which connects the metal casing of an equipment to Earth, earthing the
appliance continuously to ensure electrical safety of the user in case the metal casing becomes live
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(i) describe the wiring in a mains plug
Wiring in a mains plug
Description
The cable is made up of 3 wires: the live, netural and earth wires
Wire
Colour
Explanation
Live
Brown
 Wired into the pin on the right
 A fuse is placed between the live
terminal and the live pin in the circuit
 The fuse breaks the circuit if too
much current flows
Neutral
Blue
Wired into the pin on the left
Earth
Green and
yellow stripes
Wired into the pin on the top
(j) explain why switches, fuses, and circuit breakers are wired into the live conductor
Wiring of safety devices
Switches, fuses and
circuit breakers are wired
into the live conductor
Explanation
 Switches, fuses and circuit breakers work by breaking an electric circuit
 By being wired into live conductor, it will be able to prevent current flow from
flowing into the conductor at all
 Damage to the conductor is prevented
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20. Magnetism
Content



Laws of magnetism
Magnetic properties of matter
Magnetic field
Learning Outcomes
Candidates should be able to:
(a) state the properties of magnets
Properties of magnets
#
Aspect
Description of property
1
Magnetic poles
Have magnetic poles, where the magnetic effects are strongest
2
Alignment when suspended freely
Align themselves to the north and south poles of the Earth when
suspended freely
3
Interaction with magnetic materials
Attract magnetic materials, which are iron, steel, nickel and cobalt
4
Interaction with other magnets
Repel from another magnet with like poles and attracts magnets
with unlike poles
5
Identification
Can only be identified by repulsion
(b) describe induced magnetism
Meaning of induced magnetism
Mechanism of induced magnetism
Magnetic materials are magnetised temporarily when
near or in contact with a permanent magnet
Magnetic field from the magnetic material aligns
with the domains of the permanent magnet
(c) describe electrical methods of magnetisation and demagnetisation
Electrical magnetisation
 Magnetic object placed in a solenoid (a
cylindrical coil of insulated copper wires
carrying currents)
 Strong magnetic field produced when
direct electric current, D.C., flows through
the solenoid
 The magnetic field produced will
magnetise the magnetic object
 Field is determined by right-hand grip rule:
Electrical demagnetisation
 Magnet is inserted into a solenoid and an alternating
current, A.C., flows through it
 When the magnet is withdrawn slowly from the coil, the
magnet is constantly being magnetised in opposite
directions by the alternating current
 The domains in the magnet will be arranged different
directions, cancelling their magnetic effect
 Magnetic field around the solenoid causes the magnet to
lose its magnetism
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Properties of magnetised objects
Properties of demagnetised objects
 Have properties of a magnet
 Magnetic domains point in the same direction
 Do not have any properties of a magnet
 Magnetic domains point in random directions
 No resultant magnetic effect present
(d) draw the magnetic field pattern around a bar magnet and between the poles of two bar
magnets (e) describe the plotting of magnetic field lines with a compass
Examples of magnetic field patterns
Method to draw magnetic field pattern
 The magnetic field pattern of
a single permanent magnet is
shown on the right
 Field lines travel from N to S
outside the magnet
 Field lines travel from S to N
through the magnet
 Place the bar magnet at centre of piece
of paper so that its North pole faces north
and its South pole faces south
 Place a compass near one pole of the
magnet and mark with dots the positions
of the North and South ends of the
compass needle, labeling them Y and X
respectively
 Move the compass such that the south
end of the compass needle is exactly
over Y
 Mark the new posltlon of the north end
with a third dot labeled Z
 Repeat the above until the compass
reaches the other pole of the bar magnet
 Join the series of dots with a curve and
this will give a field line of the magnetic
field
 Repeat for more field lines and indicate
the direction of the lines
(f) distinguish between the properties and uses of temporary magnets (e.g. iron) and
permanent magnets (e.g. steel)
Differences
Temporary magnets
Permanent magnets
Example
Magnetised iron
Magnetised steel
Nature
Soft magnetic material
Hard magnetic material
Ease of magnetisation
Easily magnetised
Hard to magnetise
Retainment of magnetism
Do not easily retain magnetism
Easily retains magnetism
Uses
 Electromagnet
 Transformer core
 Shielding
 Magnetic door catch
 Moving-coil ammeter
 Moving-coil loudspeaker
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21. Electromagnetism
Content




Magnetic effect of a current
Applications of the magnetic effect of a current
Force on a current-carrying conductor
The d.c. motor
Learning Outcomes
Candidates should be able to:
(a) draw the pattern of the magnetic field due to currents in straight wires and in solenoids
and state the effect on the magnetic field of changing the magnitude and/or direction of the
current
Scenario
Current in
solenoids
Case
Patterns of magnetic field due to current
Clockwise
Anti-clockwise
Front-view
 The arrows represent the direction
of current
 A cross indicates magnetic field
lines travelling inwards into the
plane (away from you)
 The arrows represent the direction of
current
 A dot indicates magnetic field lines
travelling outwards from the plane
(towards from you)
Representations of arrows and
cross/dot can be interchanged (i.e.
cross/dot can represent direction of
current, arrows represent magnetic
field)
Representations of arrows and
cross/dot can be interchanged (i.e.
cross/dot can represent direction of
current, arrows represent magnetic
field)
Side-view
Currents in
straight
wires
Case
Current in the same direction
Current in opposite directions
Magnetic
field
Illustration
Remarks
The most common rule used here is the right hand grip rule [which has been illustrated in
learning outcome 20(c)]
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(b) describe the application of the magnetic effect of a current in a circuit breaker
Magnetic effect of current
 When current is increased to a high level, the solenoid of circuit breaker gains magnetism and becomes a
strong electromagnet
 Stronger magnetic fields produce a force that enables the solenoid to attract iron armature connected in
the circuit, breaking the circuit
When current is within the limit
When there is a short circuit or overload
 The solenoid magnetic field is not
strong enough to attract the soft iron
latch
 The interrupt point remains closed
and current flows normally through
the circuit
 A sudden surge of current is present
 Solenoid gains magnetism and becomes a strong electromagnet
due to larger current
 It is able to attract the soft iron latch and release the spring
 The safety bar is pushed outward
 The interrupt point opens and current is cut off
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(c) describe experiments to show the force on a current-carrying conductor, and on a beam
of charged particles, in a magnetic field, including the effect of reversing (i) the current (ii)
the direction of the field
Current-carrying conductor in magnetic field
Current-carrying
conductor
Magnetic field
from magnets
Explanation
 In this case, current that flows outwards in a straight line instead
of in a solenoid will cause magnetic field lines to travel anticlockwise
 Field lines at the top of the wire flow in the same direction as
the magnetic field from the magnets
 On the other hand, field lines at the bottom of the wire flow in
the opposite direction as the magnetic field from the magnets
Combined diagram
Explanation
Experimental setup
 As a result, when the conductor
is placed in the magnetic field
from the magnets, the magnetic
field produced above the wire
will be much stronger than the
magnetic field produced below
the wire
 The strong resultant magnetic
field at the top causes a force to
push the conductor downwards
Remarks
 The most common rule used here is Fleming’s left-hand rule [which will be illustrated in the next learning
outcome]
 This rule is used only when current from a source causes a force to be produced
Beam of charged particles in magnetic field
Case
Positive charge
Negative charge
Force
direction
A cross indicates magnetic field lines travelling inwards into the plane (away from you)
Remarks
 The most common rule used here is Fleming’s left-hand rule [which will be illustrated
in the next learning outcome]
 This rule is used only when current from a source causes a force to be produced
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(d) deduce the relative directions of force, field and current when any two of these
quantities are at right angles to each other using Fleming’s left-hand rule
Fleming’s left-hand rule
Function
 The relative directions
of force, field and
currents for both a
current-carrying
conductor and a beam
of charged particles
illustrated above can
be found using your
left hand by Fleming’s
left-hand rule
 This rule is used only
when current from a
source causes a force
to be produced
Illustration using current-carrying conductor
F
B
Legend
Finger
Direction
Symbol
1
Force
F
2
Magnetic
field
B
3
Current
I
I
(e) describe the field patterns between currents in parallel conductors and relate these to
the forces which exist between the conductors (excluding the Earth’s field)
Differences
Case
Magnetic
field
Currents in parallel conductors
Current in the same direction
Current in opposite directions
 The magnetic field lines in between
the conductors (both currents
travelling inwards) are in opposite
directions, cancelling out each other
 This causes the magnetic field to be
stronger in all other areas, pushing
the conductors towards each other
 The magnetic field lines in between the
conductors (currents in opposite
directions) are in the same direction,
which intensifies the magnetic field
present there
 Since the magnetic field is now
stronger in between the conductors
than all the other areas, the conductors
are pushed away from each other
Respective
Combined
Illustration
Explanation
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(f) explain how a current-carrying coil in a magnetic field experiences a turning effect and
that the effect is increased by increasing (i) the number of turns on the coil (ii) the current
Turning effect due to current-carrying coil in a magnetic field
Case
Due to pivot
Due to axis
 As current through the thick, stiff copper
wire and magnetic field are perpendicular
to each other,
 by Fleming’s left hand rule,
 a force is produced that pushes the wire
away from the powerful permanent magnet
 Since the bent stiff copper or brass wire
acts as a pivot,
 a perpendicular distance between the pivot
and the force is present,
 thus a clockwise turning effect  is also
produced
 As current through the coil and magnetic
field are perpendicular to each other at
both sides,
 by Fleming’s left hand rule,
 a force is produced
 The coil at the side nearer to the N pole is
pushed forward as current travels upwards
 whereas the coil at the side nearer to the
S pole is pushed backward as current as
travels downwards
 This produces an anti-clockwise turning
effect  about a central axis (dotted lines)
Diagram
Explanation
Increasing force of the turning effect
By increasing number of turns of coil
By increasing current
 Each loop of wires produces its own magnetic field
 Since the magnetic field strength is the sum of the field lines,
 more lines will produce a stronger magnetic field and hence
greater force
 A larger current will produce a greater
concentration of field lines
 A strong field will lead to a larger force
(g) discuss how this turning effect is used in the action of an electric motor
Uses of electrically produced turning effects
Differences
D.C. motors
A.C. motors
Examples
 Toy cars
 DVDs
 Hard disks
 Electric fans
 Hair dryers
 Washing machines
Reason
Rotation in a fixed direction is
required
Alternating rotation in the clockwise and anticlockwise
directions is required
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(h) describe the action of a split-ring commutator in a two-pole, single-coil motor and the
effect of winding the coil on to a soft-iron cylinder
Split-ring commutator
Diagram
Description
 Constant magnetic field by two permanent magnets interacts with the
magnetic field in the U-shaped coil due to the direct current
 Based on Fleming’s left hand rule, the wires at each side of the coil
experience an equal but opposite force
 The turning effect created by the two forces causes the coil to rotate
continuously in the same direction
Split-ring commutator
Main components
Function of components
Two permanent
magnets
 N and S poles of both magnets face each other
 Provides the magnetic field (B)
D.C. circuit
Provides the direct current flow (I)
Pair of carbon
brushes
 Maintains continuous contact between the stationary external D.C. circuit and the
split-ring commutator, which is linked to the rotating coil
 Ensures that the circuit is never broken during rotation
Split-ring
commutator
 Placed between the coil and carbon brushes
 Reverses direction of current in the coil every half a turn by the coil
 Ensures the coil rotates in the same (clockwise) direction thoroughout (if it is a
continuous ring commutator, the coil will rotate in alternate directions instead)
Soft-iron cylindrical
core
Winding the coil on to a soft-iron cylindrical core concentrates the magnetic field,
increasing magnetic field strength
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22. Electromagnetic Induction
Content




Principles of electromagnetic induction
The a.c. generator
Use of cathode-ray oscilloscope
The transformer
Learning Outcomes
Candidates should be able to:
(a) deduce from Faraday’s experiments on electromagnetic induction or other appropriate
experiments: (i) that a changing magnetic field can induce an e.m.f. in a circuit (ii) that the
direction of the induced e.m.f. opposes the change producing it
Electromagnetic induction
Laws
Faraday’s law
Lenz’s law
Definition
 E.m.f. generated in a conductor
 is proportional to the rate of
change of the magnetic lines of
force linking with the circuit
Principles
Changing magnetic field can
induce an e.m.f. in a circuit
Direction of the induced e.m.f. opposes the
change producing it
 Changing magnetic field produces
a continuously changing magnetic
flux linking with the secondary
solenoid
 Since Faraday’s law states e.m.f.
generated in a conductor
 is proportional to the rate of
change of the magnetic lines of
force linking with the circuit,
 e.m.f. will be induced, producing a
current that will allow power to be
transmitted
 Since Lenz’s law states direction of the induced
e.m.f.
 and hence the induced current in a closed circuit
 is always such as to oppose the change in the
applied magnetic field,
 the drawing in of a north pole of a magnet into a
solenoid
 (or drawing out of a south pole)
 will produce a north pole at the end of the solenoid
nearest to the magnet
 as the solenoid will repel the magnet,
 and vice versa
Description
of principle
 Direction of the induced e.m.f.
 and hence the induced current in a closed circuit
 is always such as to oppose the change in the
applied magnetic field
Experiments
Opposite direction
of magnetic field
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Opposite direction
of magnetic field
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(iii) the factors affecting the magnitude of the induced e.m.f.
Factors to increase the magnitude of induced e.m.f.
Increased number of
turns of coil
Increased strength
of magnet
 Increased number
of turns of coil
 since more
magnetic lines of
force
 produce stronger
magnetic field and
hence greater force
 Increased strength
of magnet
 will produce a
stronger magnetic
field
 and hence greater
force
Increased speed of
movement of magnet or coil
 Increased speed of
movement of magnet or coil
in displacement to each
other
 will increase rate of change
of magnetic field lines
 and frequency of the emf
against time graph
Addition of a soft iron
core
 Addition of a soft iron
core
 since it becomes a
magnet within the field
lines
 such that it increases
the concentration of
magnetic field lines
The above factors increase the rate of change of magnetic flux linking the circuit and hence emf by
Faraday’s law
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(b) describe a simple form of a.c. generator (rotating coil or rotating magnet) and the use of
slip rings (where needed) (c) sketch a graph of voltage output against time for a simple a.c.
generator
A.C. generator [read ‘Remarks’ to understand Fleming’s right hand rule first]
Diagram of generator
Diagram of electrical load
A.C. voltage from the generator may
be received by an electrical load
(e.g. light bulb) connected to it
Graph of induced e.m.f. / time
induced e.m.f. / mV
Description of action of A.C. generator
Use of slip rings
 Keeps the electrical load in a fixed
position (instead of rotating
continuously)
 Maintains continuous contact with
the carbon brushes when the coil is
rotating
 This ensures that the alternating
current induced in the coil is
transferred to the external circuit
 Electromagnetic device which transforms mechanical energy into
electrical energy
 Coil is rotated (usually with a handle) about an axis between the
two opposing poles of a permanent magnet
 When rectangular coil is parallel to the magnetic lines of force,
both sides of the coil cuts through the magnetic field lines at the
greatest rate, hence induced e.m.f. is maximum
 The next time rectangular coil becomes parallel to the magnetic
lines of force, current will be reversed and thus induced e.m.f. will
be minimum
 When rectangular coil is perpendicular to the magnetic lines of
force, it is not cutting through the magnetic field lines
 The rate of change of magnetic lines of force at this instance is
zero, hence no e.m.f. is induced
Remarks
 The most common rule used here is Fleming’s right-hand rule, which is used when the application of a
force causes current to be produced
 This is as opposed to Fleming’s left-hand rule, which is used only when current from a source causes a
force to be produced
B
F
I
Factors affecting graph of induced e.m.f. against time
Number of coils
Strength of magnet
Speed of rotation
When number of coils doubles,
 amplitude doubles,
 frequency doubles and
 wavelength halves
When strength of magnet doubles,
 only amplitude doubles
When speed of rotation doubles,
 only amplitude doubles
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(d) describe the use of a cathode-ray oscilloscope (c.r.o.) to display waveforms and to
measure potential differences and short intervals of time (detailed circuits, structure and
operation of the c.r.o. are not required)
Cathode-ray oscilloscope
Diagram for understanding only
Mechanism for understanding only
 The electron gun emits a cathode-ray (i.e. beam of electrons)
through thermonic emission
 The electron beam then strikes the flourescent screen,
forming a bright spot
 The deflection system of X and Y plates controls the position
the electrons strike on the fluorescent screen
 It does so by varying the voltage across the X and/or Y plates
Uses
Component required to function
Measure potential
differences
Voltage to be measured is applied to the Y-plates via the Y-input terminals
Display
waveforms of
potential
differences
 The voltage measured is displayed on the fluorescent screen
 Time-base is switched off to show a fixed voltage or the amplitude of varying voltage
 Time-base is switched on to check for varying voltage or its frequency and wavelength
Measure short
time intervals
 The device used to measure short time intervals between occurrences (e.g.
microphone, when a sound is received at intervals) transmits the information received
into voltage
 The voltage display shown represents the short time intervals to be measured
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(e) interpret c.r.o. displays of waveforms, potential differences and time intervals to solve
related problems
Time base / Hz
Y-gain / V
 Signals being measured will have a wide range of frequencies
 Adjusting the time base of input allows us to view the signals to a
appropriate range on the screen
Examples
 The gain determines sensitivity of
oscilloscope
 Adjusted to measure the voltage
Example 1
Example 2
Example 3
Example 4
2V
-4 V
20 V
-20 V
1 V/div
2 V/div
5 V/div
5 V/div
Line is produced
2/1 = 2 div above
Line is produced
-4/2 = 2 div below
Normal sine curve
20/5 = 4 div
Inverted sine curve
20/5 = 4 div
A.C. Input
Not A.C. (i.e. 0 Hz)
Not A.C. (i.e. 0 Hz)
50 Hz
25 Hz
Time base
25 Hz
25 Hz
25 Hz
25 Hz
0/25 = 0 Cycles
0/25 = 0 Cycles
50/25 = 2 Cycles
50/25 = 1 Cycle
Input
Y-gain
Gain-input
relationship
Cycles
Graph
Graph when
time base is
turned off
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(f) describe the structure and principle of operation of a simple iron-cored transformer as
used for voltage transformations
Simple iron-cored transformer
Structure
Principle
 Primary coil is
wound on one
side of laminated
soft iron core and
secondary coil on
the other side
with different
number of turns
 The lamination
reduces heat loss
due to eddy
currents in the
soft iron core
 Applied alternating voltage at primary
coil sets up changing magnetic field
passing through soft core to the
secondary coil
 Since Faraday’s law states e.m.f.
generated in a conductor is proportional
to rate of change of magnetic lines of
force linking with the circuit,
 alternating current at the secondary coil
produces a changing magnetic field
(based on the turns ratio) which
induces e.m.f. by electromagnetic
induction
(g) recall and apply the equations VP / VS = NP / NS and VPIP = VSIS to new situations or to
solve related problems (for an ideal transformer)
Term
Turns ratio
Power for transformers
of 100% efficiency
Equations

Primary input voltage
Number of turns in primary coil

Secondary input voltage Number of turns in secondary coil

VP NP

VS NS
 Power  Primary input voltage  Current in primary coil
 Secondary input voltage  Current in secondary coil
 P  VP IP  VSIS
Power for transformers
of less than 100% efficiency
 Secondary input voltage  Current in secondary coil
 Efficiency  Primary input voltage  Current in primary coil
 VSIS  Efficiency VP IP
(h) describe the energy loss in cables and deduce the advantages of high voltage
transmission
Energy loss in cables
Advantages of high voltage transmission
 Energy loss is due to Joule heating as the product of
time, square of current flow and resistance of cables
 A decrease of either current flow or resistance of
cables or both will decrease energy loss
 Having increased voltage will reduce current flow but
increase insulation costs
 Having thick cables will reduce resistance but
increase construction costs
 As output power is the product of voltage and
current, increased voltage will reduce current
flow greatly
 Since Joule heating is the product of the square
of current flow and resistance of cables
 Power loss in the form of heat is thus
decreased, allowing more power to be
transmitted to households
-EndNotice
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