IGCSE Physics
Volume, Density and Mass
Volume (cm3) – the amount of space an object occupies
How to measure volume:



For Liquids – use measuring cylinder and read the volume directly
For Regular Solids – calculate using the objects measurements:
o Cuboid: height x width x length
o Sphere: 4/3 x x radius3.
o Cylinder: x radius2 x height
For Irregular Solids – use the displacement method
Displacement method – place a selection of water in a measuring cylinder and measure the
volume. Then add the object into the water and measure it again. The volume of the object
is the difference in volumes. E.g.
Initial Volume = 30cm3
Final Volume = 40cm3
40cm3 – 30cm3 = 10cm3
Object Volume = 10cm3
Density (g/cm3) – mass per unit of volume
Relative Density – the ratio between the density of that substance and the density of water.
It has no limit.
Mass (g) – a measure of the amount of matter present in an object as well as the
characteristic which resists change in motion
m
The calculation of volume is volume =
The calculation of density is density =
The calculation of mass is mass = density x volume
Density of air – 1.225 kg/m3
Density of water – 1000 kg/m3
ρ
V
Mechanics – the study of energy and forces and their effect on material bodies
Kinematics – the study of motion
Dynamics – the cause of motion
Scalars – physical quantity that is fully defined by an amount (magnitude) and a unit e.g.
time, distance, temperature, speed, mass, pressure, energy, volume, density
Vectors – physical quantity that is fully defined by an amount, a unit and a direction. e.g.
force, displacement, velocity, weight, acceleration, momentum
Speed (m/s) – the rate at which distance changes over time
Distance (m) – the total length of travel irrespective of direction of motion
The calculation of speed is speed =
d
The calculation of time is time =
s
The calculation of distance is distance = speed x time
t
The calculation of average speed is average speed =
Velocity (m/s) – the rate, at which displacement changes over time, it has a direction
Displacement (m) – how far something has moved from its starting position
disp
The calculation of velocity is velocity =
v
The calculation of time is time =
t
The calculation of displacement is displacement = time x velocity
Acceleration (m/s2) – the rate at which velocity changes
The calculation of acceleration is acceleration =
–
The calculation of an average velocity is average velocity =
We find the average velocity when the acceleration in a time period is not constant
acceleration
.
Motion Graphs
Distance/Time
Velocity/Time
Shown on Graph
Velocity
Area under line
Acceleration
Stationary
Constant Velocity
Constant Acceleration
Distance Calculation
Gradient Shows
Measurements
Random Errors – an error in the way of measuring due to a fault in the observation of
measurement.
 Parallax Errors – in which the reading of the measurement is incorrect due to looking
at the measurement from an angle less than or greater than 90 degrees
Systematic Errors – errors in experimental observations caused by a fault/flaw in the
measuring instruments
 Zero Errors – in which the instrument does not read zero when the quantity is
measured to be zero
 Mechanical Errors – in which the instrument consistently reads changes in the
quantity to be greater or lesser than the actual changes
Accuracy – associated with how close your estimate is to the true value you are measuring
Precision – the degree to which you can measure your value
Simple Pendulum - a device consisting of a mass, suspended from a fixed point, that
oscillates with a known period under the influence of gravity, commonly used to track the
process of time in an oscillation with the starting point and A and B.
Vernier Scale - a small sliding scale which is 9mm long but is divided into 10 equal divisions.
Micrometer screw gauge – a device that is used to incorporate a calibrated screw. Its
measurement of small objects is very precise up to 0.001 cm.
Tickertape timers – measures time by marking a certain number of dots (usually 50) on
tickertape per second. The distance between the fifty successive dots equals the average
speed of whatever is pulling the tape. The spacing between the dots can show whether the
object is accelerating or not.
Ticker tapes place 50 dots every
second. Thus a dot is placed
every 0.02 seconds.
If there are ten spaces on a
piece of tape, time taken is 10 x
0.02 = 0.20 s.
You can work out the speed
between each dot by measuring
distance and then distance/time
Forces
Force (N) – push or pull upon an object resulting from the object's interaction with another
object
Contact Forces – a force that acts at the point of contact between two things e.g. Friction,
Support, Tension, Thrust
Non-Contact Forces – a force that acts on an object that is not in direct contact with it e.g.
Gravity, Electric, Magnetic
Friction Force – the force exerted by a surface as an object moves across it or makes an
effort to move across it.
Support (Normal Reaction) Force – the support force exerted upon an object that is in
contact with another stable object
Tension Force – the force that is transmitted through a string, rope, cable or wire when it is
pulled tight by forces acting from opposite ends
Thrust Force – a force that is exerted on an object by the expulsion or acceleration of mass
in one direction
Electric Force – a force that is exerted between objects or particles with electric charge.
Resultant (Net) Force – the sum of all forces acting on a body
Weight Force – the force generated when two objects with mass (and therefore have a
gravitational field) interact with each other.
Gravity – a force that attracts a body towards the centre of a physical body having mass. (10
OR 9.8)
Air Resistance (Drag) –the force opposite the relative motion of an object moving through
air
The calculation of gravity is gravity =
The calculation of mass is mass =
The calculation of weight is weight = mass x gravity
W
m
V
g
Free Fall




As a body falls, initially it has no resistive forces so the only force is weight (caused
by gravity) bringing it to earth at an acceleration of 9.8m/s2
As the body begins to move through the atmosphere the air resistance builds up.
The faster the motion the higher the resistance. This air resistance is a force which
applies in opposition to the weight force
The resultant force is the difference between these two forces. The resultant force
is also the factor which controls the acceleration. As air resistance increases the
resultant force decreases, which causes a reduction in the acceleration
Eventually the air resistance force will equal the weight force and the resultant will
be zero. At this time there is no acceleration. The object has reached its Terminal
Velocity
Newton’s Laws
1. A body stays at rest, or if moving it continues to move with uniform velocity, unless
an external force makes it behave differently
2. The sum of the forces of an object is equal to the total mass of that object multiplied
by the acceleration of the object (F = m x a)
3. If body A exerts a force on body B, then body B exerts an equal but opposite force on
body A
The calculation of acceleration is acceleration =
F
The calculation of mass is mass =
m a
When given two forces, the calculation of net force is force = resistive force – driving
V force
The calculation of net force is force = mass x acceleration
Hooke’s Law - extension is directly proportional to stretching force
Extension/Load Graphs – graphs used to show Hooke’s Law. The gradient of an
Extension/Load graph shows the ease of stretch of a spring measured in N/m.
Load (N)
This point is known as the Limit
of Proportionality. At this point
extension is no longer
proportional to load, so to
calculate extension and force
(load) we use F = kx (k being the
spring constant), as F = x no
longer works.
Extension (mm)
Vector Additions


Pythagoras Theorem is used to work out the vector quantity, when two forces are
applying in different directions.
Pythagoras Theorem = a2 + b2 = c2
40 N
40 N
30N
30N
50N
Motion in a Circle
Centripetal Forces – a force which acts on a body moving in a circular path and is directed
towards the centre around which the body is moving
Acceleration
Force
Velocity
When an object is moving
with a constant speed and
we apply a force at right
angles to the motion it
causes the object to move
in a curved path.
Centre Of Mass - the point at which applying a force will not cause rotation. The effects of
the centre of mass are:
 The lower the height of the centre of mass, the more stable
 The wider/larger the support base, the more stable
Finding the Centre of Mass:


In Regular Shapes: Centre of object
In Irregular Shapes: Suspend the shape from a point, and then another. Draw plumb
lines and find the intersection
Torque and Equilibrium
Turning Effects (Moment/Torque) (Nm) - forces acting about a pivot cause a turning motion
The calculation of force is force =
τ
The calculation of (perpendicular) distance from the pivot is distance =
F d
V
Equilibrium - when the resultant forces acting on a body are zero and the resultant moment
The calculation of the torque is torque = force x distance
is also zero.
Stable Equilibrium – There is stable equilibrium, when the object
concerned, after having been disturbed, tends to resume its original
position. Thus, in the case of a stable equilibrium, there is a tendency
for the object to revert to the old position.
Unstable Equilibrium – The equilibrium is unstable when a slight
disturbance evokes further disturbance, so that the original position is
never restored. In this case, there is a tendency for the object to
assume newer and newer positions once there is departure from the
original position.
Neutral Equilibrium – It is neutral equilibrium when the disturbing
forces neither bring it back to the original position nor do they drive it
further away from it. It rests where it has been moved. Thus, in the
case of a neutral equilibrium, the object assumes once for all a new
position after the original position is disturbed.
4kg
2m
40N
τ=FXd
τ = 40 x 2
τ = 80 Nm
5m
1.6kg
16N
The clockwise
and the
Energymoment
and Work
anti-clockwise moment are equal
τ=FXd
τ = 16 x 5
τ = 80 Nm
Energy (J) – the ability to do work
Work (J) – energy that is transformed/change in energy
Law of conservation of energy – energy cannot be created or destroyed
W
The calculation of force is force =
The calculation of distance is distance =
d
F
The calculation of work is work = force x distance
Active Energy – energy which can be detected e.g. kinetic, heat, electrical, sound, light
Potential Energy – energy which is stored e.g. gravitational, elastic, chemical, nuclear
Chemical Energy – that part of the energy in a substance that can be released by a chemical
reaction
Gravitational Potential Energy – energy stored in an object as a result of its vertical
position/height
Gravitational Potential Energy = mass x gravity x height (gravity on earth = 10)
Electrical Energy - the energy created through the flow of power in a conductor
Heat (Thermal/Internal) Energy - energy that is transferred by a difference in temperature
Kinetic Energy – energy that a body possesses whilst moving
The calculation of mass is mass = 2(
Ek
)
½ M V2
The calculation of velocity2 is velocity2 =
The calculation of kinetic energy is kinetic energy = ½ mass x velocity2
Elastic Potential (Strain) Energy – potential energy that is stored when a body is deformed (as in a
coiled spring).
The calculation of the spring constant is spring constant = 2(
)
U
The calculation of the extension is extension =
The calculation of elastic energy is elastic energy = ½ spring constant x
extension2
½k
x2
Power (Watt) – a measure of the rate at which energy is converted to another form
W
The calculation of power is power=
The calculation of time is time =
The calculation of work is work done = power x time taken
P
t
Efficiency – the percentage of power that is useful
The calculation of efficiency is efficiency =
Energy Sources
Non-renewable Sources – once used up, it cannot replenish new energy


Farming of Coal and Oil causes pollution and produce CO2 and SO2 and worsens the
formation of acid rain.
Nuclear fuels such as Uranium-235 must be stored to last their half life so it does not
pollute the environment with nuclear waste.
Renewable Sources – can be reused to gain more energy






Solar energy from Solar Panels, Solar Furnace and Solar Cells
Wind Energy from Wind Turbines
Tidal/Hydroelectric Energy from Dams
Wave Energy
Geothermal Energy
Biomass from biofuels and biogas
Power Stations
Thermal Power Plant (Non-renewable) = Boiler or Heat Exchange  Steam Turbine 
Generator
Dam (Renewable) = High Level Reservoir  Water Turbine  Generator
Pressure
Pressure (Pa) – force per unit of area
F
The calculation of pressure is pressure =
The calculation of area is area =
The calculation of force is force = pressure x area
p
A
Pressure in Liquids – in Liquids, their density does not change very much. This is because
liquids are not very compressible compared to gases. The pressure at one depth acts equally
in all directions.
The calculation of pressure in liquid is pressure = density x gravity x depth (height)
Atmospheric Pressure – the pressure exerted on the surface by the weight of air. At sea
level, atmospheric pressure is 1 x 105 Pa.
Measuring Pressure
The Mercury Barometer – used to measure atmospheric pressure. Mercury is used as it is
the densest liquid. As the atmospheric pressure increases the air applies a force to the
surface of the mercury and causes the mercury to rise up the tube (and vice versa).
Manometer – used to measure gas pressure. It consists of a U-tube containing mercury (or
water). When both ends of the tube are exposed to the same pressure, the heights are the
same. When one end is exposed to a different pressure this causes different heights (which
can be used in p = ρgh).
If one end is connected to a
gas supply equal to
atmospheric pressure, the
heights of the liquid will be
equal on both ends of tube.
If one end is connected to a
gas supply that is greater than
atmospheric pressure, the
liquid goes lower on that end
and higher on the other.
If one end is connected to a
gas supply that is smaller than
atmospheric pressure, the
liquid goes higher on that end
and lower on the other.
Gas Pressure = Atmospheric
Pressure
Gas Pressure = Height +
Atmospheric Pressure
Gas Pressure = Atmospheric
Pressure – Height
Hydraulic Systems
Hydraulic Systems work by using liquids
under pressure. They use two properties of
liquids:
 Liquids are incompressible
 If pressure is applied to an enclosed
liquid, the pressure is transmitted
to all parts of the liquid
A2d2 = A1d1 and
F1 F2

A1 A2
States of Matter
Solid
Liquid
Gas
Fixed shape and volume
Particles are held together
by relatively strong forces
Incompressible
Particles do not have free
movement but can vibrate
around fixed positions
No fixed shape, fixed volume
Particles have weaker forces
so are further apart
Slight compressibility
Particles can move
throughout bulk of liquid
No fixed shape or volume
Particles are very far apart
Compressible
Particles are very spread out
and move in random fashion
Temperature of a Gas




Temperature is a measure of the kinetic energy of the particles concerned
As the particles are heated, their kinetic energy increases
Gases have the highest level of kinetic energy and hence are higher temperature
At absolute zero, molecular motion ceases and a substance has no kinetic energy
Pressure of a Gas
 The free moving particles of a gas will spread evenly within a container and collide
with the walls. This will exert a force on the wall when it bounces off.
 When this happens on a large scale (billions of particles) there is an average force
exerted on the wall. A pressure is created with the new force in Pressure =
Evaporation
 When the molecules of a liquid are close to the surface of the liquid through
collisions and absorbing external energy, some of the molecules will have sufficient
kinetic energy to change state from liquid to gas and escape from the surface of the
liquid.
 This means that the average kinetic energy of the remaining particles is lower
causing a cooling effect
 Evaporation can occur at any temperature
 To increase evaporation you can increase the temperature or the surface area. A
draft will also increase the rate of evaporation
Gas Laws


Gas laws show the relationship between Volume (in centimetres3/millilitres),
Pressure (in Pascals) and Temperature (in Kelvin). Kelvin is calculated by adding 273
to the degrees Celsius. -273°C/0K is absolute zero.
Charles’ Law – If pressure is kept constant, the volume of a fixed mass is directly
proportional to its absolute temperature.

. A temperature increase means the
particles have more kinetic energy and occupy more space, thus increasing volume
and the particles move faster.
Pressure Law – If volume is constant, the pressure of a fixed mass of gas is directly
proportional to its absolute temperature.
. A temperature increase means

the particles have more kinetic energy and the average speed of molecules increase,
thus having more frequent and violent collisions of molecules and increasing
pressure.
Boyle’s Law – If temperature is constant, the pressure of a fixed mass of gas is
inversely proportional to its volume. P1V1 = P2V2. A volume decrease means the
number of molecules per unit of volume decreases and the number of collisions
increase, thus causing a pressure increase.

Ideal Gas Law –
Heat Measurement
Range – how far the scale can extend (dependant on their melting and boiling points)
Sensitivity – how much the property changes per unit of temperature
Linear – whether or not the change occurs as at a steady rate
Liquid in Glass Thermometer – liquids that expand and contract in a tube
due to change in temperature. The expansion/contraction can be measured
and give the temperature of an object. Mercury and coloured alcohol is
often used for this due to their wide range, ability to contract and expand
easily, ability to not stick to the inside of the tube and their ease of visibility.
Vacuum
Capillary
Tube
Bulb
Thermocouple Thermometer – can measure the temperature using the thermoelectric
effect. There are two different types of wire connected together and the junctions are
placed in a hot and cold source. A voltage is generated which corresponds to the difference
in temperature between the two junctions.
Resistance Thermometer – uses the fact that the electrical resistance of a platinum wire
increases with temperature
Thermistor Thermometer – uses the change in the pressure of gas to measure temperatures
over a wide range
Thermochromic Liquids – these change colour with temperature and are limited to rtp.
Specific Heat Capacity
Specific Heat Capacity (J/kg°C)– the heat required to produce a 1°C rise in 1 kg.
Quantity of heat energy received/given out = mass x change in temp x specific heat capacity
Q = m x ΔT x C
Linear Expansivity (m) – the increase in length of 1m for a 1°C rise in temperature
Expansion = original length x linear expansivity x change in temperature
L = Lo x α x ΔT
Thermal Expansion – when two objects are made to touch they both eventually reach the
same temperature
Thermal Capacity (J/°C) – the quantity of heat needed to raise the temperature of the whole
body by 1°C
Thermal capacity = mass x specific heat capacity
Specific Latent Heat
Gas
Vaporising
Liquid
Melting
When the object is melting or vaporising, heat energy is
being added but the temperature is not changing. The
average kinetic energy stays the same. Energy changes
to potential energy by separating.
Solid
Latent heat of Fusion – the energy that enables the molecules of a solid to overcome the
intermolecular forces that hold them in place. Vibration changes to a slightly greater range
of movement. Molecules’ potential energy increases but not their average kinetic energy.
There is no temperature rise.
Specific latent heat of fusion (J/kg) – the quantity of heat needed to change unit mass from
solid to liquid without temperature change.
Quantity of heat energy needed to change state = mass x specific latent heat of fusion
Q = m x lf
Latent heat of Vaporization – increases the total potential energy of the molecules but not
their kinetic energy. It also gives the molecules the energy required to push back the
surrounding atmosphere in the large expansion that occurs when liquid vaporises
Specific latent heat of vaporization (J/kg) – the quantity of heat needed to change unit mass
from liquid to vapour without change of temperature.
Quantity of heat needed to change state = mass x specific latent heat of vaporisation
Q = m x lv
Conduction
Conduction – the flow of heat through matter from places of higher temperature to places
of lower temperature without movement of the matter as a whole
Conduction and Kinetic Energy
 Metals have free electrons. When metals are heated, the free electrons move faster
and farther. As a result they collide more frequently and make atoms in cooler parts
vibrate more. This process is fast.
 The atoms themselves at the hot part make colder neighbouring atoms vibrate more
vigorously. This process is slow and occurs in metals and non-metals.
Convection
Convection – the flow of heat through a fluid from places of higher temperature to places of
lower temperature by the movement of fluid itself. Fluid can be liquid or gas.
Principles of Convection
 Fluids will flow from high temperature to low temperature
 Fluids through flow from high pressure to low pressure
 As fluids are heated, they expand and become less dense. They will rise above the
more dense colder fluid and form convection currents.
Radiation
Radiation – the flow of heat from one place to another by means of electromagnetic waves.
The rate of energy transfer by radiation is affected by surface temperature, colour and
texture of the surface, and surface area.
Infra-red Radiation – as it is an electromagnetic wave it will behave like light and can be
reflected.
Vacuum flask – will separate the inner and outer
layers with a cavity which is a vacuum. This
prevents transfer of thermal energy from one to
the other by conduction or convection. The inner
and outer surfaces of both layers will be coated
with a silver shiny layer to prevent the absorption
or reflection of infra-red energy. Little heat loss
occurs through conduction through the top/lid.
Waves
Wave motion – the process in which energy is transferred from one point to another
without any transfer of matter between the points.
Mechanical Waves – produced by a vibrating object in a medium and are transmitted by the
particles of that medium
Electromagnetic Waves – waves that do not need a medium to travel
Longitudinal Waves – vibration is parallel to the direction of wave motion e.g. sound waves,
primary waves in earthquakes
Transverse Waves – vibration is perpendicular to the direction of the wave e.g.
electromagnetic rays, secondary waves in earthquakes
Wavelength
Crest
Amplitude
Medium
Trough
Wavelength (m) – length between two consecutive crests or compressions
Wave Velocity (m/s) – travelling speed; depends on medium.
Frequency (Hz) – number of waves passing any point per second/number of oscillations for
a point per second. Lower pitch = Lower Frequency.
Hertz – one oscillation per second
v
The calculation of wavelength is wavelength =
The calculation of frequency is frequency =
λ
f
The calculation of wave velocity is velocity = wavelength x frequency
Period (s) – time taken for one wavelength to pass any point/time for one point to complete
one oscillation. Period =
Phase – the relationship between two oscillations
Reflection
Reflected Ray
Incident Ray
ϴi ϴr
Laws of Reflection


The incident ray, reflected ray, and normal are all in the same plane
The angle of incidence is equal to the angle of reflection
Total Internal Reflection – If the angle of incidence is greater than the critical angle, the
refracted ray disappears and all of the incident light is reflected inside the denser medium.
Critical Angle – the angle of incidence when angle of reflection is 90°
Refraction
Refraction – the change in direction of light when it passes from one medium to another.
Refraction happens because light is an electromagnetic wave and it travels at different
speeds in different media.
Incident Ray
ϴi
ϴr
Refracted Ray
Laws of Refraction


The incident and refracted rays are on opposite sides of the normal at the point of
incidence and all three are in the same plane
The ratio of the sine of the angle of refraction is a constant for a given pair of media:
Refractive Index – a measure of the speed of light in that medium. A bigger refractive index
refracts light more, has smaller angle of refraction, is more optically dense, and light travels
slower.
n1sinϴ1 = n2sinϴ2
Images
Terms Used to Describe an Image
Enlarged/Diminished/Same
Upright/Inverted
Real/Virtual
Relationship between the Di and Do
Description of a Plane Mirror
Same Size
Upright, Laterally Inverted
Virtual
Di = Do
Number of Images formed =
1. Incident rays parallel to principle axis are refracted through the focal point
2. Incident rays through the focal point are refracted parallel to the principle axis
3. Incident rays through the optical centre are unchanged
Object
Focal Point
Focal Point
Object Position
Beyond 2F
At 2F
Between 2F and F
At F
Less than F
Image
Image Position
Between 2F and F
2F
Beyond 2F
No Image
Behind object
Upright/Inverted
Real, Inverted
Real, Inverted
Real, Inverted
Virtual, Upright
Size
Smaller
Same Size
Larger
Larger
Sound
Sound waves – longitudinal, mechanical waves. Sound is created when particles vibrate.
When particles vibrate between 20-20000 Hz (limits of audibility) and they travel through a
medium to our ear we can hear them.
Echo – sound reflecting off of barriers and coming back to the origin
Reverberation – when the echo joins with the original sound
Characteristics of sound





330-340 m/s in air; 1500 m/s in water; around 3000 m/s in most solids
Speed of sound will increase with temperature
Generally the higher the density, the higher the speed
Increasing the amplitude, increases the volume of a sound
Increasing the frequency will increase the pitch of a sound
Lenses
Convex Lenses – converging lenses that will curve light towards the focal point. Rays of light
at right angles to the lens will pass through the focal point. Images further than the focal
point will be real images.
Short Sighted
Short Sighted with Convex Lens
Retina
Retina
Concave Lenses – diverging lenses that will cause parallel rays of light to spread out. The
image will be virtual, upright and reduced in size.
Long Sighted
Long Sighted with Convex Lens
Retina
Dispersion
Prisms – refract light through two non-parallel boundary layers. Because different
frequencies (colours) of light refract different amounts (they travel at different speeds so
bend at different amounts) when they pass through a prism, they remain separated which
we see as a rainbow – or the spectrum of visible light. Red bends the least, violet bends the
most.
Electromagnetic Spectrum
Monochromatic – one frequency
Water Waves
Reflection in Water – water waves will reflect off objects or sides of a container. The normal
rules of reflection apply.
Wave front – the leading edge of a propagating wave. As a wave moves away from a source
it will usually spread out (propagate) meaning the wave front will get wider.
Refraction in Water – as the depth of water changes, waves will refract. Waves will travel
slower in shallow water. The direction of travel is bent towards the normal in shallow water
Diffraction in Water – waves diffract when they pass around barriers or pass through gaps.
The effect is maximised when the gap is the same size as the wavelength
Magnets




Magnets have a north and south pole
Like poles repel, opposite poles attract
Magnets will create a field around them which will affect other magnets
The spacing between the lines of a magnetic field shows the field strength
Ferrous Magnets – magnets formed from metals such as iron, steel and cobalt
Induced Magnetism – metals like iron and steel are attracted to magnets and will have a
magnetic field created in them (magnetism has been induced in them). When steel is pulled
away from a magnet, it keeps its magnetism (hard magnet). When iron is pulled away from
a magnet, it loses its magnetism (soft magnet).
Demagnetisation – when the crystal structure of the magnet
is shifts; dropping magnets causes them to lose their strength.
Charge
Charge – a measure of the positive or negative particles that an object has. The standard
unit of charge is a Coloumb (C).
Conductor – a material which has free moving electrons which are able to flow when a
voltage is applied e.g. metals
Insulator – has no free electrons so will not allow a current to flow when a voltage is applied
e.g. non-metals, plastic
Electric Fields – a region where an electric charge will experience force. It is generated
around charged particles. They move towards negative charges and away from positive
charges.
Unlike charges will attract
Like charges will repel
+
+
Static Charge – refers to a build up of charged particles. They are static because they do not
move or flow like convectional current. Static charge can be created by friction between two
surfaces.
Current – flow of charged particles. The circuit must be complete in order for current to
flow.
Ampere (A) – the unit of measurement of Current. One ampere = 600000000 electrons
passing a point in a circuit every second. It is measured with an ammeter.
The calculation of current is current =
Q
The calculation of number of seconds is time =
The calculation of charge is charge = current x time taken
I
t
Charge is also calculated in the formula charge =
Conventional Current – the flow of current from positive to negative, whereas electron flow
is negative to positive. This is used unless otherwise stated.
Circuits
Circuit – the path which a current moves along.
Short Circuit – a circuit that allows current to travel on an unintended path.
Series Circuit – a circuit that has only one path for current to travel.
Parallel Circuit – a circuit that has more than one path for current to travel.
Current
(Amps)
Voltage
(Volts)
Total Resistance
(Ohms)
Series Circuit
A1 = A2
Stays the same through all
components.
V1 + V2
The sum of all voltages equal to
the total.
R1 + R 2
The sum of all resistances equal
to the total.
Parallel Circuit
A1 + A2
The sum of the currents equal
to the total.
V1 = V2
Stays the same through all
components.
R1 x R 2
R1 + R 2
Potential Difference (Voltage) – a measure of the energy per unit of charge. It is measured in
volts.
P
The calculation of current is current =
The calculation of voltage is voltage =
The calculation of power is power = current x voltage
I
V
V
Voltage is also calculated in the formula Energy = Current x Voltage x time
Resistance – a measure of how difficult it is for current to flow through a component.
Ohm’s Law – the current flowing through a metal wire is proportional to the voltage across
it (provided the temperature remains constant)
V
The calculation of current is current =
The calculation of resistance is resistance =
The calculation of voltage is voltage = current x resistance
What affects resistance in a wire?
1.
2.
3.
4.
As length increases, resistance increases
As cross sectional area increases, resistance decreases
Type of wire (whether good conductor or bad conductor)
As temperature increases, resistance increases
I
V
R
Components
Cell – device that produces electrical energy from chemicals.
Battery – device made from two or more cells
Filament Lamp – device that changes electricity into light
Fixed Resistor – device that restricts the flow of current
Variable Resistor – device with a resistance that can be changed
Rheostat – type of variable resistor that changes the current in a circuit
Potentiometer – type of variable resistor that changes the voltage applied to a device
Switch – device that turns a circuit on/off.
(open)
(closed)
Voltmeter – meter to measure the voltage difference between points, must be in parallel.
V
Ammeter – meter to measure electrical current. It must be connected in series.
A
Diode – device that only lets current flow in one direction. If placed the wrong way, a
current will not flow. A voltage of -40V would damage a diode. Diodes are used as a
rectifier, to change A.C. to D.C.
Light Emitting Diode (LED) – devices that light when current flows through. If the current
entering it is reversed it will not light and will cause damage if it exceeds 5V. A resistor must
be in series with it to limit the current.
Thermistor – a device which is sensitive to change in temperature. As temperature
increases, the resistance will decrease.
Capacitors – a device that stores charge. There are two conducting plates
separated by a non-conducting layer. Electrons are pushed by a voltage towards
one plate where a negative charge builds and a positive charge builds on the other plate.
They will discharge over time. The capacitance (how much a capacitor can store) is
measured in farads (F). A capacitor blocks d.c. current but passes a.c. as the capacitor
charges and discharges continuously with the alternating current, despite no current
actually passing through the capacitor.
Relays – uses a small current flow to activate an electromagnetic switch for a large current
flow in another circuit or part of the circuit.
Light Dependent Resistor (LDR) - devices that are sensitive to light. As light intensity
increases, resistance decreases
Transistors – a small, reliable, electrically operated switch which has no moving parts.
Current will only flow through the Collector to the Emitter when the current is above a
Collector
threshold point (0.6V) through the Base to Emitter.
Base
Emitter
Solanoid – a cylindrical coil of wire acting as a magnet when carrying electric current.
To increase the magnetic field, you:



Add an iron core
Increase the current
Increase the number of turns in the coil
Electromagnetic Effect
Electromagnets – temporary magnets that can be switched on and off. It has a core of soft
iron which is magnetized only when current flows in the surrounding coil. The strength of an
electromagnet increases if:



Current in coil increases
Number of turns on the coil increases
The poles are moved closer together
Electromagnetism – when you pass a current through a wire it creates a magnetic field
around the wire.
Electric Motors – transfers electrical energy to kinetic energy. A motor is made up of a coil
which is positioned between two poles of the magnet. When the current flows through the
coil, it creates a magnetic field which interacts with the magnetic field produced by the two
permanent magnets. The combination of these two magnetic fields exerts a force, pushing
the wire at right angles to the permanent magnetic field. To increase the turning effect, you:




Increase the current
Use a stronger magnet
Increase the number of turns on the coil
Increase the area of the coil
Electromagnetic/Voltage Induction – when you move a wire/coil in a magnetic field it
induces a voltage that causes current to flow. The size of the induced voltage (and current
flow) can be increased by:



Increased relative speed
Increased magnetic field strength
More coils of wire
Lenz’s Law – the direction of the induced current opposes the change causing it
Faraday’s Law - the size of the induced potential difference is directly proportional to the
rate at which the conductor cuts magnetic field lines
D.C. Motor – one side of the rectangular coil of wire will experience an upwards force and
the other a downwards force. These forces rotate the coil in a clockwise direction until it is
vertical. The brushes are then in line with the gaps in the commutator and the current stops.
However, because of inertia, the coil overshoots the vertical and the commutator halves
change contact from one brush to the other. This reverses the current through the coil and
so also the directions of the forces on its sides, therefore causing the coil to continue
rotating clockwise.
D.C. Generators – in a direct current, the electrons flow in one direction only. An a.c.
generator becomes a d.c. generator if the slip rings are replaced with a commutator. The
brushes are arranged so that as the coil goes through the vertical, changeover of contact
occurs from one half of the split ring of the commutator to the other. In this position the
voltage induced in the coil reverses and so one brush is always positive and the other
negative.
A.C. Generator – in an alternating current, the direction of the flow reverses regularly. An
a.c. generator consists of a rectangular coil between poles of a C-shaped magnet. The ends
of the coil are joined to two slip rings on the axle and against which carbon brushes press.
When the coil is rotated it cuts the field lines and a voltage is induced in it. As the coil moves
through the vertical position with one side uppermost, the two sides are moving along the
field lines and no cutting occurs, thus an induced voltage of zero. The next 180 degrees
rotation then reverses the current
Logic Gates
Digital – discrete; a binary code is digital – values of 0 (low voltage) or 1 (high voltage) only.
Analogue – continuous
NOT Gates – an electronic circuit that produces an inverted version of the input at its
output.
Input
1
0
Output
0
1
Input
Output
OR Gate – an electronic circuit that gives a high output (1) if one of its inputs are high.
Input A
0
0
1
1
Input B
0
1
0
1
Output
0
1
1
1
Input A
Output
Input B
NOR Gate – an electronic circuit that gives a low output (0) if any of the inputs are high (1).
Input A
0
0
1
1
Input B
0
1
0
1
Output
1
0
0
0
Input A
Output
Input B
AND Gate – an electronic circuit that gives a high output (1) only if all the inputs are high.
Input A
0
0
1
1
Input B
0
1
0
1
Output
0
0
0
1
Input A
Output
Input B
NAND Gate – an electronic circuit that gives a high output (1) if any of the inputs are low (0).
Input A
0
0
1
1
Input B
0
1
0
1
Output
1
1
1
0
Input A
Input B
Output
Transformers
Mutual Induction – when coils are magnetically linked so that changing current in one coil
causes an induced electromagnetic force in the other.
Transformers – transforms the voltage from one coil to another.
Simple Transformer:


Alternating current flows through
the primary coil. This sets up an
altering magnetic field in the core
Coils of the secondary coil ‘cut’
the altering magnetic field, thus
inducing an alternating voltage in
the output of the coil

Step-Up Transformers – where voltage is
increased from the primary coil to the
secondary coil. The number of output coils is greater than the number of input coils. This is
used next to generators, to increase the voltage of electricity travelling along power lines so
they reduce the current flow and thus reduce the energy loss due to heating the lines.
Step-Down Transformers – where voltage is decreased from primary coil to the secondary
coil. The number of output coils is less than the number of input coils. This is used to turn
the high voltage from power lines to a small voltage of 240V as they go into houses.
Power in Transformers

Input = Output (Transformers are 100% efficient)


Input Voltage x Input Current = Output Voltage x Output Current
Electrical Safety



Damaged insulation can lead to a short circuit which can cause a fire. It can also
shock a person if they come into contact with a bare wire
Overheating of cables can cause a fire and also damage insulation
Damp conditions increase the risk of shocks as current can flow through water
Household Wiring
The Live Wire – connected between the mains supply and the appliance needing to be
supplied. It will carry the voltage to the appliance and touching it will result in a shock. If
there is a fuse in the socket it will be connected in series with the live wire.
Neutral Wire – connected from the appliance to the mains supply. As the voltage has
been used by the appliance, the neutral wire should have 0 Voltage.
The Earth Wire – if an appliance has a metal body, they will connect that metal body to
the earth wire so that if there is a fault in the appliance and the body becomes
connected to the live wire, the current will flow through the earth wire. This usually
results in the fuse blowing as the current load will exceed the capacity of the fuse.
Fuses – a thin section of wire. Fuses will be made to carry up to a specific level of
current. When this level is exceeded the wire becomes hot and breaks, which breaks the
circuit. They are connected to the live wire so that no more voltage is supplied to the
appliance.
Circuit Breakers – measure the level of current through the circuit and when the level
exceeds their safety point they switch off the circuit. It acts in the same way as a fuse
but can be reset rather than having to replace a section of blown fuse.
Right Hand Rules
Magnetic Field Around A Wire
Current Around A Solanoid
Current in Electromagnetic Induction
Force on a Current Carrying Wire
Current
Motion
Magnetic
Field
Current
Magnetic
Field
Force
Cathode Rays
Cathode Ray – thermionic emission of electrons
Thermionic emission – the process of emitting electrons from a metal filament by heating.
There is a certain minimum threshold energy which the electrons must have to escape. The
higher the temperature of the metal, the greater the number of electrons emitted. The
electrons are attracted to the positive anode and are able to reach it because there is a
vacuum in the bulb.
Cathode Ray Oscilloscope
Cathode Ray Oscilloscope – this contains a cathode ray tube with three parts: the electron
gun, the deflecting plates and the fluorescent screen
Electron Gun – this consists of a
heater, cathode, grid and
(possibly multiple) anodes. The
grid is at a negative voltage with
respect to the Cathode and
controls the number of electrons
passing through its central hole.
The anodes are at high positive
voltages relative to the Cathode; they accelerate
the electrons along the highly evacuated tube and
also focus them into a narrow beam.
Deflection Plates – potential differences can be
applied to two pairs of deflecting plates; horizontal
Y-plates which deflect the beam vertically, and
vertical X-plates which deflect the beam
horizontally.
Time Base On:
Y-input 0
A.C.
D.C.
Y-input 0
A.C.
D.C.
Fluorescent Screen – a bright spot of light is produced on the screen where a beam hits it.
Atoms
Nuclide Notation – a standard way of representing information about an atom. The same
method is used for emitted particles.
A
Z
X
A = Mass Number
Z = Atomic Number
X = Atom or Particle
The Atomic Number is the number of Protons and Electrons unless it is an ion. (Protons = Electrons)
The Mass (Nucleon) Number is the number of Protons + Number of Neutrons. To work out the
number of neutrons you must calculate: Mass Number - Atomic Number = Number of Neutrons
Particle
Proton
Neutron
Electron
Relative Mass
1836
1839
1
Charge
+e
0
-e
Location
In Nucleus
In Nucleus
Outside Nucleus
Isotope – an element that occupies the same place in periodic table but has a different
number of neutrons. The number of protons and electrons are the same.
E.g. Hydrogen has three isotopes: Protium (0 Neutrons), Deuterium (1 Neutron), Tritium (2
Neutrons)
Rutherford’s Experiment – Rutherford fired alpha particles at a thin gold foil.
Observations
1. Most of the alpha
particles pass
straight through
with little or no
deflection
2. Some angles
were deflected
through big
angles
3. A few particles
bounced back
Deduction
Most of the atom is
empty space
The nucleus of an
atom is positively
charged
Evidence for the
existence of nucleus
Radioactive Decay
Radiation – the random and spontaneous process of an unstable nucleus decaying. The
process releases energy in the form of either a particle or a wave, and sometimes both.
Alpha Decay – an alpha particle is a helium nucleus having 2 neutrons and 2 protons. When
an atom decays, its nucleon number decreases by 4 and it’s proton number by 2.
e.g.
Ra 
226
88
222
86
Rn + 42 He
Beta Decay (β-) – In beta decay a neutron changes to a proton and an electron. The proton
remains in the nucleus and the electron is emitted as a beta particle. The new nucleus has
the same nucleon number but its proton number increases by one.
e.g.
C
14
6
14
7
N + -10e
Positrons (β+) can also be emitted in beta decay. They are subatomic particles with the same
mass as an electron but with an opposite (positive) charge.
Gamma Emission – after alpha or beta emission, some nuclei are left in an ‘excited’ state.
Rearrangement of the protons and neutrons occurs and a burst of gamma rays is released.
Property
Type
Alpha
Helium Nucleus
Speed
Slow (10% Light Speed)
In an Electric Field
In a Magnetic Field
Stopped By
Mass
Charge
Distance in Air
Ionising Ability
Deflected to Negative
Deflected Slightly
Paper, Skin
4u
Positive
Few centimetres
Strong
Beta
High Energy
Electrons
Fast (90% Light
Speed)
Deflected to Positive
Deflected
Thin Aluminium
Negligible
Negative
A few metres
Weak
Gamma
High frequency
electromagnetic ray
Very Fast (Light
Speed)
Not Deflected
Not Deflected
Thick Lead/Concrete
Zero
No Charge
Infinite
Very Weak
Geiger Muller Tube – when an alpha , beta or gamma radiation enters the tube it produces
ions in the gas. The ions created in the gas enable the tube to conduct. A current produces a
voltage pulse. Each voltage pulse corresponds to one ionising radiation entering the GM
tube. The voltage pulse is amplified and counted.
Background Radiation – naturally occurring radioactive decay of isotopes. Examples of
sources of background radiation includes cosmic rays, earth minerals, nuclear power plants,
medical and dental x-rays.
Nuclear Stability
Stability Line
i.
ii.
iii.
iv.
80
N=Z
60
20
For Unstable Nuclides:
Regions of
Instability
40
N = Z for the lightest nuclides
N > Z for the heaviest nuclides
Most nuclides have even N and
Z, implying that the alpha
particle combination of two
neutrons and two protons is
likely to be particularly stable
Number of Neutrons (N)
i.
ii.
iii.
100
For Stable Nuclides:
Disintegration tends to produce
new nuclides nearer the stability
0
20
40
60
80
100
line and continues until a stable
Number of Protons (Z)
nuclide is formed
A nuclide above the stability line decays by β- emission so that the N/Z ratio decreases
A nuclide below the stability line decays by B+ emission so that the N/Z ratio increases
Nuclei with more than 82 protons usually emits an α-particle when they decay
Half Life
Half-Life – a measure of the time it will take for half of the source to decay.
Quantity of a Substance = Original Amount x ½ number of half-lifes
E.g. the half life for this graph is 2 days.
Uses of Radioactivity
Carbon Dating – all living organisms have absorbed some Carbon-14 from the atmosphere.
When they die the Carbon-14 level in their body decays with a half-life of 5700 years so the
levels of radioactivity will decrease. This can be used on a half-life graph to determine when
an organism dies.
Treating Cancer –cancer cells are so busy replicating that they are easier to kill than health
cells. Radiotherapy localises the exposure of radioactivity to the area of the cancer growth.
Chemotherapy is a whole body exposure to radioactivity. The idea with both systems is to
kill cancer cells faster than killing healthy cells.
Medical Tracers – the radioactive substance is injected into the body and it will migrate to
the area doctors are investigating and then they use detectors to investigate activity at the
site of interest.
Thickness Gauge – if a radioisotope is placed on one side of a moving sheet of material, and
a GM tube on the other, the count-rate decreases if thickness increases. Because of their
range, beta emitters are suitable, but gamma emitters would be used for thicker materials.
Flaws in a material can also be detected as the count rate increases when a flaw is present.
Sterilization – Gamma rays are used to sterilise medical instruments and food by killing
bacteria. They are safe to use as no radioactive material goes into the food or instruments.
Dangers of Radioactivity






As alpha is the largest charge and attracts electrons, it has the largest ionising effect.
For beta to ionise an atom it must pass close enough to an electron and repel the
electron away from its atom. This is less likely so the effect is a less ionising particle. This
is also why it can penetrate further.
Gamma is the least ionising because it has no charge. To ionise it must pass its energy to
an electron and excite it enough for it to break from its atom.
Because living cells are constructed from atoms bonded together it is possible to disrupt
their structure and function by stripping off electrons, which is what ionising particles do
to cells. Thus precautions for different sources has to be taken.
Alpha emitters will need little shielding
Beta emitters will need thin lead or thick aluminium