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UPDATED TO 2023-2025 SYLLABUS
CAIE IGCSE
PHYSICS
SUMMARIZED NOTES ON THE THEORY SYLLABUS
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CAIE IGCSE PHYSICS
1. Motion, Forces and Energy
1.1. Physical Quantities and
Measurement Techniques
The area of a square with sides 1 cm long is 1 square
centimetre (1 cm²).
Area formula: area = length × breadth.
SI unit of area: square metre (m²), which is the area of a
square with sides 1 m long.
Volume
Units and basic quantities
A standard or unit must be chosen before a
measurement can be made.
The size of the quantity to be measured is found using
an instrument with a scale marked in the unit
Three basic quantities are measured in physics: length,
mass, and time.
Units for other quantities are based on length, mass, and
time.
The SI (Système International d’Unités) system is a set
of units used in many countries
Length
Unit of length: metre (m)
1 decimetre (dm) = 10⁻¹ m
1 centimetre (cm) = 10⁻² m
1 millimetre (mm) = 10⁻³ m
1 micrometre (μm) = 10⁻⁶ m
1 nanometre (nm) = 10⁻⁹ m
Multiples for large distances:
1 kilometre (km) = 10³ m
1 gigametre (Gm) = 10⁹ m
Many length measurements are made with rulers/meter
rule
For any length less than a meter, we use a tape measure
Volume is the amount of space occupied.
Unit of volume: cubic metre (m³).
Commonly used unit for volume: cubic centimetre (cm³).
Volume of a cylinder: V = πr2 h
A measuring cylinder can measure the volume of a
liquid. Ensure the cylinder is upright and the eye is at
bottom level of the meniscus.
Time
Unit of time: second (s).
Time-measuring devices use oscillations.
Choose a timer that is precise enough for the task (e.g., a
stopwatch for the pendulum period or a millisecond
timer for measuring the speed of sound).
Scalars and Vectors
Note: Take ± readings for accuracy
Area
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Scalar quantity: has magnitude (size) only.
Examples: distance, speed, time, mass, pressure, energy,
temperature.
Vector quantity: described by both magnitude and
direction.
Examples: force, gravitational field strength, electric field
strength, weight, velocity, acceleration, momentum.
Representing Vectors: a straight line with length
indicating the magnitude and an arrow showing
direction.
Adding scalars: ordinary arithmetic.
Adding vectors: geometrically, considering both
magnitude and direction.
For two vectors, FX and FY, at right angles:
The magnitude of the resultant
F =
FX2 + FY2
​
Distance and displacement
Distance is a length a body travels between two points. It
is a scalar quantity.
Displacement is similar to distance but as it is a vector
quantity, direction is also considered.
​
Distance-Time Graph Examples
Angle θ between FX and F
tan θ = FFXY
​
​
​
At rest ( BC).
Constant speed (AB and CD)
Speed is higher when the gradient is steeper. For
example, the speed of the train at CD is 2m/s, but that at
AB is 1m/s. It is higher in CD, which can be seen as CD
being steeper.
Non-Constant Speed
When speed changes, the gradient of the distance-time
graph varies.
Upward curve of increasing gradient: accelerating.
The upward curve of decreasing gradient: decelerating.
Example:
1.2. Motion
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Gradient of the tangent at T:
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CAIE IGCSE PHYSICS
AB
40m
BC = 2s = 20m/s
​
Velocity is the distance travelled in unit time in a given
direction. Ie. Velocity = Speed given in a specific direction.
Speed is the distance travelled in unit time.
Example: If two trains travel due north at 20 m/s, they
have the same speed and velocity due north. If one
travels north and the other south, their speeds are the
same, but not their velocities.
Key definition: Velocity is the change in displacement
per unit of time.
Velocity formula:
in a given direction
Velocity = Distance moved
=
Time taken
​
​
Displacement
T ime
Speed
Speed is the distance travelled by a body in unit time.
When the distance travelled is (s) over a short time
period (t), the speed (v) is given by:
v = st
​
Key definition: Speed is the distance travelled per unit
time.
General formula:
distance travelled
Average speed = Total
Total time taken
​
Example: If a car travels 300 km in five hours, its average
speed is: Average speed = 3005 hkm = 60 km/h
​
Velocity is the speed in a given direction.
A body's velocity is uniform or constant if it moves at a
steady speed in a straight line.
Velocity is not uniform if the body moves in a curved
path.
Speed and velocity units are the same: km/h, m/s.
Note: Speed is a scalar quantity and velocity a vector
quantity. Displacement is a vector, unlike distance which
is a scalar
Acceleration
When the velocity of an object changes, the object
accelerates.
Acceleration is defined as the change of velocity in
unit time:
​
Velocity
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Acceleration = Δv
Δt
Time (s)
0
1
2
3
4
5
6
​
Speed (m/s)
0
5
10
15
20
25
30
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CAIE IGCSE PHYSICS
Example: If a car starts from rest and reaches a
velocity of 2 m/s after 1 second, its acceleration is
2m/s2 , due north
Key definition: Acceleration is the change in velocity per
unit time.
Example: For a steady increase of velocity from 20 m/s to
50 m/s in 5 seconds: Acceleration = (50−20),m/s
=
5s
2
6m/s
Acceleration is a vector, and its magnitude and direction
should be stated.
For motion in a straight line, the magnitude of the
velocity equals the speed, and the magnitude of the
acceleration equals the speed change in unit time.
Example: A car accelerating on a straight road with the
following speeds:
The speed increases by 5 m/s every second, and the
acceleration is constant at 5 m/s².
Acceleration is positive if the velocity increases.
Acceleration is negative if the velocity decreases (also
called deceleration or retardation).
​
The linear shape (AB) of the graph indicates constant
acceleration.
The speed increases by 4 m/s every second, indicating
constant acceleration.
Variable Acceleration
Example 1: The figure shows acceleration from rest,
constant speed, and deceleration.
Speed-Time Graphs
Speed-time graphs plot the speed of an object against
time.
Used to solve motion problems.
Constant Speed
Example: AB is a speed-time graph for an object moving
with a constant speed of 25 m/s.
A straight horizontal line on a speed-time graph indicates
constant speed.
Example 2: The figure shows changing acceleration with
a curved shape.
Constant Acceleration
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First Equation
If an object is moving with constant acceleration ( a )
in a straight line and its speed increases from ( u ) to (
v ) in time ( t ):
Acceleration is given by:
a = v−u
t
​
Rearranging gives:
v = u + at
Second Equation
For an object moving with constant acceleration, its
average speed equals half the sum of its initial and
final speeds:
Speed increases over time, but by a smaller amount each
second, indicating decreasing acceleration.
Using Gradient to Calculate Acceleration
The gradient of a speed-time graph represents the
acceleration.
For constant speed, the gradient is zero, indicating zero
acceleration.
For constant acceleration, the gradient is given by: \n
Y <i>2−Y </i>1
Δy
Gradient = Δx
= X<i>2−X</i>1
For changing acceleration, the gradient changes,
indicating changing acceleration.
An object accelerates if the speed increases and
decelerates if the speed decreases with time.
​
(Equation 1)
Average speed = u+v
2
​
If (s) is the distance moved in time (t), then:
Average speed = st
​
Combining these, we get
​
s
u+v
t = 2
​
​
Rearranging gives:
s = (u+v)
⋅ t (Equation 2)
2
Air Resistance and Free Fall
​
Area Under a Speed-Time Graph
In the air, a coin falls faster than a small piece of paper
due to air resistance.
In a vacuum, both fall at the same rate.
Air resistance has a greater effect on light bodies
compared to heavy bodies.
Air resistance is negligible for dense, heavy objects at low
speeds.
Acceleration of Free Fall
Measures the distance travelled.
The rule applies even if acceleration is not constant.
The distance equals the shaded area under the graph.
Equations for constant acceleration
All bodies falling freely under gravity accelerate
uniformly if air resistance is negligible.
This uniform acceleration is called the acceleration of
free fall, denoted by ( g ).
The value of (g) varies slightly but is about 9.8 m/s² on
average.
The velocity of a free-falling body increases by about
9.8m/s every second.
A ball shot upwards with a velocity of 30 m/s decelerates
by about 9.8 m/s every second, reaching its highest point
after 3 seconds.
As an object falls, air resistance increases, reducing its
acceleration.
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CAIE IGCSE PHYSICS
Mass
The mass of an object is the measure of the amount of
matter in it. It is a measure of the quantity of matter in
an object at rest relative to an observer.
The standard unit of mass is the kilogram (kg), with the
gram (g) being one-thousandth of a kilogram: 1g =
10−3 kg = 0.001kg
Mass is different from weight, which is a gravitational
force on an object with mass.
Weight
When air resistance equals the object's weight, it falls at
a terminal velocity.
Terminal velocity depends on the object's size, shape,
and weight.
A small, dense object has a high terminal velocity and
accelerates for a longer distance.
A light object or one with a large surface area, like a
raindrop or parachute, has a low terminal velocity and
accelerates over a shorter distance.
Following is the velocity-time graph for a falling
parachutist:
Explanation:
Initial Phase: When the parachutist jumps out of the
plane, they experience free fall. During this phase, their
velocity increases steadily due to the acceleration of
gravity (approximately 9.8m/s2 acting downwards. The
graph slopes upwards steeply.
Slowing down of Parachute: Air resistance increases
significantly when the parachutist deploys their
parachute. This causes a decrease in acceleration,
leading to a less steep slope on the graph. The
parachutist’s velocity continues to increase but at a
slower rate compared to free fall.
Terminal Velocity: As the parachutist continues to fall,
their velocity eventually reaches a maximum constant
value known as terminal velocity. At terminal velocity, the
forces of gravity and air resistance (drag) balance out,
resulting in zero net acceleration. On the velocity-time
graph, this appears as a horizontal line where the
velocity remains constant.
1.3. Mass and Weight
Weight is the gravitational force acting on an object that
has mass.
The weight of an object can vary with location due to
differences in gravitational field strength.
The unit of force is the Newton (N). Weight is measured
in newtons and can be determined using a spring
balance.
Aspect
Definition
Units
Measurement
Dependency
Mass
Weight
Measure of the amount of matter in Gravitational force acting on an object
an object
with mass
Kilogram (kg), gram (g)
Newton (N)
This can be measured using a
Measured using a spring balance or
balance
scale
Independent of location and
Depends on location and gravitational
gravitational field
field strength
Symbol in
Equations
m
(W ), or, (Fg )
​
Gravitational Field
Gravity acts through space, causing objects not in
contact with the Earth to fall towards it.
Gravitational field strength (g) is the force per unit mass
and is a vector quantity with magnitude and direction.
On Earth's surface, g = 9.8 N/kg or 9.8 m/s^2,
representing both the acceleration due to gravity and the
gravitational field strength.
1.4. Density
Definition
Density (ρ) is the measure of mass per unit volume
ρ= m
V
​
Standard units for density include kilograms per cubic
meter (kg/m³) or grams per cubic centimeter (g/cm³).
Calculation Methods
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Regular Shape: Measure mass (m) using a balance, and
measure volume (V ) by direct measurement of
dimensions.
Irregular Shape: Measure mass (m) using a balance.
Measure volume (V ) using displacement methods:
Method 1: Immerse the object in a measuring cylinder filled
with water, record the initial and final water levels to find
volume.
Liquid: To determine the mass of an empty container,
add liquid, measure total mass, and subtract to find the
mass of the liquid. Divide by the known volume to find
density.
Air: Measure the mass of a flask filled with air, then
remove the air with a vacuum pump. Calculate air
density by dividing the mass difference by volume
measured using water displacement.
Example Calculations
Example 1: Calculate the density of copper given a mass
63 g
of 63 g and a volume of 7 cm³ ρ = m
V = 7 cm³ =
9 g/cm³
Example 2: Determine the mass of an aluminium sheet
with a volume of 73 cm³ and a density of 2.7 g/cm³
m = ρ × V = 2.7 g/cm³ × 73 cm³ = 197.1 g
​
​
Floating and Sinking:
Method 2: Displacement Can. Fill the can until the spout.
Immerse the object in the water and find the volume of
water displaced. That volume of water is the volume of
the object.
Objects float or sink in liquids based on their density
relative to the liquid's density. A higher-density object
sinks in a lower-density liquid and vice versa.
1.5. Forces
Force
A force is a push or a pull that can change the motion,
speed, or shape of an object.
It can cause objects at rest to move or alter the direction
of moving objects.
Extension in Springs
Springs follow Hooke's Law, where extension is
proportional to the stretching force up to the limit of
proportionality.
Symbolically, extension ∝ stretching force
Spring Constant
The spring constant (k) measures the force needed to
cause a unit extension in a spring.
k = Fx , where (F ) is the force applied and (x) is the
resulting extension.
​
Load-Extension Graphs
Used to graphically represent the relationship between
applied force (load) and resulting extension in materials
like springs.
Non-linear graphs beyond the limit of proportionality
indicate permanent deformation.
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CAIE IGCSE PHYSICS
Friction and Air Resistance
Forces and Resultants
Forces have magnitude and direction, represented by
arrows in diagrams.
Multiple forces acting on an object can be balanced (e.g.
weight and support force) or have a resultant force.
The resultant force is the single force that has the same
effect as all forces acting together.
A resultant force can change the velocity of an object by
altering its speed or direction of motion.
Forces like friction and air resistance cause objects to
slow down and eventually come to rest.
In their absence, objects would continue moving
indefinitely with constant speed.
Newton’s Second Law
States that the acceleration of an object is directly
proportional to the force acting on it and inversely
proportional to its mass.
Mathematically expressed as:
F = ma
where (F ) is the resultant force in newtons (N ), (m) is
the mass in kilograms (kg ), and (a) is the acceleration in
meters per second squared (m/s2 ).
Proportional Relationships
Acceleration (a) is directly proportional to the force (F )
when mass (m) is constant
a∝F
Acceleration (a) is inversely proportional to mass (m)
when force (F ) is constant
a ∝ m1
​
Newton’s First Law
An object remains at rest or continues to move at a
constant speed in a straight line unless acted upon by a
resultant force.
This means that no force is required to maintain
constant velocity if no external forces act on the object.
Units and Constant (k )
The unit of force, the newton (N ), is defined as the force
that gives a 1 kg mass an acceleration of 1m/s2
k in F = kma equals 1 when m = 1kg and a = 1 m/s2
Resultant Force and Motion
Resultant force (F ) causes an object to accelerate in the
direction of the force.
When forces are balanced, there is no acceleration, but
changes in shape may occur due to internal forces within
the object.
Friction
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Friction is the force that opposes the motion o of one
surface over another.
It is essential for walking and gripping surfaces but can
prevent proper movement on surfaces like ice.
Types of Friction
Static Friction: The frictional force that opposes the
starting of motion between surfaces in contact.
Kinetic Friction: The frictional force that opposes the
motion of surfaces sliding past each other.
Fluid Friction (Drag): Resistance encountered by an
object moving through a fluid (air or liquid), increasing
with speed and reducing acceleration.
Effect of Force and Mass on Friction
Increasing the force pressing surfaces together increases
friction initially.
Friction converts kinetic energy into thermal energy,
causing a rise in temperature when contacting surfaces.
Centripetal Force
In a circular motion, an object moves in a curved path
due to a force directed towards the centre of the circle.
Despite constant speed, circular motion involves
acceleration because velocity direction changes
continuously.
Acceleration towards the centre of the circle is necessary
to maintain circular motion.
Factors Affecting Centripetal Force
Centripetal force magnitude depends on the following:
Speed (v): Increasing speed increases centripetal force.
Radius (r): Decreasing radius increases centripetal
force.
Mass (m): Increasing mass increases centripetal force.
Role of Centripetal Force
It ensures the object maintains a constant distance from
the centre of the circle.
Moment of a Force
The turning effect of a force around a pivot point is called
the moment of the force.
It depends on both the magnitude of the force and the
perpendicular distance from the pivot to the line of
action of the force.
Mathematically, the moment is given by:
M =F ×d
where d is the perpendicular distance from the pivot to
the line of action of the force.
The unit of moment is the Newton metre (N m).
Balancing a Beam and the Law of Equilibrium
Acceleration in Circular Motion
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To balance a beam around a pivot point, the principle of
moments (or law of moments) is used.
The law states that for a beam in equilibrium, the sum of
clockwise moments about any point equals the sum of
anticlockwise moments about the same point.
This principle is essential for designing and
understanding the equilibrium of lever systems and
other balanced structures.
Conditions for Equilibrium
An object is in equilibrium if:
The sum of all forces acting on it equals zero (static
equilibrium).
The sum of all moments (clockwise and anticlockwise)
around any point is zero (rotational equilibrium).
Centre of Gravity
The centre of gravity (or centre of mass) of an object is
the point through which the entire weight of the object
acts.
It behaves as if all the mass were concentrated at this
single point.
For a uniform object, such as a ruler, the centre of gravity
is at its geometric centre.
The stability of an object depends on the position of its
centre of gravity relative to its base.
An object is stable if its centre of gravity remains over its
base of support.
Toppling occurs when the vertical line through the centre
of gravity falls outside the base of support.
Increasing the base area and lowering the centre of
gravity improves stability.
Types of Equilibrium
Stable Equilibrium: An object returns to its original
position when displaced slightly (e.g., a ball in a bowl).
Unstable Equilibrium: An object moves further away
from its original position when displaced slightly (e.g., a
ruler balanced on its edge).
Neutral Equilibrium: An object remains in its new
position when displaced (e.g., a ball sitting on a flat
surface).
Determining the Centre of Gravity
Finding the centre of gravity of an irregularly shaped
lamina involves suspending the object from different
points and using a plumb line to mark the vertical line
through which it hangs. The centre of gravity is where
these lines intersect.
Momentum
Momentum (p) is the product of an object's mass (m)
and its velocity (v ).
Mathematically, p = mv
It is a vector quantity, meaning it has both magnitude
and direction.
The SI unit of momentum is kilogram metre per second
(kgm/s) or newton second (N s).
Conservation of Momentum
Stability and Toppling
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The total momentum of a closed system of objects
remains constant if no external forces act on it (such as
friction or air resistance).
This principle is known as the conservation of
momentum.
Momentum is conserved in collisions (both elastic and
inelastic) and explosions. For example, in a collision, the
total momentum before and after the collision remains
the same.
pinitial = pfinal
​
​
Example:
A trolley of mass m1 = 3 kg moving with velocity u1 = 5
m/s collides and couples with a stationary trolley of mass
m2 = 2 kg. They move off together with the same
velocity (v). We need to find (v).
1. Calculate initial momentum (pinitial ):
pinitial = m1 ⋅ u1 = 3 kg ⋅ 5 m/s = 15 kgm/s
2. Calculate final momentum (pfinal ):
Since they move off together with velocity (v):
pfinal = (m1 + m2 ) ⋅ v = (3 kg + 2 kg) ⋅ v =
5 kg ⋅ v
3. Apply conservation of momentum (pinitial =
pfinal ):
15 kgm/s = 5 kg ⋅ v
4. Solve for (v):
= 3 m/s
v = 15 5kgm/s
kg
So, the velocity (v ) of the two trolleys moving together
after the collision is 3 m/s
​
​
​
​
​
​
​
1.6. Energy, work and power
Types of energy stores
Chemical Energy: Energy stored in chemical bonds of
substances like food, fuels (oil, gas, coal, wood).
Gravitational Potential Energy: Energy an object
possesses due to its position relative to a reference point
(usually the Earth's surface).
Elastic Strain Energy: Energy stored in an object when it
is compressed, stretched, or deformed.
Kinetic Energy: Energy possessed by a moving object.
Electrostatic Energy: Energy stored in charged objects
due to their separation in an electric field.
Nuclear Energy: Energy stored in the nucleus of an
atom..
Internal (Thermal) Energy: Total energy stored in the
microscopic motions and interactions of particles within
a substance.
​
​
​
​
​
​
​
​
Impulse
Impulse (J ) is the change in momentum (Δp) of an
object when a force acts on it over a period of time (Δt).
Mathematically, J = F Δt = Δp
Impulse is also a vector quantity and has the same
direction as the force causing it.
Energy Transfers
Mechanical Working: Transfer of energy by the action
of a force, like lifting a weight.
Electrical Working: Transfer of energy by an electric
current, such as in batteries or electric motors.
Waves (Electromagnetic and Sound): Transfer of
energy through waves, like light or sound waves.
Heating: Transfer of energy through thermal processes,
like heating water in a boiler.
Principle of Conservation of Energy
Energy cannot be created or destroyed, only
transformed from one form to another. Thus the total
amount of energy is constant.
Energy Forms
Force and Momentum:
Relation of force to the rate of change of momentum:
(F = Δp
Δt ), which is an alternative form of Newton's
second law.
​
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Kinetic Energy (Ek ): Energy possessed by an object due
to its motion.
Ek = 12 mv 2 , where (m) is mass and (v) is velocity.
Example Calculation: For a football of mass 0.4 kg
moving at 20 m/s:
Ek = 12 × 0.4 × (20)2 = 80 J
Potential Energy (Ep ):Energy an object has due to its
position or condition or configuration.
Ep = mgh , where (m) is mass, (g ) is acceleration
due to gravity, and (h) is height.
Example Calculation: For a 0.1 kg mass raised vertically
by 1 m:
Ep = 0.1 × 9.8 × 1 = 0.98 J
Energy Type
Renewable or
Non-renewable
​
​
​
Fossil Fuels
Non-renewable
Nuclear Fuels
Non-renewable
Solar Energy
Renewable
Wind Energy
Renewable
Wave Energy
Renewable
Tidal Energy
Renewable
Hydroelectric
Energy
Renewable
Geothermal
Energy
Renewable
Biofuels
Renewable
​
​
​
​
​
Work
Work (W ) is done when a force (F ) displaces a body
through a distance (d) in the direction of the force.
Formula: W = F ⋅ d
Unit: The unit of work is the joule (J), where 1 J = 1 N ⋅
m
Example Calculation
If a force of 50 N is used to move a crate 3 m
horizontally:
W = 50 N × 3 m = 150 J
If lifting a mass of 3 kg vertically by 2 m (where g ≈
10 m/s2 ):
W = 30 N × 2 m = 60 J
Energy resources
Advantages
Disadvantages
High energy density,
readily available during
peak demand.
Limited supply,
environmental pollution
(CO2, SO2), finite resource.
Radioactive waste disposal
High energy output, low
issues, potential for
CO2 emissions.
accidents (e.g., Chernobyl,
Fukushima).
Abundant, no emissions Intermittent availability, high
during operation, diverse initial costs for large-scale
applications.
installations.
Clean energy source,
Visual
and noise impacts,
abundant in suitable
intermittent nature of wind.
locations.
Renewable, predictable in Technologically challenging,
coastal areas with
potential environmental
consistent waves.
impacts.
Predictable and consistent, High infrastructure costs,
minimal greenhouse gas environmental impacts on
emissions.
marine ecosystems.
Disruption of aquatic
Reliable, long operational
ecosystems, potential
life, minimal greenhouse
displacement of
gas emissions.
communities, limited
suitable sites.
to geologically active
Reliable, low emissions, Limited
areas,
high
upfront costs for
constant energy source.
exploration and drilling.
Renewable, lower
emissions compared to
fossil fuels.
Competition with food
production, land use issues,
varying energy content.
How Fossil Fuels are used in Power Stations
Coal: In coal-fired power stations, coal is burned in a
boiler to produce heat.
Natural Gas: In gas-fired power stations, natural gas is
burned directly in a gas turbine.
The heat generated from burning these fuels is used to
boil water, creating high-pressure steam.
The steam drives turbines connected to electrical
generators.
Turbines are designed with sets of blades (rotor)
mounted on a shaft, which rotates when steam is
directed onto them.
As steam expands through the turbine, its energy is
transferred to the rotor, causing it to spin.
The spinning rotor generates electricity through
electromagnetic induction in the generator.
How hydroelectric power stations work
They run using the kinetic energy generated from the
flow of water moving downstream.
This kinetic energy spin turbines which are connected to
generators.
These generators then produce electricity that can be
used by households.
How Nuclear Fuels (uranium) are used in Power Stations
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Nuclear power stations use controlled nuclear fission
reactions with uranium to generate heat.
This heat is used to produce steam indirectly through a
heat exchanger.
The steam, similar to fossil fuel stations, drives turbines
connected to generators to produce electricity.
The operation involves the steam passing through a
turbine's fixed blades (stator) onto the rotating blades
(rotor), where the expansion of steam energy is
converted into rotational motion.
The rotational motion of the rotor then drives the
electrical generator, producing electricity for
consumption.
Power
The power of a device is the work it does per second, or
the rate at which it does work.
Power also represents the rate at which energy is
transferred from one store to another.
Formula:
work done
power = time
taken
W
P = t where W is the work done in time t
P = ΔE
t where ΔE is the energy transferred in time
t
Key definition: Power is the work done per unit time
and the energy transferred per unit time.
Unit of power: watt (W ), where 1 W = 1 J/s
Larger units:
1 kW = 1000 W = 103 W
1 M W = 1,000,000 W = 106 W
Example: If a machine does 500 J of work in 10 s, its
power is:
500J
10s = 50W
​
Work done on load = 300 J
Calculate Efficiency:
J
Efficiency = ( 300
400 J ) × 100 = 75%
Example b: Electric Drill
​
Given:
Power input to drill = 300 J/s
Useful power output (excluding thermal losses) = 200 J/s
Calculate Efficiency:
J/s
Efficiency = ( 200
300 J/s ) × 100 = 66.67%
​
Sankey Diagrams
Sankey diagrams are used to represent energy transfers
and efficiencies visually.
They show how input energy is divided into useful output
energy and wasted energy.
The width of the arrows in a Sankey diagram is
proportional to the amount of energy they represent.
A wide arrow represents a large amount of energy, while
a narrow arrow represents a small amount.
​
​
​
Efficiency
1.7. Pressure
% Efficiency formula for energy
Energy Output
Efficiency (%) = ( Useful
Total Energy Input ) × 100%
​
% Efficiency formula for power
Power Output
Efficiency (%) = ( Useful
Total Power Input ) × 100%
​
Example a: Electric Motor
Given:
Pressure is the force per unit area.
Formula:
pressure = force
area
Key definition: Pressure is the force per unit area.
Unit of pressure: pascal (P a), where 1 P a = 1 N /m²
Greater area over which a force acts results in less
pressure.
​
Liquid Pressure
Energy input = 400 J
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Pressure in a liquid increases with depth because the
further down you go, the greater the weight of liquid
above.
Pressure at one depth acts equally in all directions.
Pressure depends on the density of the liquid; the
denser the liquid, the greater the pressure at any given
depth.
The change in pressure Δp at a depth Δh below the
surface of a liquid with density ρ is determined by
considering a horizontal area A.
Force acting vertically downwards on area A equals the
weight of the liquid column of height Δh and crosssectional area A above it.
Volume of the liquid column: ΔhA
Mass of the liquid column: m = ρΔhA (mass =
density × volume)
Weight of the liquid column: mg = ρΔhAg
Force on area A: ρΔhAg
Pressure due to the liquid column:
pressure = force
area
ρΔhAg
=
ρgΔh
A
Formula: Δp = ρgΔh
Δp is the change in pressure beneath the surface of the
liquid at depth Δh due to the weight of a liquid of
density ρ
g is the gravitational field strength
This pressure acts equally in all directions at depth
Δh and depends only on Δh and ρ.
Value will be in pascals (P a) if Δh = is in meters (m) and
(ρ) is in kilograms per cubic meter (kg/m³).
​
​
2. Thermal Physics
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2.1. Kinetic Particle Model of Matter
States of Matter
Matter consists of tiny particles like molecules and
atoms.
Matter exists as solids, liquids, or gases, each with
different characteristics.
Solids have a definite shape and volume, and particles
are close together in fixed positions.
Liquids have a definite volume and take the shape of
their container. The particles are further apart and can
slide over each other.
Gases have no definite shape or volume, and particles
move much further apart and freely.
Brownian Motion
Describes random motion of particles in fluids (liquids
and gases) and is caused by collisions with smaller,
faster-moving particles.
Temperature and kinetic energy
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Particles in solids vibrate in fixed positions at room
temperature.
Heating solids increases particle vibrations, raising their
average kinetic energy.
Cooling a solid reduces particle vibrations until absolute
zero (-273°C or 0 K) stops all motion.
Absolute zero is the lowest possible temperature
achievable.
Reducing the volume of a gas increases the
concentration of particles.
More particles per unit volume lead to more collisions
with the container walls.
The pressure increases proportionally to the decrease in
volume:
Variations in Gas Pressure with Volume
Boyle's Law states that at constant temperature, the
product of pressure and volume is constant:
Pressure and Kinetic Energy
Gases have particles moving randomly at high speeds.
Each gas particle collision with a container wall changes
its momentum, creating a force.
The average force per unit area on container walls
remains constant at a constant temperature.
Increasing temperature raises collision frequency,
increasing average force and gas pressure.
Effect on Pressure of a Change in Temperature (Constant
Volume)
Heating a gas increases the kinetic energy of its particles.
Higher kinetic energy leads to more frequent and
energetic collisions with the container walls.
Increased collisions result in higher pressure according
to a gas law:
( PV = nRT )
Effect on Pressure of a Change in Volume (Constant
Temperature)
(p1 V1 = p2 V2 )
​
​
​
​
Graphing pressure ( p ) against the reciprocal of volume
( V1 ) gives a straight line.
​
Absolute Zero and Kelvin Temperature Scale:
Absolute zero, at −273°C or 0 K, is the lowest possible
temperature.
Kelvin scale temperatures are derived by adding 273 to
Celsius temperatures: (T (K) = θ(°C) + 273)
In the Kelvin scale, all temperatures are always positive
and directly proportional to the average kinetic energy of
particles.
2.2. Thermal properties and
temperature
Thermal expansion of solids, liquids and gases
Solids and Liquids: When heated, particles vibrate more,
causing them to push apart slightly, resulting in
expansion.
Gases: Heating increases particle speed and collisions
with container walls, which causes container expansion
to maintain pressure.
Applications
Bimetallic Strips: Made from metals with different
expansion rates (e.g., copper and iron). Used in:
Fire Alarms: Bends to complete an electrical circuit
when exposed to heat, triggering alarms.
Thermostats: Maintains temperature by bending to
break or complete electrical circuits
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Shrink-fitting: Cooling components contracts them, fitting
tightly into other parts upon warming. Used in
manufacturing for tight connections without fasteners.
Lid Removal: Expanding metal lids with hot water
loosens them from glass jars, leading to easier opening.
Precautions
Expansion joints are spaces left between rail tracks used
in railways, and pipes to allow for thermal expansion
without damage
Internal Energy and Heating
Internal energy increases when an object is heated.
Different materials require varying amounts of heat to
raise their temperatures due to differences in specific
heat capacity.
Specific heat capacity (c) measures the amount of heat
required to raise the temperature of a substance by 1
degree Celsius per unit mass.
Specific heat capacity (c) is defined as the energy
required per unit mass per unit temperature increase,
measured in joules per kilogram per degree Celsius
(J/(kg°C)
The formula relating heat energy (ΔE ), mass (m),
specific heat capacity (c), and temperature change (Δθ)
is: \n ΔE = mcΔθ
Specific heat capacity quantifies how much heat energy
is needed to raise the temperature of a substance.
Materials with higher specific heat capacities require
more heat energy per unit mass to achieve the same
temperature change.
Worked Example Calculation
Given:
Heat energy supplied, (ΔE = 20000, J)
Mass of the substance, (m = 5, kg)
Temperature change, (Δθ = 10°C)
Calculate the specific heat capacity (c) of the substance.
Formula:
The specific heat capacity (( c )) is given by:
ΔE
c = mΔθ
​
Substituting the given values:
c = 20000
5×10
Calculation:
​
c = 20000
50
c = 400J/(kg°C)
​
Temperature and Thermal Energy
Temperature is related to the average kinetic energy of
particles.
Thermal energy is the total energy of particles in a
substance, and more particles can hold more total
thermal energy even if they have lower individual particle
energies.
Heat Transfer and Equilibrium
Heat transfers from higher to lower temperature bodies
until thermal equilibrium is reached.
This transfer is caused by collisions between particles,
making their average kinetic energies equal.
Specific Heat Capacity
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Change of State
Heating can change a solid to a liquid (melting) and a
liquid to a solid (freezing).
Pure substances melt and freeze at specific
temperatures, such as water at 0°C.
Melting involves particles of a solid overcoming
intermolecular forces to become a liquid.
Solidification (freezing) involves the transfer of potential
energy from particles to surroundings as a liquid
becomes solid.
Vaporisation requires substantial energy to overcome
intermolecular forces in a liquid to become gas (vapour).
Condensation involves gas particles losing potential
energy to their surroundings as they return to a liquid
state.
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Convection
Evaporation
Higher temperatures, larger surface areas, and wind or
draughts increase the rate of evaporation.
Energy is transferred to the surroundings from the liquid
during evaporation, cooling the liquid.
Evaporation cools the body through sweat, helping to
maintain a constant temperature.
Differences between boiling and evaporation
Feature
Temperature
Process
Energy
Requirement
Speed
Throughout
Liquid?
Boiling
Evaporation
Occurs at a specific boiling
Occurs at any temperature below
temperature.
the boiling point.
Bubbles of vapour form within the Occurs at the surface of the liquid.
liquid.
Requires sufficient heat to reach Requires less heat and occurs due to
boiling point.
energetic particles escaping.
Rapid compared to evaporation.
Slower compared to boiling.
Happens throughout the entire
Happens
only at the liquid's surface.
volume of the liquid.
Heat transfer method in fluids like liquids and gases.
Transfer of thermal energy by movement of the matter
itself.
Convection Currents
Warm fluids rise because they expand and become less
dense.
Cooler, denser fluids sink and replace the rising warm
fluid.
This movement of fluids due to temperature differences is
known as a convection current.
2.3. Transfer of thermal energy
Conduction
Conduction is heat transfer through matter from hot to
cold without moving matter.
Metals conduct heat well (e.g., copper, aluminum);
insulators (wood, plastic) are poor conductors.
Metals feel colder due to rapid heat transfer from the
hand compared to insulators at the same temperature.
Liquids and gases conduct heat slowly because the
particles are further apart and need time to transfer
energy to each other.
Metals transfer heat via fast-moving free electrons,
raising temperatures in cooler areas and lattice
vibrations.
Non-metals transfer heat through slower atomic or
molecular vibrations, lacking free electrons.
Radiation
A method of thermal energy transfer which occurs
without matter, even in vacuum.
Emits as electromagnetic waves, travels at speed of light.
Absorption and Reflection
Surfaces vary in radiation absorption.
Black surfaces absorb more than shiny white ones.
Emission
Surface Type
Shiny White
Dull Black
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Absorption of Radiation
Poor absorber
Good absorber
Emission of Radiation
Poor emitter
Good emitter
Reflectivity
High
Low
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Surfaces emit radiation differently when hot.
Dull black surfaces emit more than shiny surfaces.
All bodies emit radiation above absolute zero.
Greenhouse effect
Greenhouse gases trap heat similar to glass in a
greenhouse.
Balance between incoming solar radiation and emitted
Earth radiation crucial for climate stability.
Increased carbon dioxide and methane upset this
balance and absorb more infrared which cannot escape.
Wavelength (λ): Distance between 2 successive crests/
troughs.
Frequency (f ): Number of complete waves created per
second, measured in hertz (Hz).
Wave speed (v): Distance moved by a crest or any point
on the wave in 1 second.
Amplitude (a): Height of a crest or depth of a trough
from the undisturbed or mean position.
Phase: Particles in ‘phase’ have the same speed and
direction of vibration.
Wave equation
Faster vibration produces a shorter wavelength.
Therefore, a higher frequency results in a smaller
wavelength.
Wave equation:
v = fλ
Wavefronts and rays
Wavefront: A straight line where the wave has the same
phase at all points.
Ray: Line drawn at right angles to a wavefront showing
the direction of travel.
3. Waves
3.1. General Properties of Waves
Progressive waves carry energy from one place to
another without transferring matter.
Two Types of Progressive Waves
Transverse waves
Longitudinal waves
Reflection of a wave at a plane surface
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Straight water waves (transverse waves) hit a metal strip
in a ripple tank at x° angle.
Angle of incidence (i) and angle of reflection (r)are both
x° .
Angle of incidence equals angle of reflection: (i = r)
Same wavelength as reflected wave
Same wave speed
Straight water waves meet narrow gaps and create
circular wavefronts.
Diffraction can also occur at the edges of obstacles
causing wave spreading.
3.2. Reflection and Refraction of Light
Refraction
Continuous straight waves in shallow water have shorter
wavelengths than in deeper water.
Waves in shallower water have a smaller speed and
smaller wavelength.
When waves move from shallow to dense regions, they
bend towards the normal, and when they move from
dense to shallow regions, they bend away from the
normal.
Light travels in a path called a ray.
A beam is a stream of light shown by several rays.
Beams can be parallel, diverging, or converging.
Speed of Light
The speed of light is about 1 million times faster than the
speed of sound.
The speed of light is 3 × 108 meters per second.
Reflection of light against a plane mirror
Diffraction
The normal is perpendicular to the mirror at the point
where the incident ray strikes.
The angle of incidence (i) is between the incident ray
and the normal.
The angle of reflection (r) is between the reflected ray
and the normal.
The law of reflection states that the angle of
incidence is equal to the angle of reflection.
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Light refracts due to speed change when entering a
different medium.
In air, light travels at 300, 000 km/s (3 × 10⁸ m/s)
In glass, it slows to 200,000 km/s (2 × 10⁸ m/s)
Refractive index (n) is the ratio of light speed in air to
light speed in the medium.
For glass: n = 300,000km/s
= 32 = 1.5
200,000km/s
Refractive index is the ratio of speeds of a wave in two
different regions.
sin(i)
Experimentally it is true that n = sin(r)
where (i) is the
angle in air and (r) is the angle in glass.
Higher refractive index means greater bending of light as
it slows down more.
​
Real and Virtual Images
A real image can be produced on a screen and is formed
by rays that pass through the screen.
A virtual image cannot be formed on a screen.
A virtual image is produced by rays that seem to come
from it but do not pass through it.
The image in a plane mirror is virtual. Rays from an
object are reflected at the mirror and appear to come
from a point behind the mirror where the rays would
meet when extrapolated (extended) backward.
​
​
Critical Angle
When light passes from an optically denser to an
optically less dense medium at small angles of incidence,
there is a strong refracted ray and a weak reflected ray.
Increasing the angle of incidence increases the angle of
refraction.
Critical angle (c) occurs when the angle of refraction is
90°.
For angles of incidence greater than (c), light undergoes
total internal reflection.
Total internal reflection means that the light does not
cross the boundary and reflects inside the denser
medium.
For the critical angle: sin(c) = n1 where n is the
refractive index.
​
Refractive Index
3.3. Lenses
Converging and Diverging Lenses
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A converging (or convex) lens is thickest in the center and
bends light inwards.
A diverging (or concave) lens is the thinnest in the center
and spreads the light out.
The center of a lens is its optical center (C) and the line
through C at right angles to the lens is the principal axis.
Draw a straight line (parallel to the principal axis).
Start the line from the top of the object towards the lens.
After refraction through the lens, draw this direct ray
through the focal point F on the opposite side of the
lens.
Principal focus
When a beam of light (parallel to the principal axis)
passes through a converging lens, it refracts to converge
at a point called the principal focus (F ).
The principal focus of a converging lens is a real focus.
A diverging lens has a virtual principal focus behind the
lens, from which the refracted beam appears to diverge.
A lens has two principal focuses, one on each side, each
equidistant from the optical center (C).
The distance (CF ) is the focal length (f ) of the lens.
Central Ray (Ray 2):
Draw a straight line from the top of the object through
the optical center C of the lens.
This ray will continue in the same direction without
bending at all.
Image formed:
Ray diagrams
A ray parallel to the principal axis is refracted through
the principal focus (F ).
A ray through the optical center (C) is undeviated (not
refracted) for a thin lens.
A ray through the principal focus (F ) is refracted parallel
to the principal axis.
The intersection of rays (in one beam) after refraction
gives the location of the image.
How to draw a ray diagram step-by-step
Parallel Ray (Ray 1):
These two will intersect on the opposite side of the lens
to form the image of the object.
Magnification
The linear magnification (M ) is given by:
image size
M = object
size
Magnification can also be expressed as:
distance of image from lens
M = distance
of object from lens
Image properties at different object positions are shown
below:
​
​
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Object Position
At 2F
Between 2F and F
At F
Between F and lens
Image Position
At 2F
Beyond 2F
At infinity
On the same side of lens
Image Nature
Real, inverted
Real, inverted
Real, inverted
Virtual, upright
Image Size
Same size
Larger
Infinitely large
Larger
When white light passes through a triangular glass prism,
it separates into a band of colors known as a spectrum.
This separation of colors is called dispersion and occurs
because the refractive index of glass varies with the
wavelength of light.
White light consists of many colors with different
wavelengths, and the prism separates them based on
their refractive indices.
The colors of the visible spectrum, from longest to
shortest wavelength, are: red, orange, yellow, green,
blue, indigo, and violet
Red light, with the longest wavelength and lowest
frequency, is refracted the least by the prism.
Violet light, with the shortest wavelength and highest
frequency, is refracted the most by the prism.
Applications of Lenses in Vision Correction
Short-Sightedness (Myopia)
Cause: The eye lens focuses light in front of the
retina instead of on it. This causes distant objects to
appear blurry.
Correction: A diverging (concave) lens is used to
spread out light rays before they enter the eye, so the
lens can focus them correctly on the retina.
Long-Sightedness (Hypermetropia)
Cause: The eye lens focuses light behind the retina.
This causes nearby objects to appear blurry.
Correction: A converging (convex) lens is used to
focus light rays closer together before they enter the
eye, so they focus correctly on the retina.
3.4. Dispersion of Light
Refraction by a Prism
In a triangular glass prism, a ray bends due to refraction
at each surface.
The bending at the first surface combines with the
bending at the second surface.
This combined change in direction is called the
deviation.
Unlike in a parallel-sided block, where the emergent
(exiting) ray remains parallel to the incident ray, these
bendings do not cancel out in a prism.
3.5. Electromagnetic Spectrum
Light waves and Electromagnetic Spectrum
Light is part of the electromagnetic spectrum, which
extends beyond visible light in both directions (with
greater wavelength vs. smaller wavelength)
The spectrum includes gamma rays, X-rays, ultraviolet,
infrared, microwaves, and radio waves.
Wavelength increases from gamma rays to radio waves,
while frequency increases from radio waves to gamma
rays.
Properties of Electromagnetic Waves
Dispersion
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Electromagnetic waves travel at the speed of light in a
vacuum, approximately 3 × 108 m/s.
They can undergo reflection, refraction, and diffraction
and are transverse waves.
They follow the wave equation v = f λ, where (v ) is the
speed of light, (f ) is the frequency, and (λ) is the
wavelength.
Higher frequency means smaller wavelength and
therefore more energy carried.
Radio Waves and Microwaves
Radio waves are the longest-wavelength electromagnetic
waves used for communication, radio and television
transmission, astronomy, and radio frequency
identification.
Microwaves have shorter wavelengths than radiowaves
and are used in telecommunications, satellite
communication, radar, and microwave ovens.
X-rays have smaller wavelengths than ultraviolet rays
and are used in medical imaging, security screening, and
industrial inspection.
Gamma rays are highly penetrating (smallest wavelength
and largest frequency) and used in cancer detection
cancer treatment to kill cells, sterilization, and material
inspection.
Communication Systems
Below are the differences between digital and analog
signals:
Aspect
Digital Signals
Signal Type
Discrete, binary (0s and 1s)
Transmission
Rate
Examples
Higher transmission rates
Digital data, internet signals,
computer memory
Analog Signals
Continuous, varying amplitude and
frequency
Limited by bandwidth and signal
degradation over distance
Audio signals, analog television, older
telephone systems
Infrared Radiation
Detected as heat by the body; used in thermal imaging,
heating, and remote controls.
Also used in communication (optical fibers), electric grills,
and intruder alarms.
However, high-intensity infrared can cause burns and
eye damage.
Visible Light
Red light has the longest wavelength, and violet light has
the shortest.
Monochromatic light consists of one color (single
frequency), where frequency is more responsible than
wavelength to express the colour.
Visible light enables vision and is used for illumination
and photography.
Optical instruments like microscopes and telescopes use
light properties to form images.
Infrared Optical Fibers
Infrared optical fibers use the principle of total internal
reflection to make infrared or light travel along the fiber
without much loss.
Used for long-distance data transmission, offering high
bandwidth and low signal loss compared to electrical
transmission.
Ultraviolet Radiation
Shorter wavelengths than visible light; causes sunburn
and skin damage.
Used in fluorescent applications (e.g., security marking,
water treatment, artificial skin-tanning) and sterilising
water.
Can be harmful in high doses.
X-rays and Gamma Rays
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3.6. Sound
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Longitudinal Waves
Sound waves are longitudinal
Particles in the medium (like air or water molecules)
vibrate back and forth parallel to the direction of wave
propagation.
This creates areas of compression (where molecules are
closer together) and rarefaction (where they are far
apart) as the wave travels through the medium.
The movement of particles transfers energy through the
medium.
This vibration causes the sound to be heard
Compressions and Rarefactions
Humans can only hear sound frequencies ranging from
about 20Hz (low pitch) to 20,000Hz (high pitch).
The upper limit of audibility decreases with age due to
changes in the sensitivity of the ear.
Audibility can also be affected by the intensity (loudness)
of the sound which is determined by amplitude.
Reflection of sound (Echo)
Sound waves reflect off hard and flat surfaces like how
light reflects off a mirror.
When sound reflects, it creates an echo, which is a
repetition of the original sound heard after a short delay.
Sound waves are made of compressions (C ) and
rarefactions (R) as they move through a medium.
Compressions are regions where air molecules are
densely packed together and the regions have higher
pressure.
Rarefactions are regions where air molecules are less
densely packed and the regions have lower pressure.
Speed of Sound
Frequency and Wavelength
Frequency (f ) of a sound wave is the number of
complete wave cycles per second and is measured in
Hertz (Hz ).
Higher frequencies mean higher-pitch sounds, while
lower frequencies mean lower-pitch sounds.
Wavelength (λ) is the distance between two consecutive
compressions or rarefactions in a sound wave.
The speed of sound (v ) in a medium is determined by the
product of its frequency and wavelength: (v = f λ).
The speed of sound in air is approximately 330–350
meters per second (m/s) at room temperature.
In other materials, such as water (with a speed of
approx. 1500m/s) or steel (with a speed of approx. 5100
m/s), the speed of sound may vary due to differences in
the density.
Temperature affects the speed of sound in air and it
increases with temperature because warmer air
molecules move faster.
Measurement of the Speed of Sound
Limits of hearing
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Echo Method
Stand at a known distance (like more than 300 meters)
from a large wall.
Clap hands or produce a sharp sound and start a
stopwatch simultaneously.
Wait for the distinct echo from the surface and stop the
stopwatch when you hear it.
Calculation: Use the formula (v = 2dt ), where (d) is the
distance to the surface and (t ) is the time interval
measured with the stopwatch.
The pitch of the note is determined by the frequency of
the sound wave (higher frequencies produce higher pitch
notes).
Loudness is determined by the amplitude of vibrations (
greater amplitude produces louder sounds)
Quality (timbre) of a sound is its unique shape or texture,
caused by the instrument's construction.
​
Note: Twice the distance is used because the
sound travels away from you and then back
again, covering the entire distance two times.
Direct Method
Place two microphones a known distance (like 10 meters)
apart.
Connect microphones to an oscilloscope to detect the
sound.
Produce a sound source equidistant from both points
and start timing when the sound is produced.
Stop timing when the sound is detected at the second
point.
Use the formula (v = dt ), where (d) is the known distance
between the two microphones and (t) is the measured
time interval between detection at the two points.
​
Ultrasound
Ultrasound refers to sound waves with frequencies
above the upper limit of human hearing (> 20, 000Hz ).
It is used in medical imaging and industrial applications
for precision and non-destructive testing.
Ultrasound waves behave similarly to audible sound
waves but can penetrate materials and provide detailed
imaging without harmful effects.
4. Electricity and Magnetism
4.1. Simple Phenomena of Magnetism
Magnetic Materials
Musical Notes
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Ferromagnetic materials like iron can be made into
magnets.
Magnetic materials are naturally attracted to magnets
even when not magnetized..
Magnetic Poles
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Magnetic poles attract magnetic materials and are found
near the ends of magnets.
Poles always come in pairs: north and south.
Every magnet has a North Pole (N ) and a South Pole (S ).
The North Pole of a magnet points towards the Earth's
geographic North Pole.
Law of Magnetic Poles
Similar poles (N − N or S − S ) repel each other.
Opposite poles (N − S ) attract each other.
The attraction or repulsion decreases as poles move
farther apart.
Iron nails and steel paper clips can be magnetised by
hanging them from a magnet.
Each nail or clip magnetises the next in a chain, with
unlike poles attracting each other.
Removing an iron chain by pulling the top nail causes it
to collapse because iron shows temporary magnetism.
Steel chains do not collapse when removed because they
have permanent magnetism.
Soft materials (e.g. iron) are easily magnetised but lose
magnetism quickly.
Hard materials (e.g. steel) are harder to magnetise but
remain magnetised longer.
Induced Magnetism
Magnetic materials can become magnetized when near a
magnet.
Magnetisation of Iron and Steel
Magnetic and Non-magnetic Materials
Magnetic materials (iron, steel, nickel, cobalt) are
attracted to magnets and can be magnetised.
Non-magnetic materials (e.g., aluminium, wood) are not
attracted to magnets and cannot be magnetised.
Magnetic Fields
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A magnetic field is the region around a magnet where
magnetic forces act.
Field strength is higher where magnetic field lines are
closer together and lower where they are further apart.
Magnetic fields are shown using lines of force, showing
the direction from North to South poles.
The density of these lines indicates field strength: closer
lines represent stronger magnetic fields.
Electromagnets
They are formed from a coil of wire through which an
electrical current passes.
Magnetism is temporary and can be switched on and off,
unlike permanent magnets.
They contain a core of soft iron that only becomes
magnetised when current flows through the coil.
Factors Affecting Electromagnet Strength
Current Increase: Higher current in the coil results in
stronger magnetism.
More Turns: Increasing the number of turns in coils
around the core increases magnet strength.
Closer Poles: Moving the magnetic poles closer together
increases electromagnet strength.
4.2. Electrical quantities
Electric Charge
Like/same charges (+ and + or – and – ) repel, while
unlike charges (+ and –) attract.
Force Between Charges
The force between electric charges decreases as their
separation increases.
Positive charges repel other positive charges and attract
negative charges.
Negative charges repel other negative charges and
attract positive charges.
Charges, Atoms, and Electrons
Atoms consist of a central nucleus with protons (positive)
and electrons (negative) orbiting around it.
Protons and electrons have equal but opposite charges,
making atoms electrically neutral overall.
Production of Charges
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Charges are produced by friction, which transfers
electrons between materials.
Electrons move between materials during rubbing;
protons remain in the nuclei and do not move.
Units of charge
Charge is measured in coulombs (C ) and defined in
terms of the ampere (A)
The charge on an electron is (e = −1.6 × 10−19 ) C .
Electrons, Insulators, and Conductors
Insulators: Electrons are firmly bound to atoms; rubbing
can charge them statically.
Conductors: Electrons can move freely; they require
insulation to hold a charge.
Type
Insulators
Conductors
Description
Electrons are firmly bound to atoms;
rubbing can charge them statically.
Electrons can move freely; require
insulation to hold a charge.
Examples
Plastics (polythene, cellulose acetate),
Perspex, nylon
Metals, carbon
Electric Fields
When charges are near each other, they experience a
force known as the electric force.
Electric field is a region where a charge feels a force due
to nearby charges.
Uniform electric field exists between oppositely charged
parallel metal plates, shown by evenly spaced lines
perpendicular to the plates.
The direction of the electric field is indicated by arrows,
representing the force acting on a small positive test
charge (pointing away from positive charges and towards
negative charges).
The Ampere and the Coulomb (units of current and
charge)
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Electric Current is defined as charge passing a point per
unit time, symbolized as
(I = Qt ).
Unit of current is the ampere (A), with one milliampere (
mA) equal to one-thousandth of an ampere and is
measured by an ammeter.
Unit of charge is the coulomb (C ), defined as the charge
passing a point when a steady current of 1 ampere flows
for 1 second (1C = 1As).
​
Charge Calculation
Q=I ×t
where Q is charge, I is current, and t is time in seconds.
Conventional Current
Conventional current flows from positive to negative
terminals of a battery, opposite to electron flow.
Circuit diagrams show conventional current direction
with arrows, while electrons move in the opposite
direction.
Direct and Alternating Current
Direct Current (d.c.)
Alternating Current (a.c.)
Electrons flow continuously in one direction. Electrons regularly change their direction of flow.
Provided by batteries
Produced by generators.
Frequency of Alternating Current
Frequency refers to the number of complete cycles per
second.
It is measured in Hertz (Hz ), where 1 Hz equals one
cycle per second.
4.3. Voltage, Resistance and Power
Electromotive Force (e.m.f .)
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Chemical actions inside a battery produce electron
excess at the negative terminal and shortage at the
positive terminal
Battery maintains electron flow (electric current) in a
connected circuit as long as chemical actions last.
The battery does work when moving the charge around
the circuit.
Electromotive force (e.m.f .) is the electrical work done
by a source in moving unit charge around a complete
circuit.
Electromotive force is measured in volts (V ).
Potential Difference
Electric current transfers energy from a battery to circuit
components and surroundings.
Potential difference (p.d.) is the work done by unit
charge passing through a component
P .d. is measured in volts.
Voltage is sometimes used instead of p.d.
1 volt = 1 joule per coulomb 1 V = 1 CJ )
Formula: V = W
Q or W = Q × V
​
​
Resistance
Electrons move more easily through some conductors
when p.d. is applied.
Resistance is the opposition of a conductor to current.
Good conductors have low resistance while poor
conductors have high resistance
Ohm (Ω) is the unit of resistance.
Formula: R = VI
They can change current in a circuit (rheostat mode) or
act as a potential divider by dividing voltage across
components as desired.
Resistance depends on the length, cross-sectional area,
and material of the wire
Resistance increases with length but decreases with a
larger cross-sectional area
Formula: (R ∝ Al )
​
I–V graphs and Ohm’s Law
Metals and some alloys give I–V graphs that are straight
lines through the origin, showing that I is directly
proportional to V or that I ∝ V .
Doubling V doubles I .
Such conductors obey Ohm’s law: V = IR
Ohmic or linear conductors are the conductors where
resistance does not change with V .
​
Variable Resistors
Semiconductor Diode
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Diode has small resistance when connected one way and
very large resistance when p.d. is reversed.
It conducts electricity in one direction only, and it is a
non-ohmic conductor.
Filament Lamp
Non-ohmic conductor at high temperatures
I–V graph curve flattens as V and I increase, showing
increasing resistance with increasing current and
increasing temperature.
An increase in temperature generally increases the
resistance of metals.
Thermistors' resistance is different and decreases with
rising temperature.
It is a non-ohmic conductor
Light-dependent Resistor (LDR)
Resistance of some semiconductors decreases with
increased light intensity.
Light-dependent resistors (LDRs) use this property to
function.
I–V graph for an LDR is similar to that of a thermistor
LDR is also a non-ohmic conductor.
Power in Electric Circuits
Power defined as work done or energy transferred per
time taken: P = Wt
P is power in watts (W ), W is work done in joules (J ), t
is time in seconds (s)
For a steady current (I) in a device with a potential
difference (V ) across it, the work done has a formula
W =I ×t×V
Substituting work done with the power P = IV
multiplied by time in seconds (t), the energy transferred
is: E = Pt = IV t
​
Thermistor
Example
Lamp with 240 V supply and 0.25 A current
Power = P = IV = 240 V × 0.25 A = 60 W
60 J of energy transferred to the lamp each second
Voltage in terms of power and current
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Volt can be defined as a watt per ampere: V = PI
If all energy transferred to thermal energy in a resistor of
resistance R:
P = V × I = IR × I = I 2 R
Doubling the current produces four times the thermal
energy per second P = I 2 R
Larger unit for energy: kilowatt-hour (kWh)
1 kWh = 1000 Js × 3600 s = 3600000 J = 3.6 M J
The cost of electricity in houses is calculated by using
kWh where each kWh has a fixed price and is multiplied
by the units you consume.
​
In a parallel circuit, components are connected side by
side, providing alternative paths for current flow.
The total current is the sum of the currents through
each branch
If the total current from the source is (I0 ), and the
current through each branch is I1 , I2 and I3 then I0 =
I1 + I2 + I3
​
​
​
​
​
​
​
​
​
4.4. Electric Circuits
Electrical component symbols
Potential Difference (p.d.) in Series and Parallel Circuits
In a series circuit, the total potential difference across
the components is the sum of the individual potential
differences: V0 = V1 + V2 + V3
In a parallel circuit, the potential difference across each
component is the same as the potential difference across
one branch: Vacross each branch = V0
​
Current in a Series Circuit
In a series circuit, there is a single path for the current to
flow.
The current remains the same throughout:
Current (I ) is consistent at every point in the series
circuit.
The reading on an ammeter will be identical no matter
where it is placed in the circuit.
Current in a Parallel Circuit
​
​
​
​
​
Cells, Batteries, and Electromotive Force (e.m.f .)
Cells in series increase the total e.m.f . of the battery.
For example, if two 1.5 V cells are connected in series
then the e.m.f .= 1.5 V + 1.5 V = 3.0 V
Resistors in Series
In a series circuit, the total resistance (R0 ) is the sum of
the individual resistances: R0 = R1 + R2 + R3
Given resistors R1 , R2 , and R3 the total voltage (V )
across them is: V = I × R
​
​
​
​
​
​
​
​
Worked Example
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For a 4.5 V battery across resistors of 3 Ω, 4 Ω and 5 Ω in
series:
Combined resistance: R0 = R1 + R2 + R3 = 3 Ω + 4 Ω
+ 5 Ω= 12 Ω
Current (I ): I = VR = 4.5V
12Ω = 0.375 A
p.d. across 4 Ω resistor: V2 = I × R2 = 0.375 A × 4 Ω =
1.5 V
​
​
​
​
​
​
​
​
Resistors in Parallel
The combined resistance (R0 ) of resistors in parallel is
given by: R10 = R11 + R12 + R13 …
Two resistors R1 and R2 have resistance of R10 = R11 + R12
1 ×R 2
= R0 = R
R 1 +R 2
​
​
​
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​
In a thermistor, resistance decreases with increasing
temperature.
When it’s used in a potential divider circuit:
As temperature rises, the thermistor's resistance
decreases.
This lowers the combined resistance of the two
resistors, increasing the current if the supply voltage
remains constant.
The potential difference across the fixed resistor
increases relative to that across the thermistor.
A variable resistor can also act as a potential divider by
adjusting the position of the contact, changing the
output potential difference.
​
​
Properties of Parallel Circuits
1. The current from the source is greater than the
current in each branch.
2. The combined resistance of parallel resistors is less
than that of any individual resistor.
4.5. Applications of electric circuits
Increase in Resistance of a Conductor
In metals, current is carried by free electrons. As the
temperature of the metal increases:
The atoms vibrate more, making it harder for electrons
to move.
This results in an increase in resistance.
Potential Divider
For two resistors R1 and R2 in series with a supply voltage
(V ):
​
The total current (I) is given by: I = R1 V+R2
​
From Ohm's Law V = IR , if resistance (R) increases while
maintaining a constant current(I), the potential difference (
V ) across the conductor also increases.
Variable Potential Divider
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​
​
Light-Dependent Resistor (LDR)
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An LDR’s resistance decreases with increasing light
intensity.
In a circuit, as light intensity increases:
The LDR’s resistance decreases, allowing more
current to flow.
This increase in current can light a lamp or cause
other actions.
A relay allows a small current to control a larger current
needed to operate an appliance.
In a switching circuit:
If the switching circuit output is high, a small current
flows through the relay, closing the mains switch.
This isolates the low voltage circuit from the high
voltage mains supply.
Light-Emitting Diode (LED)
An LED emits light when forward-biased (cathode
connected to the negative terminal):
Reverse bias (anode connected to the negative
terminal) does not emit light and can damage the
LED if the reverse voltage exceeds 5 V .
A suitable resistor R (e.g. 300 Ω on a 5 V supply) is
needed to limit the current.
Semiconductor Diode
Thermistor
A thermistor's resistance decreases significantly with
temperature increase.
In a series circuit with a thermistor:
As temperature rises, its resistance drops, decreasing
the potential difference across it.
This causes an increase in voltage across a series
resistor, which can trigger a relay or alarm.
A diode allows current to pass in only one direction:
Forward-biased: current flows when the anode is
connected to the positive terminal and the cathode
to the negative terminal.
Reverse-biased: the diode does not conduct and has
high resistance.
4.6. Electrical safety
Dangers of Electricity
Relays
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Damaged Insulation: Exposes wires, increasing shock
and fire risk.
Overheated Cables: Can lead to fire.
Damp Conditions: Increase shock severity due to
reduced resistance.
Excess Current: From overloaded plugs, extension leads,
and multiple sockets.
Electric Shock: Current flows from an electric circuit
through a person's body to earth.
Dry Skin: Resistance ~10,000 Ω and current around
24 mA (it is safe).
Wet Skin: Resistance ~1,000 Ω and current ~240 mA
(can be deadly).
Larger currents are more dangerous.
Longer exposure increases risk.
Reducing Risk
Turn off power before repairs.
Use earth pin and cord grips.
Keep appliances dry and away from water.
Avoid trailing cables and damage, especially with cutting
tools.
First Aid for Electric Shock
Switch off the power if the person is still in contact with
the equipment.
Call for medical assistance.
Causes of fires
Flammable materials near hot appliances or wiring.
Overheated wiring produces excessive current and can
lead to fire.
Preventive Measures:
Match fuse rating to appliance.
Do not overload sockets or use too many adapters.
Use thick wires for high-power appliances.
House Circuits
Live and Neutral Wires: Both supply electricity and the
neutral is earthed.
Earth Wire: Provides safety by connecting metal cases to
earth.
Switches and Fuses
Switches and fuses are in the live wire to prevent shocks.
Fuse breaks the circuit if the current exceeds safe levels.
Circuit Breakers
Electromagnetism breaks the circuit when current
exceeds a preset level.
Advantages: Faster operation and can be reset.
Earthing
Prevents shock by providing a path for fault currents.
Earth pin connects appliance metal cases to earth,
preventing them from becoming live.
Double Insulation
Appliances with two layers of insulation don’t need an
earth wire.
4.7. Electromagnetic induction
Process of generating electricity from a changing
magnetic field.
Electromagnetic Induction Experiments
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Straight Wire and U-shaped Magnet
Wire held still between magnet pole leads to no induced
current.
Moving wire vertically (up or down) between poles
induces current because of changing magnetic flux
(cutting magnetic field lines)
Upward movement: current flows in one direction.
Downward movement: current flows in the opposite
direction.
Deflection on meter is temporary and occurs only while
wire is moving.
Inserting magnet into coil (solenoid) induces current in
one direction.
A solenoid is a coil of wire wound in a helical shape
that generates a magnetic field when an electric
current passes through it.
Removing magnet from solenoid induces current in the
opposite direction.
No current is induced when magnet is stationary inside
solenoid.
Current direction reverses with the direction of magnet
movement.
This also works if the solenoid is moved instead of the
magnet.
Factors Affecting Induced e.m.f .
Bar Magnet and Coil (solenoid)
Faster movement of magnet or coil increases induced
e.m.f.
More turns in the coil increase the induced e.m.f.
Stronger magnets increase the induced e.m.f.
e.m.f . is directly proportional to the rate at which the
conductor cuts through magnetic field lines.
Direction of Induced e.m.f . (Lenz’s Law)
Induced e.m.f . always opposes the change causing it.
If a magnet approaches a coil, the induced current
generates a magnetic field that opposes the motion.
If a magnet is withdrawn, the coil’s induced current
generates a field that attracts the magnet.
Magnetic Fields
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Straight Wire:
When current flows through a vertical wire, iron
filings around it form circles.
Meaning that around a straight wire, there are
circular magnetic field lines.
Field direction changes with current direction
(upwards or downwards through the wire)
Use right-hand grip rule: direction of thumb (upwards
or downwards) indicates magnetic field direction by
the remaining fingers (clockwise or anti-clockwise).
Variation of Magnetic Field Strength
Magnetic field strength decreases with distance from the
wire.
Field lines spread out as distance increases.
Increasing current strengthens the magnetic field and
lines become closer together.
Reversing current direction reverses the direction of the
magnetic field.
4.8. Applications of electromagnetic
effects
Relay
Solenoid
A long cylindrical coil produces a magnetic field
similar to a bar magnet.
End A behaves like the north pole, and end B behaves
like the south pole.
Right-hand grip rule: grip solenoid in current
direction, thumb points to the north pole.
Magnetic field inside the solenoid is stronger and
denser compared to outside.
A relay is a switch that operates using an electromagnet.
It allows one circuit to control another
When current flows through the coil, it magnetizes the
soft iron core.
The magnetized core attracts the L-shaped iron
armature.
The armature rocks on its pivot and closes contacts in
another circuit.
Components
Coil: Creates the magnetic field.
Soft Iron Core: Magnetized by the coil, attracts the
armature.
L-shaped Iron Armature: Moves to close or open
contacts.
Contacts: Switches the second circuit on or off.
Reed Switch
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A reed switch uses magnetic fields to control a circuit.
Operated by current flowing through a coil, which
magnetizes reeds of magnetic material.
Current flows: Reeds become magnetized, attract each
other, and close the circuit.
Current stops: Reeds lose magnetization, separate, and
open the circuit.
A device that produces sound by ringing is an electric bell
Pressing the bell push completes the circuit.
Current flows through electromagnet coils, magnetizing
them.
Electromagnet attracts a soft iron bar (armature),
causing the hammer to hit the gong.
The circuit breaks at contact screw point
Electromagnet loses magnetism, armature returns to its
original position.
The springy metal strip reconnects the circuit, and the
cycle repeats as long as the bell push is pressed.
Loudspeaker
It converts electrical signals into sound waves.
Varying currents pass through a coil placed in a magnetic
field.
Magnetic fields interact, causing the coil to vibrate.
A paper cone attached to the coil moves with it.
Vibrations create sound waves in the surrounding air.
Components
Coil: Receives electrical signals and vibrates.
Magnet: Provides the magnetic field for interaction.
Paper Cone: Moves with the coil to produce sound.
4.9. Motors and generators
Simple d.c. Electric Motor
Electric Bell
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Components
Rectangular coil: Fixed up on an axle that can rotate.
C-shaped magnet: Provides the magnetic field.
Split-ring commutator: A copper ring split into two
halves, connected to the ends of the coil. It rotates
with the coil.
Brushes: Carbon blocks pressed against the commutator
to supply current continuously.
Fleming’s Left Hand Rule is used for the d.c.
motor
The a.c Generator
Components
Operation
When direct current (d.c.) flows through the coil, a force
acts on the coil due to the interaction with the magnetic
field.
This force creates a turning effect, causing the coil to
rotate.
The split-ring commutator reverses the direction of
current in the coil as it rotates, making sure there is
continuous rotation by maintaining the direction of
force.
Rectangular coil: Positioned between the poles of a Cshaped magnet.
Slip rings: Connected to the ends of the coil, rotate with
the coil.
Carbon brushes: Press against the slip rings to conduct
current.
Operation
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As the coil rotates in the magnetic field, it cuts through
the field lines, inducing an electromotive force (e.m.f .)
The e.m.f . varies as the coil moves
Vertical Position: No e.m.f . as the coil cuts the least
number of field lines.
Horizontal Position: Maximum e.m.f . as the coil cuts the
most field lines.
The direction of e.m.f . reverses as the coil continues to
rotate, producing alternating current (a.c.) in the circuit.
The frequency of the a.c. is determined by the rotation
speed of the coil. For example, a coil rotating twice per
second generates an a.c. with a frequency of 2 Hz.
This occurs when current changes in one coil, inducing a
voltage in a neighboring coil.
Magnetic field lines from the primary cut through the
secondary coil, inducing voltage.
Induced voltage increases with a soft iron rod or
complete iron ring core due to increased magnetic field
lines.
Fleming’s Right Hand Rule is used for the a.c.
generator.
Transformer Equation
The alternating voltage applied to the primary induces an
alternating voltage in the secondary.
V
N
Relationship given by Vps = Nps
Vp and Vs the primary and secondary voltages.
Np and Ns are the primary and secondary turns.
Step-up transformer: More turns are on secondary
(Vs > Vp ).
Step-down transformer: fewer turns on secondary, (
Vs < Vp ).
​
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​
​
​
​
4.10. Transformers
​
​
​
​
The transformer changes alternating voltage to different
values.
Consists of primary and secondary coils on a soft iron
core.
Coils can be wound on top of each other or separate
limbs.
Mutual Induction
​
​
​
​
Worked Example
A transformer steps down the mains supply from 230V
to 10V.
N
23
Turns ratio: Nps = 230V
10V = 1
If the secondary has 80 turns, the primary has 80 × 23=
182 turns.
​
​
​
​
​
Energy Losses
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If V s stepped up, current I is stepped down
proportionally.
Ideal transformer (100% efficient): Ip Vp = Is Vs
Ip and Is are primary and secondary currents.
If V is doubled, I is halved.
​
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​
5. Nuclear Physics
5.1. Nuclear model of the atom
Current atomic model
The nucleus of an atom consists of protons and
neutrons.
Three basic particles in an atom include protons,
neutrons, and electrons.
Proton = a hydrogen atom minus an electron charge
+1, mass about 2000 times that of an electron.
Neutron: Uncharged and with a mass almost equal to
that of a proton.
Relative charges: Proton = +1 and neutron = 0 while
electron = -1.
Protons and neutrons are located in the nucleus and
are together called nucleons.
Electrons orbit a positively charged nucleus.
Mostly empty space between the orbits and the nucleus.
Scattering experiments by Ernest Rutherford
α-particles directed at thin gold foil.
Observations of α-particles:
Particle
Proton
Neutron
Electron
Most α-particles
Observation
Description
Passed through the gold foil
without deflection.
Some α-particles
Deflected at small angles.
Approximately 1 in 8000 αparticles
Deflected back towards the
source at large angles.
Proof of atomic model
Atom is mostly empty space.
Presence of a dense, positively
charged nucleus which repels
the α-particles
Nucleus is very small and dense
compared to the rest of the
atom.
Rutherford’s nuclear model
Positive charge and most mass are concentrated in a
small, dense nucleus.
Electrons orbit the nucleus at a large distance away.
Nucleus and electrons occupy about one-millionmillionth of the atom’s volume.
Relative Mass
1
1
1
1840
​
Relative Charge
+1
0
-1
Location
In nucleus
In nucleus
Outside nucleus
In a neutral atom the number of protons equals the
number of electrons.
Atomic number (Z ): Number of protons in the nucleus (it
also equals the number of electrons).
Mass number (A): Total number of nucleons (protons +
neutrons) in the nucleus.
Relationship: Number of neutrons = A − Z .
Nuclide notation: Atom X is represented as A
Z X , where
A is the nucleon number and Z is the proton number.
Relative charge: Product of proton number (Z ) and the
charge of a proton.
Relative mass: Total mass of neutrons and protons;
approximately A times the mass of a proton.
​
Isotopes
The nucleus
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Forms of the same element with the same number of
protons but different number of neutrons.
37
Example: Chlorine has isotopes 35
17 Cl and 17 Cl while
1
2
Hydrogen has isotopes 1 H , deuterium 1 H , and tritium
3H .
1
​
​
​
​
Reactors use controlled chain reactions to produce
energy.
Control rods absorb neutrons to regulate the reaction.
Graphite moderates neutrons to slow down fission.
​
Isotopes have identical chemical properties
but different physical properties.
Nuclides
Radioactive isotopes are called radioisotopes or
radionuclides and have unstable nuclei.
Nuclear Energy
Einstein’s equation: E = mc2 , where E is energy, m is
mass, and c is the speed of light.
Mass loss in nuclear reactions results in energy release.
Nuclear reactions involve large energy changes
compared to other physical and chemical changes.
Nuclear fission
Uranium-235 is an isotope that undergoes fission when
struck by neutrons.
Fission breaks the nucleus into smaller radioactive
nuclei, releasing additional neutrons and energy.
Mass loss is converted into kinetic energy of fission
products.
Neutrons from fission can trigger further fission
reactions.
Nuclear Reactor
5.2. Types of Radioactivity
Natural Background Radiation
Radiation sources include:
Cosmic rays (high-energy particles from the Sun) are
mostly absorbed by the atmosphere, but some reach the
Earth's surface.
Radon gas present in the air.
Granite rocks in homes, particularly in Scotland, emit
radioactive radon gas that can accumulate in poorly
ventilated areas.
Radioactive potassium-40 is present in food and
absorbed by our bodies.
Various radioisotopes are used in medical procedures.
Radiation from nuclear power stations and fallout from
nuclear bomb testing
Ionising Effect of Radiation
The ability of radiation to make atoms lose or gain
electrons and become charged.
A charged electroscope discharges when a lighted match
or a radium source is brought near the cap.
Electroscope Discharge: Neutral Atom → Positive Ion
+ Electron
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A lighted match knocks electrons out of air molecules,
creating positive ions.
Radiation causes ionisation by neutralising the charge on
the electroscope.
Ionisation: Neutral Atom + Electron → Negative Ion
Geiger–Müller (GM) Tube
The ionising effect of radiation is used to detect
radiation.
Radiation entering a GM tube creates argon ions and
electrons, which then cause more ionisation.
Alpha, Beta, and Gamma Radiation
Alpha Particles (α)
The nucleus with two protons and two neutrons
Stopped by thick paper; range in air is a few
centimetres.
The high ionising power of alpha particles is due to
their increased mass (compared to gamma and beta),
so it's more likely to ionise an atom
Deflected by electric and magnetic fields.
Represented as helium ions with a double positive
charge.
Beta Particles (β )
fast-moving electron
Stopped by a few millimetres of aluminium; range in
air is several metres.
Lower ionising power than alpha particles.
Deflected by electric and magnetic fields.
Streams of high-energy electrons.
Gamma Radiation (γ )
Electromagnetic radiation having high frequency
Most penetrating
Stopped only by many centimetres of lead.
Least ionising power.
Not deflected by electric and magnetic fields.
Electromagnetic radiation.
Type of
Radiation
Alpha (α)
Mass
Charge
Penetrating Power
High (Helium nucleus)
+2
Beta (β)
Low (electron)
-1
Gamma (γ )
None (electromagnetic
wave)
0
Low (stopped by paper)
Moderate (stopped by few mm
of aluminum)
High (stopped by several cm of
lead)
Ionising
Power
High
Moderate
Low
Particle Tracks
Cloud chambers reveal the tracks of particles based on
the ionisation they produce.
Alpha Particles: Straight, thick tracks.
Beta Particles: Thin, straight or twisted tracks.
Gamma Rays: Eject electrons which then produce
tracks similar to β particles.
Electric deflection
The positive alpha particles are heavier and slowly
deflect towards the negative plate.
The negative beta particles are lighter and quickly deflect
towards the positive plate.
The neutral electromagnetic gamma radiation remains
undeflected.
Magnetic deflection
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Alpha particles follow the rule of positive conventional
current.
Fleming’s left-hand rule is used with the middle finger
pointing in the direction of alpha particles.
Beta particles are shown in the direction opposite to the
middle finger, as they represent electron flow, which is
the opposite of conventional current.
Gamma radiation is not deflected.
In β-decay, a neutron changes into a proton and an
electron.
The proton remains in the nucleus, while the electron is
emitted as a β-particle.
The nucleon number stays the same, but the proton
number increases by 1.
Example: Radioactive carbon 14
6 C decays into nitrogen (
14 N) by β-emission.
7
14
0
The equation for this decay is: 14
6 C →7 N +−1 e
​
​
​
​
​
Gamma Emission (γ-emission)
After α- or β-decay, some nuclei are left in an excited or
energetic state.
Rearrangement of protons and neutrons releases energy
in the form of γ-emissions.
γ-emissions are high-energy electromagnetic waves with
no mass or charge.
Nuclear Stability
5.3. Radioactive decay and half-life
Radioactive Decay
Radioactive decay is the emission of an α-particle or a βparticle from an unstable nucleus.
This changes the nucleus into that of a different element
until a stable element is formed.
These changes are spontaneous and random
Alpha Decay (α-decay)
An α-particle is a helium nucleus with two protons and
two neutrons.
When an atom undergoes α-decay, its nucleon number
decreases by 4 and its proton number decreases by 2.
Example: When radium (226
88 Ra) emits and alpha particle,
222
it becomes radon (86 Rn).
222
4
The equation for this decay is: 226
88 Ra →86 Rn +2 He
Stability of a nucleus depends on the number of protons
(Z ) and neutrons (N ).
Stable nuclides fall within a specific stability level called
the stability line.
For light nuclides, N = Z .
For heavier nuclides, N > Z .
Unstable nuclides decay to move towards the stability
line.
Nuclides above the stability line decay by β-emission to
decrease the N
Z ratio.
Nuclides below the stability line decay by beta emission
(β+) to increase the N
Z ratio.
Nuclei with more than 82 protons usually decay by αemission.
​
​
​
​
​
​
Half-Life
​
Beta Decay (β-decay)
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The half-life of an isotope is the time taken for half the
nuclei in a sample to decay.
It is a measure of the rate at which a radioactive
substance decays.
Each isotope has its own special half-life.
It can be from fractions of a second to millions of years.
A decay curve plots the activity of a sample over time,
showing the exponential decrease in activity.
The activity decreases by half in each half-life period
from the previous half-life period.
Example: If a sample's activity is 80 decays per second, it
will reduce to 40 in one half-life, then to 20 in the next,
and so on.
Radioactive decay is random and unpredictable; the
exact time when a particular nucleus will decay cannot
be determined.
The overall decay rate of a sample follows a predictable
pattern, called its half-life.
Exposure to small doses of radiation is not damaging,
but large doses are harmful to health.
Nuclear radiation's ionising effect damages cells and
tissues, it can lead to gene mutations.
Damage can cause cell death and cancers.
α-particles are less dangerous unless the source is
ingested or inhaled.
β- and γ-radiation can cause radiation burns, eye
cataracts, and cancer.
Radiation hazard signs warn of the presence of
radioactive material.
Safety Precautions
5.4. Safety precautions
Dangers of Nuclear Radiation
Minimize exposure time to radiation.
Keep a large distance between the radiation source and
individuals.
Use shielding materials that absorb radiation to protect
people.
In industry, sources are handled with long tongs and
transported in thick lead containers.
Workers are protected by lead and concrete walls and
wear radiation dose badges.
Radiation dose badges track the amount of radiation
exposure over a period, typically one month.
The badge has windows that allow different types of
radiation to expose photographic film, indicating
exposure levels when developed.
6. Space Physics
6.1. The Earth and the solar system
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Motion of the Earth
The Earth spins on its axis, causing day and night.
One complete rotation takes 24 hours.
Day is for the half of the Earth facing the Sun and night
for the half facing away.
Waning (where the moon's illumination decreases) phases
follow, leading to the last quarter and old crescent
Rising and setting of the Sun
Earth's rotation causes the Sun to appear to move east
to west daily.
Rises exactly in the east and sets exactly in the west at
equinoxes.
In northern hemisphere summer, rises north of east and
sets north of west.
In winter, rises and sets south of these points.
The seasons
Caused by Earth's motion around the Sun (365 days) and
tilt of its axis.
Motion of the Moon
Moon is a satellite of Earth, orbiting approximately every
month
Average distance from Earth is about 400,000 km.
Revolves on its axis, always showing the same side to
Earth
Reflects sunlight, has no atmosphere, weaker
gravitational field (one-sixth of Earth)
Phases of the Moon
Moon's appearance changes during its monthly orbit
New Moon: Moon between Sun and Earth, unlit side
faces Earth
Crescent appears and increases until the first quarter
(half of the Moon visible)
Full Moon: Moon opposite Earth from the Sun, fully
visible
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Orbital speed
Average orbital speed: u = 2πr
T
r is the average radius of the orbit.
T is the orbital period (time for one orbit)
The Moon travels in a circular path around the Earth
Distance traveled in one orbit is the circumference of
the circle, 2πr
Time taken for one orbit is T
Speed is distance divided by time, so orbital speed is
​
2πr
T
​
The Solar System
It contains:
The sun as a star
Eight planets in elliptical orbits (slightly oval orbits)
Dwarf planets and asteroids orbiting the Sun
Moons orbiting many planets
Smaller bodies like comets and natural satellites
Inner Planets
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Mercury, Venus, Earth, Mars
Small, similar size
Solid and rocky with layered structures
High density
Formed close to the Sun where it was too hot for gases
to condense, allowing only metals and silicates to form
solid bodies
In the early Solar System, the Sun's heat caused lighter
gases to evaporate, leaving only heavy elements like iron
and silicon to form solid planets.
Dust embedded in ice made from water and methane
Orbits the Sun in highly elliptical paths
Develop a bright long tail when approaching the Sun due
to radiation pressure
Outer Planets
Jupiter, Saturn, Uranus, Neptune
Much larger and colder
Mainly consist of gases, low density
Many moons and rings of icy materials
Formed in cooler regions where gases could condense,
capturing even the lightest elements
In the outer regions of the Solar System, lower
temperatures allowed gases like hydrogen and helium to
remain in solid or liquid forms, leading to the formation
of gas giants with thick atmospheres.
Elliptical Orbits
Planets, dwarf planets, and comets orbit the Sun in an
ellipse
Sun is at one focus of the ellipse, not the center
Comets have highly elliptical orbits, while planets' orbits
are more circular
Origin of the Solar System
Asteroids
Pieces of rock of various sizes, mostly between Mars and
Jupiter
Orbit around the Sun
Similar density to inner planets
Burn up in Earth's atmosphere as meteors
Formed from gravitational attraction pulling together
clouds of hydrogen gas and dust (nebulae)
Solar System formed about 4500 million years ago
Planets formed from the disc of matter left over from the
nebula that formed the Sun
Inner planets formed from materials with high melting
temperatures like metals and silicates
Outer planets formed from light molecules that existed
in solid icy forms, growing large enough to capture
hydrogen
Comets
Travel Times
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Distance from the Sun to Earth: approximately 150
million km (1.5 × 108 km)
Speed of light: 300,000 kilometers per second (km/s)
Using the formula for time:
Time = Distance
Speed
Substitute the values:
8
Time = 1.5×10
300,000
Calculate the time:
8
seconds ≈ 500 seconds
Time ≈ 1.5×10
300,000
Convert the time from seconds to minutes:
Time ≈ 500
60 ≈ 8.33 minutes
​
​
​
Hot and dense enough for hydrogen to fuse into helium.
Fusion process releases energy, maintaining high core
temperatures.
Some core energy moves to outer layers, which emit
electromagnetic radiation.
Light-years
Distance light travels in a vacuum in one year.
1 light-year = 9.5 × 10¹² km = 9.5 × 10¹⁵ m
Galaxies
Large collections of stars, gas, and dust.
​
It takes light from the sun around 8 minutes to reach the
Earth.
6.2. The sun
Medium-sized star composed mainly of hydrogen and
helium.
Emits energy in the infrared, visible, and ultraviolet
regions of the electromagnetic spectrum.
Source of Energy
Energy from nuclear reactions in the core.
Hydrogen undergoes nuclear fusion to form helium,
releasing energy.
Energy from the core heats outer layers, causing them to
glow and emit radiation.
6.3. Origin and life cycle of stars
Formation
Interstellar clouds of dust and gas collapse under
gravitational attraction.
A protostar forms as mass increases and core
temperature rises.
Hydrogen fuses into helium when the core is hot
enough, resulting in a star.
Star Types
Large mass: Blue or white stars.
Smaller mass: Yellow or red dwarfs (e.g., the Sun).
Life Cycle of Stars
Stable Phase
Forces of gravity inward balance with thermal pressure
outward.
Stable phase lasts up to 10 billion years.
Hydrogen converts to helium in the core.
Red Giant/Red Supergiant
As hydrogen depletes, the star becomes unstable.
Core collapses; outer layers expand and cool.
Star turns into a red giant (or red supergiant if massive).
Helium fuses into carbon in the core.
Low Mass Stars
Nuclear Reactions in Stars
Stars like the Sun are powered by nuclear fusion.
Core conditions
End Stage
Core collapses into a white dwarf after all helium is
used.
Outer layers expelled, forming a planetary nebula.
White dwarf cools into a black dwarf over about a
billion years.
High Mass Stars (more than 8 times the Sun’s mass)
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End Stage
Use hydrogen rapidly, with a shorter stable phase
(about 100 million years).
After helium fusion, core collapses into a red
supergiant.
Fusion of carbon into heavier elements occurs until
iron forms.
Supernova explosion releases energy and heavy
elements into space.
Neutron Star: Dense core, may act as a pulsar.
Black Hole: Extremely dense core with gravitational
field so strong that even light cannot escape;
identified by X-ray radiation from nearby material.
Occurs when a source of waves (e.g., sound or light)
moves relative to an observer.
Approaching Source: Waves are compressed, resulting in
a higher frequency and pitch (blue shift for light).
Receding Source: Waves are stretched, resulting in a
lower frequency and pitch (red shift for light).
Speed of Recession
6.4. The universe
Milky Way
Approximately 100,000 light-years in diameter.
Contains around 800 billion or more stars.
A spiral galaxy with a central bulge and spiral arms.
Redshift
The phenomenon where light from distant galaxies shifts
towards the red end of the spectrum (longer
wavelength).
Light emitted from stars in distant galaxies appears
redder compared to light from closer galaxies.
Doppler Effect
The speed at which distant galaxies are moving away can
be calculated from the amount of redshift observed.
Some of the most distant galaxies are receding at speeds
up to one-third the speed of light.
The observed redshift supports the idea that the
Universe is expanding, which is consistent with the Big
Bang theory.
Big Bang Theory
Initial State: Proposes that the Universe began from an
extremely hot and dense state around 14 billion years
ago.
Expansion: The Universe has been expanding ever since
the Big Bang.
Microwave Background Radiation
This radiation is a remnant from the Big Bang and fills
the entire Universe.
The radiation has been redshifted into the microwave
region due to the expansion of the Universe.
Provides strong evidence for the Big Bang theory and
insights into the early Universe.
Age of the Universe
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Hubble’s Law: The relationship between the speed of
recession (v ) and the distance (d) of galaxies is given by:
v = H0 × d
Hubble Constant (H0 ): H0 = vd
H0 measures the rate of the Universe's expansion. A
higher value indicates a faster rate of expansion.
H0 is estimated to be approximately 2.2 × 10−18 s−1
Age Estimation: The age of the Universe is
approximately: Age of the Universe ≈ H10
​
​
​
​
​
​
​
​
Detailed Calculation
Age of the Universe ≈ 2.2×101−18 s−1 ≈ 4.5 × 1017 s
4.5×1017 s
Age of the Universe ≈ 3.2×10
7 s/year ≈ 1.4 ×
1010 years ≈ 14 billion years
​
​
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CAIE IGCSE
Physics
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