1
PHYSICAL QUANTITIES
Physics: Study of matter in relation to energy.
Physical Quantity: A property of matter than can be quantified with measurement and
can also be expressed as a number.
There are two types of physical quantities. These are
1. Basic Physical quantities
2. Derived Physical quantities
Basic Physical Quantities.
These are the fundamental physical quantities.
Quantity
Symbol
SI Units
Symbol of SI Units.
Length
Mass
Time
absolute temperature
electric current
luminar intensity
molecular quantity
s,l
m
t
T
I
L
n
metre
kilogram
seconds
Kelvin
Amperes
Candela
mol
n
kg
s
K
A
Ca
mol
Derived Physical Quantities
These are derived from one or more basic quantities.
Quantity
Symbol
SI Units
Symbol of SI Units.
Area
Volume
Velocity
Acceleration
Pressure
Energy
Density
Frequency
Voltage
Charge
Force
Resistance
A
V
u,v
a
P
E, U, Q, W
metres squared
Cubic metres
metres per second
metres per second squared
Pascals
Joules
kilograms per cubic metre
Hertz
Volts
Coulombs
Newtons
Ohms
m2
m3
m/s or ms-1
m/s2 or ms21
Pa
J
3
kg/m or kgm-3
Hz
V
C
N

f
V
Q
F
R
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2
Multiples And Submultiples Of Si Units
Power
10-18
10-15
10-12
10-9
10-6
10-3
10-2
10-1
101
102
103
106
109
1012
1015
1018
Prefix
attofemtopiconanomicromillicentidecidekahectokiloMegaGigaTeraPetaExa-
Abbreviation
A
F
P
N

M
C
D
Da
H
K
M
G
T
P
E
Unit Conversions
Sometimes it may be necessary to convert from one unit to another unit for the same physical
quantity.

To convert from a base unit to a multiple/submultiple, divide by the power of ten for
the prefix.
E.g. Change 200 metres to millimetres.
200
= 200 x 103 millimetres.
3
10

To convert from a base unit to a multiple/submultiple, multiply by the power of ten
for the prefix.
E.g. Change 300 Megavolts to volts.
300 x 106 volts.
Classwork
Perform the following unit conversions
1
10 mm to m
2.
300 GHz to Hz
3.
0.01 A to A
4.
20 km to mm
5.
480 mJ to MJ
6.
1 mm2 to m2
7.
1 m3 to cm3.
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Measurement of Time
Time: - Period between events
- Duration of an event.
Instruments used to measure time include watch/clock, pendulum, sundial, hourglass.
Time measuring instruments depend on events which can repeat themselves regularly.
Examples include
-vibration of quartz crystals
-appearance of the moon/stars/sun in the sky.
-croacking of the cock.
SI units of time are seconds (s). Other units include Minutes, Hours, Days, Week, Fortnight,
Months, Years, Decades, Centuries & Millennium.
Using a stopwatch to measure time.
A stopwatch is used in labs to measure the duration of an event and in some cases the period
between events.
Start/stop button:
Lap/reset button:
Used to initiate and end the timing process
Used to reset the watch and also to momentarily stop the watch to take
a reading.
What time is shown by the stopwatch above?
Time shown =............................
Accuracy of the stopwatch
Accuracy of any measuring instrument is the smallest measurement that can be made with the
instrument, or the smallest division in the instrument.
Thus the accuracy of the stopwatch is 0.01 seconds.
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Errors associated with the use of a stopwatch
1.
2.
Human reaction time: People do not react in a similar manner in similar situations. i.e
reaction times are not always the same. This can lead to errors
of time measurement. These errors can be minimized by taking
multiple readings and then calculating the average
Zero Error: This is where the instrument does not commence readings at zero. It is
more prevalent in analogue clocks.
Period of a Simple Pendulum
This consists of a mass attached to a string which is then allowed to swing freely. The time
taken to make one complete swing is called the Period (T) of the pendulum.
Experiment to find period of a pendulum.
Apparatus:
Pendulum bob + string
Metre ruler
Stopwatch
Retort stand + clamp.
Procedure:
1.
Setup the apparatus as shown below.
2.
Measure and record l, the length of the pendulum.
3.
Using the stopwatch, measure and record the time taken to make 20 complete
oscillations. A complete oscillation is movement from Q to R and back to Q.
4.
Calculate the period, T.
5.
6.
Repeat steps 2 and 4 for two more values of l.
Record your results in the table below.
Length (cm)
Time for 20 oscillations (s)
Period, T (s)
Factors affecting the period of a pendulum.
i)
Length
ii)
Acceleration due to gravity
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Measurement of Length
Length is a measurement of how long something is. SI units are metres (m). Instruments used
to measure length include;
- ruler
- measuring tape
- clickwheel
- vernier alipers
- micrometer screwgauge
Measurement of length using a ruler.
When using a ruler, one must try to avoid parallax error and zero error.
Measurement of length using a Vernier Calipers.
A vernier callipers is used to measure internal and external diameters, thickness of metal
sheets, small depths, etc. The vernier callipers has two scales; the main scale and the vernier
scales. The vernier scale slides over the main scale.
The final reading from the instrument is the sum of the Main Scale Reading and the Vernier
Scale Reading.
The main scale reading is the mark on the main scale which is to the left of the zero of the
vernier scale.
The vernier scale reading is any mark on the vernier scale which coincides with any other
mark on the main scale. The smallest division on the vernier scale is 0.01 cm.
Errors associated with the use of a vernier callipers include zero error and parallax error.
Accuracy of the vernier callipers is 0.1 mm.
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Measurement of length using a Micrometer Screw gauge.
A measuring cylinder is used to measure small lengths accurately. It is able to give more
accurate readings of length up to 25 mm.
The micrometer screw gauge has two scales; the main scale and the drum scales. The drum
scale slides over the main scale.
The final reading from the instrument is the sum of the Main Scale Reading and the Drum
Scale Reading.
The Main Scale Reading is the last mark on the main scale which is on the edge of the
drum/thimble. The main scale is calibrated/graduated in millimetres.
The Drum Scale Reading is any mark on the drum scale which coincides with the horizontal
line passing through the main scale. The smallest division on the drum scale is 0.01 mm.
Errors associated with the use of a micrometer screw gauge include parallax error and zero
error. There are two types of zero errors associated with the screw gauge. This are negative
zero error and positive error.
Diagram (b) shows a positive zero error of 0.02 mm.
Diagram (c) shows a negative zero error of -0.04.
Accuracy of the micrometer screw gauge is 0.01 mm.
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MOTION
Definition of Terms
Distance (s) The length of the pathway followed by an object between two points. SI units
are metres.
Displacement (s) Distance in a specified direction. SI units are metres.
Average Speed: The total distance travelled in a given period of time.
Average speed =
total distance travelled
time taken
Velocity (u-initial velocity and v-final velocity): Speed in a stated direction or the rate at
which displacement changes with time. The SI units are metres per second
Acceleration (a): The rate at which velocity changes with time.
acceleration =
change in velocity
time taken
v - u
t
If the acceleration is negative it is called deceleration or retardation.
a 
Uniform and Non-Uniform Motion
Uniform Velocity: This refers to constant or steady velocity.
t (s)
0 1 2 3 4
v (m/s) 8 8 8 8 8
Non Uniform Velocity: This refers to velocity which is not constant
t (s)
0 1 2 3 4
v (m/s) 3 4 5 8 10
Uniform Acceleration: This refers to constant or steady acceleration. It means that the
increase or decrease in velocity is the same per unit time.
t (s)
0 1 2 3 4
v (m/s) 0 4 8 12 16
a (m/s)
4 4 4 4
Non-Uniform Acceleration: This refers to acceleration which is not constant.
t (s)
0 1 2 3 4 5
v (m/s) 0 2 6 7 16 19
a (m/s)
2 4 1 9 3
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Motion Graphs
Distance-Time Graphs

Slope or gradient of a distance-time graph gives velocity.
t (s) 0 1 2 3 4 5
s (m) 0 2 4 6 8 10
m 
Y2 - Y1
8m - 2m

4s - 1s
X 2 - X1

6m
3s
= 2 m/s

If the distance-time graph is a diagonal line then the velocity is constant.

If the distance-time graph is a horizontal line then the object is at rest.
Velocity-Time Graphs

Velocity-time graph for uniform velocity is a horizontal line.
t (s)
0 1 2 3 4
v (m/s) 8 8 8 8 8
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
Velocity-time graph for uniform acceleration and uniform deceleration is a diagonal
line
Uniform Acceleration
Uniform Deceleration
t (s)
0 1 2 3 4 5
v (m/s) 0 4 8 12 16 20
a (m/s)
4 4 4 4 4

Slope/gradient of a velocity-time graph gives acceleration.
m 

t (s)
0 1 2 3 4 5
v (m/s) 20 16 12 8 4 0
a (m/s)
4 4 4 4 4
Y2 - Y1
X 2 - X1

8 m/s - 2 m/s
4s - 1s

6 m/s
3s
= 2 m/s2
Area under a velocity-time graph gives distance covered.
Area =
1
/2 x b x h =
PHYSICS NOTES: Physical Quantities & Measurement
1
/2 x 5s x 10m/s = 25 m/s
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Classwork
1.
The diagram below shows the velocity-time graph for a motor vehicle
(a)
(i)
(ii)
Describe the motion of the vehicle between
(i)
PQ
(ii)
QR
(iii)
RS
(b)
Using the graph, calculate
the acceleration of the vehicle during the first 2 seconds.
the acceleration of the vehicle during the last 2 seconds.
(c)
2.
Calculate the total distance travelled
Use the distance-time graph below to answer questions which follow
(a)
(b)
Describe the motion between
(i)
0A
(ii)
AB
(ii)
BC
Calculate speed in the last 1 second
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Equations of Motion
v  u  at
eqn 1
s  12 (u  v)t
eqn 2
s  ut  12 at 2
eqn 3
v 2  u 2  2as
eqn 4
It is important to note that

Eqn 1 does not have s

Eqn 2 does not have a

Eqn 3 does not have v

Eqn 4 does not have t

All the equations have u.
NB: This equations only apply to objects travelling with uniform motion.
M,
Classwork
(On answering these questions assume that there is no air resistance)
3.
A bus starts off from rest and reaches a velocity of 25 m/s in 10 seconds. Calculate
(i)
acceleration of the bus
the distance travelled in the first 10 seconds.
(ii)
A car travelling with a constant speed of 20 m/s accelerates at 2 m/s2 for 5 seconds.
Calculate
(i)
the velocity of the car after 5 seconds
(ii)
distance travelled in that time.
4.
A train travelling at 36 m/s decelerates at 4 m/s2 for 9 seconds. Calculate
5.
(i)
(ii)
6
An aircraft accelerates at 0.8 m/s2. It’s take off speed is 48 m/s.
(i)
(ii)
7.
the velocity of the car after 9 seconds
distance travelled in that time.
What length of runway does the aircraft need to take off.
How long does it take to reach its take off speed?
Usain Bolt, a Jamaican athlete, is the world record holder after completing the 100
metre race in 9.58 seconds recently. Calculate
(i)
His final velocity as he crossed the finish line
(ii)
His acceleration
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Vertical Motion without Air Resistance
(Acceleration due to gravity, g)
Assuming that there is no air resistance, all bodies undergoing vertical motion accelerate
uniformly at g or –g depending on whether they are ascending or descending.
Descending objects
u = 0 m/s
a = g = 10 m/s2
Ascending objects
v = 0 m/s
a = -g = -10 m/s2.
Classwork
(On answering these questions assume that there is no air resistance)
8.
(i)
(ii)
9.
A cannon ball is shot vertically upwards with an initial velocity of 40 m/s.
Calculate
the maximum height reached by the cannon ball
the time taken to reach that height.
A ball is dropped from cliff. If the ball reaches the ground after 4 seconds, calculate
(i)
the height of the cliff
(ii)
the velocity of the ball just before hitting the ground
10
(iii)
11.
A ball is thrown upwards with a velocity of 8 m/s. Calculate
(i)
the maximum height reached by the ball
(ii)
the time taken to reach that height
on falling back, the ball lands on the roof of a house 0.4 seconds after reaching
the maximum height.
A motor car travelling at a constant speed of 20 m/s drives over a cliff and hits the
ground after 4 seconds.
Calculate
(i)
(ii)
The height of the cliff
The distance from the foot of the cliff to the point where the car hits the ground
(iii) The vertical velocity of the car as it hits the ground
(vi)
The horizontal velocity of the car as it hits the ground
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Vertical Motion with Air Resistance
(Terminal Velocity)
When a body falls through a fluid, its acceleration is reduced as it encounters friction. The
acceleration is reduced because the fluid friction increases.
The diagram below shows the movement of a ball as it falls through air, from the moment it
is released.
Stage 1
Initially as the ball is dropped the only force acting on it is its weight. At this point the ball
accelerates uniformly at g.
Stage 2
The ball has started experiencing fluid friction but its weight is greater than the fluid friction.
Thus the acceleration of the ball is reduced but it is still greater than zero. As such the
velocity keeps on increasing which results in an increase in fluid friction and as such the
resultant force decreases.
Stage 3
The fluid friction increases until it becomes equal to the weight. At this point the resultant
force is zero and the acceleration is also zero. Thus the velocity stops increasing and remains
constant for the remainder of the flight of the ball. This constant velocity is called terminal
velocity.
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The diagram below shows the velocity-time graph for an object falling through a fluid until it
reaches terminal velocity.
Classwork
11.
The diagram below shows the forces acting on a raindrop which is falling to the
ground.
(i)
A is the force that causes the raindrop to fall. What is the force called?
(ii)
B is the total force opposing the motion of the drop. State one possible cause
of this force.
(iii)
What happens to the raindrop when force A = force B?
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Mass, Inertia, Weight & Centre Of Gravity
Mass: Amount or quantity of matter in an object. Mass is a constant for every object and
never changes.
Inertia: It is the tendency of an object to resist changes to its state of motion. Objects with
large mass have large inertia and those with small mass have a small inertia. As such
inertia can be seen as an indirect measurement of mass.
Weight: This is the gravitational pull on an object. Weight of an object depends on the
acceleration due to gravity and as such can change depending on the force of gravity.
weight = mass x acceleration due to gravity.
W = mg
Example:
The table below shows the value of the acceleration due to gravity in different places.
Earth
Moon
Space
g (N/Kg)
10
1.6
0
Calculate the weight of a 60 Kg austronaut in
(i)
earth
(ii)
moon
(iii)
space
Centre of Gravity (Centre of Mass)
This refers to a point within an object where its entire mass or weight seems to be
concentrated such that if the object is supported at this point it should balance.
Centre of Gravity of Regular Objects.
The centre of gravity of irregular objects is found at their geometric centre.
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Centre of Gravity of Irregular Objects.
Apparatus

Irregular lamina

Retort stand & clamp

Plumb line
Procedure
1
Make 3 holes on the edge of the lamina and label them A, B & C.
2
Suspend the lamina on the retort stand through hole A
3
4
7
Suspend the plumb line in front of the lamina
Allow both the lamina and the plumb line to come to rest.
5
Trace the plumb line along the lamina
6
Repeat steps 2 to 5 for holes B and C.
The centre of gravity of the lamina is at the intersection lines.
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Toppling
The position of the centre of gravity within an object determines if it topples over easily. A
body topples if the vertical line through its centre of gravity falls outside its base.
In figure (a) the vertical line through the centre of gravity falls within its base and as such
will not topple.
In figure (b) the vertical line through the centre of gravity falls on the edge of the base and as
such will balance on the edge.
In figure (c) the vertical line through the centre of gravity falls outside the base and as such
will topple, i.e. fall over.
Stability
A body that topples easily is not stable while one which does not topple easily isstable.
Factors affecting stability


Stability of any object depends on
Wideness of the base. If the base is wide then the object becomes more stable while
bases which are not wide make objects less stable.
Position of the centre of gravity. If the centre of gravity is positioned at a high
position then the object is less stable. If the position of the centre of gravity is low
then the object becomes more stable.
Three terms are used to describe stability of objects. These are
(i)
Stable Equilibrium
A body is in stable equilibrium if it goes to its original position after being
slightly displaced and released. The Bunsen burner below is in stable
equilibrium
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1.
(ii)
Unstable Equilibrium
A body is in unstable equilibrium if it does not retain its original position after
being slightly displaced and released. Its centre of gravity falls. The Bunsen
burner below is in unstable equilibrium
(iii)
Neutral equilibrium
A body is in neutral equilibrium if it retains its new position after being
slightly displaced and released. The position of its centre of gravity remains
the same. The Bunsen burner below is in neutral equilibrium.
Classwork
The table below gives a value for the acceleration due to gravity, g, on various
planets. Use it to answer questions which follow.
Planet g (m/s2)
Pluto
0.5
Mars
4
Earth
10
Jupiter
26
A 30 ton Spacecraft leaves earth and visits all the planets listed above. Calculate the
weight of the spacecraft in Pluto, Earth, Mars & Jupiter
2.
A bus and a racing car are travelling at the same high speed in the same direction.
They both approach a curve on the road at the same time. The bus overshoots the
curve while the racing car negotiates the curve with ease.
(i)
State two attributes of the racing car which helped it to negotiate the curve.
(ii)
State a way in which road curves are constructed so as to minimise cases of
vehicles overshooting it.
3.
A truck and a small car are travelling along a straight road at the same speed. Both
drivers see an obstacle on the road and apply the brakes at the same time. Which
vehicle is likely to stop first? Give a reason for your answer.
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ENERGY, WORK & POWER
ENERGY
Energy is the ability or capacity to do work. The SI unit of energy is the Joule (J). Energy
exists in various forms. These include
(a)
Kinetic energy (Ke)
Energy found in moving objects
(b)
Heat Energy (He)
Kinetic energy of particles in matter.
(c)
Potential energy
The energy an object has because of the height it has been moved, its chemical
composition or because of its shape/size. Forms of potential energy include
(i)
Gravitational Potential energy (GPe). The energy an object has because of the
height it has been moved.
(ii)
Chemical Potential energy (CPe). The energy an object has because of its
chemical composition.
(iii) Mechanical Potential energy (MPe). The energy an object has because of its
shape/size.
(d)
Light energy (Le)
The energy given off by luminous and non luminous objects
(e)
Electrical energy (Ee)
Energy transported by electric charges in conductors.
(f)
Sound energy (Se)
Energy found in vibrating objects.
Principle of Energy Conservation
It states that energy can neither be created nor destroyed, but can only change from one form
to another during an energy conversion.
Efficiency
The quality of a system to convert one form of energy to another without wastage. During
energy conversions, some of the energy is lost (i.e it is not changed into a useful form), heat
energy accounts for most of the energy lost. Therefore, energy conversions are never 100%
efficient.
efficiency 
energy output
X 100%
energy input
Energy conversions
A person speaking into a microphone.
Sound energy → Electrical energy
1.
2.
Listening to a loud speaker.
Electrical energy → Sound energy.
3.
Hydroelectric Power Station.
Gravitational Potential Energy → Kinetic Energy → Electrical energy
Sources Of Energy
Sources of energy can be divided into two groups.
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Renewable Sources Of Energy are those sources which can be replaced once used and are
generally non polluting.
Non-Renewable Sources Of Energy are those sources that cannot be replaced once used and
are generally polluting.
Major sources of energy in Botswana
Energy Source
1) Solar Energy
(Renewable)
2) Coal
(non renewable)
Use
Botswana enjoys a lot of
sunshine throughout the
year. Solar water heaters
are used in some
households. Photovoltaic
power can be generated
from solar panels fitted
with solar cells
Used for generating 
electricity as well as 
heating and cooking
advantages
Abundant

Cheap

Environmental friendly


Abundant
Cheap

Biomass
(Firewood, cow
dung,
charcoal,food)
(Renewable)
Wind
(Renewable)
widely used for cooking
and heating.


Abundant
Cheap

Due to the flat terrain,  Cheap

there is not much wind in
 Environmental friendly
Botswana. Windmills are
used to pump water out
of boreholes
Disadvantages
Expensive equipment
No sunshine during cloud
cover.
Air pollution
Coal mining scars the
landscape
Releases CO2 which causes
global warming
collection of fire wood leads to
deforestation
Release carbon dioxide leading
to global warming.
No wind at times
.
Sources of energy in other countries
Energy Source
Nuclear power
(non renewable)
Use
Used for generating electricity

Advantages
Little fuel is needed to produce
a lot of electricity.(Only 7 kg of
uranium fuel are needed to

produce 60 000 W of electricity
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Disadvantages
High building costs
Expensive equipment
Expensive maintenance
Puts living things at risk of radioactive
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
Hydroelectric
power
(renewable)
Water is collected/stored 
behind huge dams on high
ground such as mountains.
The water is released through
sluices and its GPe is changed
to Ke which to drive turbines
for generating electricity.
per month)
Does not release toxic gases into
the atmosphere.


Does not cause much pollution





Crude oil &
natural gas
(non renewable)
Geothermal
energy
( renewable)
Bio fuels
(renewable)
Used for generating

electricity, fuel for motor 
vehicles and industrial
machines.
Heat energy from radioactive
reactions in the earth’s core
escapes to the surface through

vents on the crust in the form
of steam. This energy can be
tapped and used for generating
electricity and heating homes.
These are alcohol based fuels
produced from biomass
through fermentation,
pyrolisis and anaerobic 
digestion. They are used for
generating electricity and fuel
for motor vehicles.

Abundant
Cheap




Cheap

Does not cause much pollution
Does not require much

structural development.
Environmentally friendly as 
waste products can be used to 
energy.
If fermentation and pyrolisis are
used there is little or no CO2
released into atmosphere.
abundant


emissions due to the possibility of nuclear
meltdown.
Requires expert skills.
Waste products pose storage problems and can
be used to make atomic weapons.
Limited number of suitable sites to build the
dam.
High building costs
The reservoir floods huge valleys which drowns
animal and kills plants thus impacting on biodiversity.
Huge numbers of people have to be relocated in
order to accommodate the reservoir.
Water loses its quality due to hydroelectric
processes.
The weight of the water in the reservoir causes
seismic activity.
Requires expert skills
Their combustion releases greenhouse gases
into the atmosphere which leads to global
warming.
Causes water pollution
Accidents during their mining and
transportation causes’ water and air pollution.
Not available in many locations.
High cost of drilling deep into the earth.
Requires expert skills.
Farming large amounts of crops is expensive
Converting the bio mass to bio fuels is
expensive.
Food plants are used to process biofuels and this
could lead to food shortages and/or increase in
food prices.
Pyrolisis is requires huge amounts of heat.
Direct combustion could lead to air pollution.
Socio-Economic and Environmental Impacts of using energy sources
As shown in the table above the use of most energies sources has several disadvantages.
Before any energy source is used it is important to determine its socio-economic and
environmental impacts. As such there is need for an Environmental Impact Assessment (EIA)
study to be carried out before any energy source is utilized
Conservation of energy
Energy which takes a form which is not useful at a particular time is said to have been wasted
or lost. Preventing this from happening is called energy conservation. This is achieved
through diligent use of available energy sources.
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Mechanical Energies
These are energies associated with the position and motion of an object. Mechanical energy
of a system is the sum of the gravitational potential energy and the kinetic energy of the
system.
Kinetic Energy
The kinetic energy of a body of mass m, travelling with a velocity v, is given by
Ke  1 mv 2
2
Gravitational Potential Energy
The gravitational potential energy of a body of mass m, which is moved through a height h, is
given by
GPe  mgh
GPe – Ke Transformations
Gain in GPe = Loss in Ke
Loss in GPe = Gain in Ke
∆ GPe = ∆ Ke
Classwork
1.
A 5 kg rocket has 500J of kinetic energy. Find the velocity of the rocket.
2.
A 100g steel ball is 1.8m above the floor. What is the amount of gravitational
potential
energy possessed by the ball?
3.
A 200 g ball is shot vertically upwards to a height of 80 metres.
Calculate
(i)
Kinetic energy of the ball as it left the ground.
(ii)
The velocity with which it leaves the ground
(iii) Time taken to reach the height
4.
A 2 kg stone is dropped from a tower and reaches the ground after 2 seconds.
Calcultate
the GPe of the stone before it is dropped.
5.
A lamp is 60% efficient, if the lamp gives out 400J of light energy.
(i)
How much electrical energy was it supplied with?
(ii)
How much energy was wasted as heat.
WORK
Work is the transfer of energy. It is measured as a product of the force applied and the
distance moved.
Work done = applied force x distance moved
W = Fs
POWER
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This is the rate at which work is done or the rate at which energy is transferred.
Power 
Work done/Energy transfer
time
P 
W/E
t
Classwork
6.
7.
A boy whose weight is 600 N runs up a flight of stairs 10m high in 12 seconds.
Calculate the power he develops in climbing the stairs.
A donkey pulls a cart with a force of 400N and takes 10 seconds to cover a distance of
100m. What is the power developed by the donkey in pulling the cart?
8.
How long does it take an electric motor rated 800 W to complete 4kJ of work in
lifting a load.
9.
A machine changes 5 kJ of electrical energy into kinetic energy in half a minute.
What is the power rating of the machine?
10.
A hydroelectric dam generates 10 000 W of electricity every 2 minutes. To achieve
this 3 000 kg of water falls down the dam to the turbines every 2 minutes.
If the height of the dam is 60 m, calculate
(i)
amount of energy in the water as it reaches the turbines.
(ii)
amount of electrical energy generated by the dam.
(iii) efficiency of the power station.
(iv)
the fate of the ‘lost’ energy.
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PRESSURE
Pressure is the force applied per unit area.
pressure 
force
area
P
F
A
The SI units of pressure are Pascals [Pa]. One Pascal is equal to one Newton per square meter
(1 Pa = 1N/m2).




Examples of the effects of pressure are:
Stiletto-heeled shoes are likely to mark floors,
A knife is often sharpened before use,
A car with tyres that have a small surface area easily sinks in sand or mud.
Astronauts wear space suits when on mission. These provide pressure to balance body
pressure.
Pressure in Fluids
The pressure in a fluid depends on



depth of the liquid
density of the liquid
acceleration due to gravity
P= ρgh
Where
ρ =density of fluid
g = acceleration due to gravity
h = depth of the fluid.
Classwork
1.
2.
3.
4.
5.
6
Calculate the pressure if a 150N force is exerted on a surface area of 0.5m2.
A concrete block of mass 90 kg and a square base of side 2 m is resting on the
ground. What is the pressure it exerts on the ground?
A pressure of 10 Pa acts on an area of 3.0m2. What is the force acting on the area?
Which of the following will damage a wood-block floor that can withstand a pressure
of 2000 kPa ?
A
A block weighing 2000kN standing on area of 2 m2.
B
An elephant weighing 200kN standing on an area of 0.2 m2.
C
A girl of weight 0.5 kN wearing stiletto-heeled shoes standing on an
area of 0.0002m2.
What is the pressure 100 m below the surface of sea water of density 1150 kg/m3?
At a weather station the pressure is found to be 100 000 Pa while the average density
of air is found to be 1.25 kg/m3. Calculate the average depth of the air above the
weather station.
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Atmospheric Pressure
This is the pressure due to the weight of the atmosphere on earth. The atmospheric pressure at
sea level is about 1.0 x 105 Pa (100 000 Nm-2). We do not feel this pressure because it is
balanced by our blood pressure.
Effects Of Atmospheric Pressure
 Bleeding: If the atmospheric pressure is smaller than the blood pressure nose bleeding
may occur. This is common during very hot days as well as at a high altitude.
 Collapsing Can: If air is removed from a can using a vacuum pump, the wall of the
can collapses as air inside the can is gradually removed. The same effect can be seen
when using a drinking straw on mini-juice packaged drink.
 Magdeburg Hemispheres: If two hemispheres are fitted together and air removed, it
becomes very difficult to separate the hemispheres.
 Drinking Straw: Atmospheric pressure helps you to push the drink up as you suck
using a straw.
 Rubber Sucker: When a rubber sucker is pressed against a smooth surface, air is
removed. The atmospheric pressure pushes and holds the cup against the surface.
Suction cups are used to lift metal sheets, glass panes or holders for towels and coats.
 Siphoning water: when siphoning water from a large tank to a smaller one,
atmospheric pressure helps you by pushing the water up the pipe.
Measuring Atmospheric Pressure
Atmospheric pressure can be measured using a barometer. Types of barometers include
 Simple Mercury Barometer
 Aneroid Barometer
 Fortin’s Barometer
Simple Mercury Barometer
This instrument is used to measure atmospheric pressure. It consists of a cylindrical tube
filled with mercury which is then inverted into a mercury bath. A small amount of the
mercury flows into the bath but most remains in the tube. Atmospheric pressure acting on the
surface of the mercury in the mercury bath supports the mercury column in the tube. The
pressure at Y due to mercury column XY is equal to the atmospheric pressure.
The height h is directly proportional to the atmospheric pressure and as such is used as a unit
of measuring pressure. The height h is about 760 mm (0.76 m) mm at sea level. Thus 760
mm of mercury is equal to 1 atmosphere (1 atm).
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U tube manometer
A u-tube manometer is used to measure gas pressure. It consists of a u-tube filled with
mercury. In figure (a), the level of the liquid in both arms of the u-tube is the same since only
atmospheric pressure is acting on the liquid in the u-tube. (the gas has not been connected
yet.) The pressures at A and at B are the same and are equal to atmospheric pressure.
In figure (b), a gas supply is connected to the manometer. If the gas pressure is greater than
atmospheric pressure it increases the pressure at A which causes level A to go down while
level B rises. At equilibrium the pressure at A must equal to the pressure at C since they are
both at the same level.
Thus the gas pressure at A, PA is equal to the pressure at C, PC. (PA = PC.)
But PC is equal to the pressure at B, PB (atmospheric pressure) + the pressure due to mercury
column BC (gh).
Therefore the gas pressure PA is given by,
PA = PB + gh
Where h = barometric height-height of the column BC
 = density of liquid in u-tube
g = acceleration due gravity
PB = atmospheric pressure
Classwork
7.
In a simple mercury barometer, the tube supports 73cm of mercury. What is the
atmospheric pressure in Pascal’s? Density of mercury is 13 600 kg/m3
8.
What would be the height of a water barometer if atmospheric pressure is 1 x 10 5pa
and the density of water is 1.0 x 103 kg/m3
9.
In a manometer used to measure gas pressure, the gas supports a 100 mm of mercury
column, calculate the gas pressure. Atmospheric pressure is 760mm Hg.
10.
The pressure at the base of a mountain is 105 000 Pa while the pressure at the
mountain top is 15 000 Pa. If the average density of air is 1.25 kg/m3, calculate the
height of the mountain.
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Weather Maps
Atmospheric pressure and other atmospheric conditions such as temperature, humidity and
cloud pattern can be used to predict weather. Such conditions can be plotted on a map to form
a weather map.
An isobar is a line on a weather map that joins places with the same atmospheric pressure.
Pressure on a weather map is quoted in pressure units called millibars.
1 Bar = 100 000 Pa  1 atm
(1 Bar = 1000 Millibars)
Cyclone
A cyclone is a region where the atmospheric pressure decreases as you approach the centre of
the region. i.e it has low pressure at the centre
.
Wind blows spirally from a high to a low pressure region. Cyclones are characterised by wet,
windy weather. The closer the isobars the stronger the wind and chances of rain. Examples of
cyclones include whirlwinds, typhoons, hurricanes, tornadoes, willi-willies etc.
Anticyclone
An anticyclone is a region with high pressure at the centre.
It is characterised by dry dense air.
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KINETIC THEORY OF MATTER




Matter is made up of small particles called atoms or a group of atoms called
molecules. The size of each particle is different for different materials.
The distance between molecules can change depending on the Internal Energy
(kinetic + potential) of the molecule or atom.
Particles are always in motion (moving). The higher the temperature the faster the
molecules move/vibrates.
At the same temperature, all molecules have the same energy. Small particles move
faster while heavy particles moves slowly.
States Of Matter
States of
matter
Properties
Distance
between
molecules
SOLID
LIQUID
GAS
Have a definite
volume and
definite shape.
Not compressible
Have a definite
volume but no definite
shape (takes the shape
of the container).
Slightly compressible
Have no definite shape and
volume. (wholly fills up the
container and takes the shape
of the container). Highly
compressible
Molecules are very
close to each other
Molecules slightly
further apart than in
solids but still close
together to have a
definite volume
Particle held by less
strong forces.
Molecules are much further
apart. So gases can be
compressed or squeezed in
smaller space.
Forces
between
molecules
Held by strong
forces of attraction
called bonds.
Motion
Molecules vibrate
to and fro at a fixed
position.
Free to move
No or less forces of attraction.
Molecules are free to move in
any direction.
Moves freely at high speed
colliding with each other and
the walls of the container.
Motion of Gas Molecules and its Temperature and Pressure.
If a gas is heated in a closed container, its molecules gain kinetic energy and begin to hit the
walls of the container more frequently than before. This causes an increase in pressure on the
walls of the container. The faster the gas molecules move, the higher the temperature they
attain. The gas container can explode if it can’t withstand the pressure build up.
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Brownian Motion
Brownian motion gives us the evidence that molecules in suspension (gases) are constantly
moving. When smoke is trapped in a glass box (smoke cell) and is observed with a
microscope, the smoke particle can be seen as bright specks moving around in a random and
haphazard manner.
This is because they collide with gas molecules that move at high velocities at random paths.
Smoke particles are bigger compared to air particles. The specks of light seen is where
collision between smoke particles and air particles occur. This phenomena is known as
Brownian motion..
Evaporation
Evaporation is the escape of high energy molecules from the surface of a liquid. Evaporation
results in a drop in the temperature of the liquid from which the molecules escaped. This is
because the molecules that escape acquire energy to do so from those which remain in the
liquid.Evaporation only takes place at the surface of the liquid and occurs at any temperature.
Factors That Affect Evaporation



A number of factors affect the rate of evaporation. These are;
Wind speed (drought).An increase in wind speed causes an increase in rate of
evaporation
Surface area. The larger the surface area the higher the rate of evaporation.
Temperature. The higher the temperature the higher the rate of evaporation
Humidity. The higher the humidity the lower the rate of evaporation.

Applications of evaporation
Ether is used in fridges to cool their interiors

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

Water sacks are put under the shade and moistened with water so that the water inside
cools as the molecules outside evaporate.
Organisms cool themselves by evaporation using different ways,
.
Dogs = Panting
Elephants= Flap their ears
Humans= Perspiration
Plants=Evaporation from leaves
THERMAL EXPANSION OF MATTER
Matter expands when heated. This happens because particles gain kinetic energy and begin to
move away from each other resulting in an increase in the space between them. When matter
is cooled it contracts. Gases expand the most and solids expand the least(Gases contract the
most and solids contract the least.
Experiment to Demonstrate Expansion in Solids
There are various experiments to show expansion in solids. These include Ball and ring
apparatus, bimetallic strip etc.
Ball and ring apparatus.
Before the ball is heated, it easily passes through the ring. But if the ball is heated it does not
pass through the ring. This is because the ball has expanded. If the ball is allowed to cool then
it will contract. This will allow it to pass through the ring again.
Bimetallic strips
A bimetallic strip is made of two different metals which are riveted together.
The two metals expand at different rates and as such when the strip is heated, it bends with
the
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most expansive metal on the outside.
Study the diagrams (a) and (b) which show the bimetallic strip after cooling and heating
respectively. Which of the two metals expand the most?
Experiment to Demonstrate Expansion in liquids
A coloured liquid is poured into a test tube which is fitted with a glass tube as shown below.
Before heating, the level of the liquid is at level A. After heating the liquid level goes up to
level B. This indicates that the liquid has expanded and increased in size.
Experiment to Demonstrate Expansion in Gases
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When the flask is heated bubbles are observed in the water as shown above. This indicates
that the air inside has expanded and some of it is escaping through the glass tube to the
outside. As the air passes through the water it causes the observed bubbles.
Applications of Expansion
1. Thermostat
These are devices that maintain a steady (constant) temperature in an appliance.
The bimetallic strip in the thermostat bends to switch off the circuit if the temperature rises
above the set temperature and straightens to switch on the circuit if the temperature falls
below the set temperature. The diagram above shows the thermostat as used in an electric
iron. Other appliances that use a thermostat include air conditioners, electric oven, electric
kettle, e.t.c.
2. Fire alarm
It uses bimetallic strip as a switch.
When there is a fire in the house, the bimetallic strip bends to close the contacts thereby
switching on the circuit. This causes the bell to ring.
3. Shrink fitting:
The axle is cooled with liquid nitrogen (-198°c) so that it fits into the gap after contracting. It
makes a tight fit after returning to normal temperature.
4. Hot riveting: A rivet is hammered in while hot and it makes a tight fit on contracting
5. Measurement of Temperature.
Materials whose expansion is directly proportional to change in temperature can be used in
thermometers for temperature measurement. E.g. mercury and alcohol are used in a liquid in
glass thermometers.
6. Hot air balloons
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Air inside expands as it is heated. This causes a reduction in density of the air inside. Since
the density of air outside the balloon is higher the balloon rising due to convection.
Consequences of Expansion
1. Railway line
The ends of the rails are tapered and made to overlap to avoid bulging during a hot day.
2. Electric cables
They are allowed to sag a bit so that in winter they do not become tight after contracting.
3. Bridges
One end is fixed and the other end rests on rollers. An expansion gap is created to give room
for expansion.
The Unusual Expansion of Water
When water is cooled, it contracts as expected until a temperature of 4oC is reached. Between
temperatures of 4oC and 0oC, the water expands while it is being cooled from 4oC to 0oC.
When the temperature of the water reaches 0oC, it expands even more as it freezes. See graph
above. This is the reason why water bottles burst as the water freezes.
As a consequence of its unusual expansion at 4oC, water has a maximum density at that
temperature. This is why marine life can survive in a frozen pond( only the water at the top
freezes while the water at the bottom remains a liquid). Ice cubes float in water for the same
reason.
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IDEAL GAS LAWS
Boyle’s Law
The volume of a fixed mass of gas is inversely proportional to the pressure if the temperature
is kept constant.
P α 1/v
P1 V1 = P2V2
Pressure law
The pressure of a fixed mass of gas is directly proportional to its absolute temperature if the
volume is constant
P α T
P1 P2

T1 T2
Charles Law
The volume of a fixed mass of gas is directly proportional to the absolute temperature if the
pressure is constant.
V α T
V1 V2

T1
T2
Classwork
(when solving problems relating to gas laws all temperatures should be expressed in the
absolute temperature scale)
1.
If a certain quantity of gas has a volume of 30cm3 at a pressure of 1 x 105 Pa, what is
its
volume when the pressure is 5 x 105 Pa?
2.
An enclosed mass of air occupies 4.0 x 103 m3at a pressure of 100 kPa, when the
pressure
is changed to 80 kPa, what will be the volume in m3 ?
3.
A gas at a temperature of 5°c and pressure of 1.0 x 105 pa is heated until it reaches a
temperature of 15°c, calculate the pressure of the gas.
4.
A syringe has a gas at a pressure of 500 Pa. The temperature of the gas is 40°c. What
will be the pressure of the gas if the temperature is reduced by half?
5.
A container holds a gas at 0°c and pressure 0.5 x 105 Pa. To what temperature must it
be
heated for the pressure to double?
6.
A quantity of helium gas occupies a volume of 60 cm3 at 25°c. The gas is then cooled
until it occupies a volume of 15cm3, calculate the temperature of the gas.
Absolute Temperature Scale (Kelvin Scale)
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If the volume-temperature or pressure-temperature graphs for an ideal gas are plotted and
then
extrapolated or produced backwards, they are found to cut the temperature axis at -273 oC.
This suggests that -273 oC is the lowest possible temperature. As a consequence this
temperature is called absolute zero and is the zero of the absolute temperature scale (Kelvin
scale).
At this temperature


molecular motion ceases
the total internal energy is zero.
This is only true for ideal gases.


Practically this is impossible because
gases generally liquefy before reaching -273 oC.
it implies that that matter ceases to exist -273 oC( since the volume is 0 and the
pressure is also 0 at this temperature).
Relationship between the Kelvin and Celsius temperature scales
TK= TC + 273
or
TC= TK – 273
Where TK= temperature in Kelvin
TC= temperature in °Celsius
NB: The size of 1 Kelvin is the same as the size of 1oCelsius.
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MEASUREMENT OF TEMPERATURE
Temperature is an indirect measurement of the average kinetic energy of particles in matter or
the degree of coldness or hotness of matter.
Thermometers are used to measure temperature. Measurement of temperature depends on
physical properties of matter which change with a change in temperature. This include
 Thermal expansion
 Voltage
 Electrical resistance
 Colour
Liquid in Glass thermometer
A liquid-in-glass thermometer makes use of the thermal expansion of liquids to measure
temperature.
It is made of a capillary tube which is sealed at one end and has a liquid filled bulb at the
other end.
When the bulb is placed at a higher temperature, the liquid expands along the bore. If the
bulb is placed at a lower temperature the liquid contracts back into the bulb.
The liquid used in the thermometer should have a low melting point and a high boiling point.
The liquid should also be clearly visible and should not stick to the sides of the bore.
Commonly used liquids include mercury and alcohol.
Mercury has a melting point of -39 oC and a boiling point of 357 oC.
Alcohol has a melting point of -115 oC and a boiling point of 78 oC.
Mercury is the least used because it is very toxic. A dye is added to alcohol to make it visible.
Examples of liquid-in-glass thermometers include the laboratory thermometer as well as the
clinical thermometer. Their design features are described below.
Laboratory Thermometer
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Design feature
Purpose or working principle
The liquid is contained in a thin The thin wall allows quick conduction of heat
walled glass bulb.
through the glass (a poor conductor of heat) to the
liquid
Small bulb
Small bulb contains a small amount of liquid which
will be more responsive to heat.
Narrow uniform bore
The narrow tube allows a noticeable movement of
the liquid column for a small change in
temperature(i.e good sensitivity).
Thick capillary tube walls
The uniform bore ensures even expansion of the
liquid.
Acts as a magnifying glass for easy reading of the
liquid thread in the stem
Clinical Thermometer
Design feature
Purpose or working principle
The liquid is contained in a thin The thin wall allows quick conduction of heat
walled glass bulb.
quickly through the glass (a poor conductor of heat)
to the liquid
Small bulb
Small bulb contains a small amount of liquid which
will be more responsive to heat.
Narrow and uniform bore
The narrow bore allows a large change in length for
the mercury thread for a small change in
temperature (i.e good sensitivity).
Oval shaped capillary tube walls
Small range (35 oC to 42 oC)
Constriction just above the bulb.
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The uniform bore ensures even expansion of the
liquid.
Acts as a magnifying glass for easy reading of the
mercury thread in the stem
Normal human body temperature is around 36.9 oC,
so the small range allows for greater accuracy and
the stem can be made reasonably shorter.
Prevents the backflow of mercury into the bulb
before a reading is taken.
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Calibrating a liquid-in-glass thermometer
Two points are marked first. These are the upper fixed point and the lower fixed point.
Lower Fixed Point (0oC)
The lower fixed point is the 0oC mark on a thermometer. The thermometer is placed in pure
melting ice. Explain why the ice has to be pure.
When all the liquid has stopped contracting, a mark is placed on the thermometer to indicate
the lower fixed point.
Upper Fixed Point (100oC)
The upper fixed point is the 100oC mark on a thermometer. The thermometer is placed in the
steam above pure boiling water. Explain why the water has to be pure.
When all the liquid in the thermometer has stopped expanding, a mark is placed on the
thermometer to indicate the upper fixed point.
Calibrating the rest of the scale
The rest of the scale is calibrated by measuring the length between the lower fixed point and
the upper fixed point. This length is then divided by 100oC.
Sensitivity of a thermometer
A thermometer is said to be sensitive if it gives a large response to a small temperature
change. A sensitive thermometer is able to detect small temperature changes. A thermometer
can be made more sensitive by
 Using a large bulb.
 Decreasing the diameter of the bore.
Range of a thermometer
This refers to the temperatures that a thermometer can measure.
Thermocouple
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A thermocouple thermometer consists of two wires of different materials joined together at
two junctions. When the two junctions are at different temperatures an electromotive force
(emf) is induced. This emf is directly proportional to the difference in temperature between
the two junctions and it causes current to flow through the wires. This current can be
measured with a galvanometer.
The two junctions are called reference and test junctions respectively. The reference junction
is always placed at a constant temperature and the test junction is the one used for measuring
the temperature.
Advantages of the thermocouple thermometer.


Used to measure rapidly changing temperatures
Used to measure very high temperatures which makes them suitable for use in
industries.
HEAT CAPACITY
When the temperature of a substance increases, the average kinetic energy of the particles in
the substance is increased. This leads to an increase in the total kinetic energy of the particles
in the substance. Thus an increase in the temperature of a substance leads to an increase in the
heat energy of the substance.
Heat Capacity
The heat capacity of a substance is the amount of heat energy needed to raise the temperature
of the substance by 1oC or 1K..
heat capacity 
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heat energy
change in temperature
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Specific Heat Capacity, (c)
The specific heat capacity of a substance is the amount of heat energy required to raise the
temperature of 1kg of the substance by 1°C or 1K.
specific heat capacity 
c 
Q
m x 
heat energy
mass x change in temperature
or
Q = m c ∆
The SI units are J kg-1K-1 (J/kg K ) or J kg-1 oC-1 (J/kg oC).
Every material has its own specific heat capacity. Examples are given below.
Specific heat capacity (J kg -1K -1)
4200
2100
400
460
130
Material
Water
Ice
Copper
Iron
Lead
Classwork
1.
Calculate the amount of heat energy gained when the temperature of 5 kg of copper
rises from 15 °C to 25 °C.
2.
How much heat energy is lost when the temperature of 100g of water drops from 30
°C to 10 °C ?
3.
A piece of aluminium mass 0,5 kg is heated to 100 °C and then placed in 0.4 kg of
water at 10°C. If the resulting temperature of the mixture is 30°C, what is the specific
heat capacity of aluminium?
4.
A tank holding 50kg of water is heated by a 2.5 kW immersion heater. Estimate the
time it takes for the temperature to rise from 150 C to 60oC.
5.
A 1 kg lead ball is dropped from a 65 m tower. Calculate the change in its temperature
on hitting the ground
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Experiment to find the specific heat capacity of aluminium
Apparatus






Aluminum cylinder with two holes drilled in it.
Immersion heater with power rating
Triple beam balance or any other suitable scale.
Thermometer
Power supply
Stop watch
Procedure
1.
Place the immersion heater in the central hole and the thermometer in the
other as shown below.
2.
3.
4.
Record the initial temperature of the block
Connect the heater to a power supply and switch it on for 5 minutes.
Wait until the temperature stops rising. Record the temperature and the time taken to
reach this temperature.
5.
Calculate the amount of heat supplied by the heater using the expression, Energy =
power x time.
6.
Assuming no heat loss, calculate the specific heat capacity of aluminium using the
expression Q = mc∆.
Changes of state
Melting: A change of state from solid to liquid at a specific temperature called melting
point.
Freezing or Solidification: A change of state from liquid to solid without a change in
temperature.
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Boiling; A change of state from liquid to gas at a specific temperature called boiling point.
Condensation; A change of state from gas to liquid.
Difference between boiling and evaporation
EVAPORATION
BOILING
-Takes place at any temperature
-takes place at definite temperature
-Takes place at the surface of a liquid
-Takes place within liquid
Cooling curve
A
……………………………………………………………………….….
B
………………………………………………………………………......
C
………………………………………………………………………......
D
………………………………………………………………………......
E
………………………………………………………………………......
Heating curve
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A
B
C
D
E
……………………………………………………………………….….
………………………………………………………………………......
………………………………………………………………………......
………………………………………………………………………......
………………………………………………………………………......
LATENT HEAT
Latent heat
This is the hidden heat energy that is absorbed or released during a change of state
Specific Latent heat of fusion,(lf)
The specific latent heat of fusion is amount of heat energy required to change 1 kg of a body
from solid to liquid (or liquid to solid) at constant temperature.
Heat energy = mass x specific latent heat of fusion
Q = m lf
Specific Latent heat of vaporization,(lv)
The specific latent heat of vaporization is amount of heat energy required to change 1 kg of a
body of mass from solid to liquid.
Heat energy = mass x specific latent heat of vaporisation
Q = m lv
Classwork
6.
7.
How much energy is required to change 2 kg of ice in to water at 0 oC.
Calculate the energy released when 1 kg of steam changes to water.
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How much heat is needed to change 40 g of ice at 0oC to steam at 100 oC.
8.
9.
10.
Calculate heat needed to change 2 kg of ice at 0oC to steam at 100oC.
How much heat is lost when 50 g of water at 60oC is changed to ice at -5oC?
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TRANSFER OF THERMAL ENERGY
There are three methods of thermal transfer and these are
1. Conduction
2. Convection
3. Radiation
Conduction
This is the transfer of heat through matter from areas of high temperature to areas of low
temperature without the movement of matter. Conduction occurs mainly in solids and it is
faster in metals as they have free or ‘lone’ electrons that can carry heat energy around.
Liquids and gases are poor conductors of heat.
The particles in a solid vibrate about fixed positions. When one end of a solid is heated the
particles at that end vibrate faster and pass on their vibrations to the neighbouring particles.
This causes the heat to be conducted along from one end of the solid to the other.
Investigating Conduction
The diagram below shows three solid rods. Pins are attached at the end of each rod with wax.
The rods are then heated at one end with the same heat source at the same time.
State the order in which the pins will fall and explain why.
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Convection
Convection is a method of heat transfer in fluids (liquids and gases). During convection,
matter moves. It is the transfer of heat from a region of high temperature to a region of low
temperature by movement of the fluid itself.
When a fluid is heated the fluid nearest the heat source is heated first, expands and becomes
less dense. This less dense fluid moves up and is replaced by the more dense fluid from
above. The colder fluid is heated and the whole process is repeated until the whole fluid is at
the same temperature. The cyclic movement of the fluid as it is heated is called convection
currents.
Demonstrating convection in fluids.
A convection tube is filled with water. A small amount of potassium permanganate is then
placed in the water as shown below.
The convection tube is then heated at one corner. The arrows indicate inside the tube indicate
the direction taken by the purple colour of (KMnO 4).
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Demonstrating convection in gases.
The air around the candle flame is heated and expands. It becomes less dense, rises and
escapes through chimney B. Colder air enters the chamber through chimney A due to
convection currents. The convection currents carry with them some of the smoke particles
and as such smoke enters through chimney A and escapes through chimney B. The arrows on
the diagram indicate the direction followed by the smoke from the cloth.
Radiation
Radiation is the transfer of heat through electromagnetic waves.
Radiant heat is

emitted and absorbed by any object that is above absolute zero(-273oC).

can pass through a vacuum, i.e. matter is not necessary for the transfer of heat through
radiation.

Infra-red radiation
Investigating Good & Bad absorbers of radiant heat.
The diagram below shows two cardboards placed at an equal distance from a heater. One
cardboard is painted white while the other one is painted black. Metals pins are pasted to each
cardboard with wax.
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Which of the two pins falls first? Explain why.
Investigating Good & Bad emitters of radiant heat.
Two test tubes, one painted black and the other painted white are filled with boiling water as
shown in the diagram below. The two test tubes are then allowed to cool while the
temperature of the water is measure over a period of time.
Which of the two thermometers will show a quick fall in temperature? Explain why.
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Applications Of Thermal Transfer Methods

Thermos flask
A thermos flask is used to maintain liquids at a constant temperature. To do this they
prevent heat loss/gain through radiation, conduction and convection. A thermos flask
has the following basic features.
Double walls:
Used to create a vacuum.
Plastic/cork lid:
It prevents heat gain/loss through convection and radiation.
Vacuum;
It prevents heat gain/loss through conduction and convection.
Silvered Walls
Prevents heat gain/loss through radiation. They reflect back the
incoming or outgoing radiation.

School Uniform
A white shirt is usually recommended to be worn during summer to absorb less heat.
Jerseys are usually dark coloured to help the students absorb more heat during winter
or cold weather.
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
Domestic water heating system
Cold water goes into the boiler at the bottom. Hot water rises through convection to
the top of the storage tank.

Car cooling system
The arrows on the diagram shows the flow of the water.
-Petrol burns in the engine cylinders
-Water surrounding the engine cylinders become hot and rises to the top from where it
is pumped to the radiator..
-Hot water rises to the top of the radiator by convection.
-Heat is passed from the water to the radiator by conduction.
-Heat is passed to the air from the radiator by conduction, convection and radiation.
-Cool water flows from the lower end of the radiator back into the engine.
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
Colour of pots & kettles as well as colours of houses in particular climates
Cooking pots and tea pots are usually shiny so that they won’t lose heat quickly. In
cold countries the colour of houses, vehicles are usually dark to help them absorb
more heat while in hot area countries they are usually light coloured to absorb less
heat during the day.
Consequences of heat transfer in nature

Land and sea breeze
This occur next to bodies of water, e.g. lakes, dams, the sea, ponds etc.
At night the land emits more heat than the water and as such becomes colder. The air
above the water rises and cool air blows in from the side of the land. This is called a
land breeze

Tropical Cyclones
-Air over warm parts of the sea becomes warm.
-The warm air rises carrying moisture high into the atmosphere.
-The movement of the earth causes the airflow to spin
-This huge spinning mass of moist air is called a tropical cyclone.
-It causes wet cloudy weather with strong winds.
-If the winds become very strong(120-350 km/h) the storm is called a hurricane or
typhoon.
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
Days & nights in deserts
Sand is a good absorber and emitter of heat. It has a very low specific heat capacity.
During the day it absorbs a lot of heat and as such days are hotter in the desert. At
night the sand emits most of its heat and as such nights can be very cold in the desert.

Desert Breezes
-During the day the desert sand becomes hotter than areas covered by vegetation. The
wind is from forest to desert
-At night the desert sand loses heat faster and warmer air rises from the forest and a
breeze develops from desert to forest.

Greenhouse effect
-
Radiant heat from the sub is absorbed by the earth
-
The earth becomes warm and emits heat most of which escapes back into
space.
-
CO2.SO2, CO and CH4 gases in the atmosphere prevent some of this heat from
escaping and as such it is trapped in the atmosphere.
-
An increase in these gases in the atmosphere means more heat is trapped and
the atmosphere becomes warmer.
-
This is known as the Greenhouse effect.
-
The Greenhouse Effect gives rise to Global warming which in turn leads to

climate change which could lead to extinction of some animal & plant
species,

melting of polar ice caps which results in flooding of coastal areas,

Increase in violent storms (especially tropical cyclones) due to the
increased energy in the atmosphere.

Desertification in some areas.
RADIOACTIVITY
Radioactivity is the spontaneous emission of ionizing radiation by unstable nuclei.
Radioactive Materials
This includes Uranium, Carbon 14, Plutonium, Cobalt 60, Radium, Radon, Krypton,
Strontium etc. Compounds of radioactive elements are also radioactive since the nucleus is
not changed
during a chemical reaction. Thus all uranium salts are radioactive.
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Properties of Radioactive Emissions.
During the process of radioactivity three emissions may be given out. These are the alpha
particles (α), beta particles (β) and gamma rays (γ). Some of the nuclei emit the three
emissions
while others two or only one.
Emmision
Gamma
Nature

Speed
Charge
Ionizing Power





Penetration Power
Deflection in
electric field
Deflection in
magnetic field.


Electromagnetic
wave
c
0
Weak
High.
Can only be stopped
by thick concrete or
at least 6cm of lead.
No deflection
Beta









No deflection
Alpha

High speed electron



0.9c
-1
Moderate
Moderate
Can be stopped by
aluminium foil.
Can travel 50cm to
100cm in air.




Deflected towards
positive plate
Deflected according
to Fleming’s left
hand rule

High speed helium
nucleus
0.1c
+2
high
Weak
Can be stopped by a
piece of paper.
Can only travel 10
cm in air.
Deflected towards
negative plate
Deflected according
to Fleming’s left
hand rule
Detection Of Radioactive Emissions.
Ionising radiation can be detected with a;
cloud chamber
-photographic film,
-a Geiger-Muler tube
Background Radiation
This refers to the ever present ionizing radiation that organism are exposed to, including from
natural and artificial sources.
Natural background radiation comes from radioactive nuclei in rocks, water, air, vegetation,
food, etc.
Artificial background radiation comes from radioactive nuclei used in hospitals, nuclear
power
stations, nuclear weapons testing sites, nuclear power accidents, etc.
Dangers of exposure to radioactive emissions.
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1.
2.
3.
4.
5.
6.
7.
8.
It may cause mutations. (leading to birth defects).
It may lead to cancer.
It can lead to sterility
It can cause cataracts, loss of hair, sickness, or death.
Ionizing effects kill living tissue.
Exposure to gamma rays can cause severe radiation burns.
Greatest hazard with beta sources is when ingested (via food or water) or inhaled.
Alpha particles are a danger only if taken into the body but are more dangerous than
beta
particles.
Safety precautions when using radioactive materials.
1. Sources should be placed in containers made from thick lead.
2. Radioactive labs should be constructed from thick concrete and have windows made
from lead.
3. Working area along with its air content should be monitored. e.g with a Geiger
counter.
4. Protective clothing should be worn.
5. Washing facilities should be readily available.
6. Time spent with source should be limited
7. Remote handling techniques should be used.
8. Work should be carried out behind shielding or at a distance from the radiation
source.
9. Film badges should be worn to detect radiation levels.
Uses of radioactive materials
1.
2.
3.
4.
5.
6.
7.
8.
Detection of leaks in pipes
Thickness gauges, eg production of papers/metal sheets.
Gamma rays are used to sterilize food and medical equipment.
Chemotherapy and Radiotherapy
Pacemaker batteries
Tracers in plants to study the pathway of minerals in water.
Production of electricity
Radio carbon dating.
Radioactive waste disposal
Radioactive waste should be sealed in lead containers and buried deep underground in
concrete bunkers.
The Nucleus.
The nucleus of an atom (also called a nuclide) consists of particles called nucleons. This
refers to protons and neutrons.
The notation below is used to denote a nuclide.
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Z
A
X
Where X = nuclide name
Z = mass number or nucleon number
A = proton number.
Isotopes
This refers to nuclides with the same A but different Z or any of two or more forms of an
element
where the atoms have same proton number but different electron number. Examples of
isotopes include Carbon 12 and Carbon 14.
Nuclear Reactions
Nuclear reactions take place in the nucleus and are responsible for radioactive decay or
radioactivity which emits radioactive emissions.
Alpha decay
During alpha decay a nuclide releases a helium nucleus, since it loses two protons and two
neutrons. Thus Z decreases by 4 while A decreases by 2.
Z
A
X →   +
Z -4
A 2
Y
Beta decay
During beta decay a neutron splits into a proton and an electron. The proton remains in the
nucleus while the electron is ejected from the nucleus at very high speed. Thus Z remains the
same while A increases by 1.
Z
A
X → 1 +
Z
A 1
Y
Gamma decay
Alpha and beta decay results in the formation of a new energized nucleus. This energy is
released as a burst of gamma rays when the nucleons reconstitute in the nucleus. Thus gamma
decay does not result in the formation of a new nucleus.
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Nuclear Energy
Nuclear energy is the use of exothermic nuclear processes to generate useful heat and
electricity.
This includes nuclear fission and nuclear fusion. Nuclear energy is calculated with the
equation
E  mc
2
Nuclear Fission
During radioactive decay is energy is released, most of it in the form of gamma rays but some
is released in the form of neutrons. If one of these neutrons hits a large energized nucleus, the
nucleus may split into two equal parts (sometimes three) releasing energy and more neutrons.
This is called nuclear fission.
Example
Uranium 235 is bombarded with a neutron.
235
92
U n 
1
137
0
54
Xe 
96
38
Sr  n  n  n
1
1
1
0
0
0
The newly formed nuclei are called fission fragments or daughter nuclei, while the one hit
by the neutron is called the parent nuclei.
The newly released neutrons are called fission neutrons and can go on and hit other nuclei.
This would result in a chain reaction which takes place very fast and may cause an explosion
if not controlled. Boron rods are used to absorb some of the neutrons so that the rate of
reaction is
slowed down.
The diagram below illustrates a chain reaction.
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The energy released during chain reactions is harnessed in a nuclear reactor, and can be used
to produce electricity in a nuclear power station or to power submarines( and other military
ships).
Nuclear Fusion
Two or more nuclei are joined together to form a larger nucleus.
2
1
H  H  He  n
3
4
1
2
2
0
For this process to start, very high temperatures are required. Nucleus fission starts the
process. The sun provides it’s energy by nuclear fission.
Advantages of nuclear energy




Little fuel is needed to produce a lot of electricity.(Only 7 kg of uranium fuel are needed
to produce 60 000 W of electricity per month)
Does not release toxic gases into the atmosphere (no greenhouse gases released, therefore
does not cause global warming.)
It does not produce smoke particles to pollute the atmosphere.
It is reliable. It does not depend on the weather.




Disadvantages of nuclear energy.
Uranium mining exposes people to radio-active dust and radon gas
Fuel processing is strenuous and expensive
Nuclear power is not renewable. Supply of high quality uranium, one of the raw
material, will last only for a few decades.
A large amount of nuclear waste is also created and disposal of this waste is a major
problem because
 The waste is radioactive and remains active for long periods of time.
 It creates heat pollution which is harmful to the environment.
 Nuclear waste can also be used to make nuclear weapons.
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


Starting a nuclear plant requires huge capital investment and advanced technology.
There are number of restrictions on the export or import of nuclear technology, fuels
etc.
Proliferation of nuclear technology increases the risk of nuclear war too.
HALF LIFE OF RADIOACTIVE ELEMENTS
The half life of a radioactive element is the time it takes for half of the radioactive atoms in a
sample to decay.
Examples
Uranium 238
4.5 x 106 years
Uranium 235
700 x 106 years
Uranium 232
69 years
Plutonium 238
88 years
Plutonium 239
24 110 years
Carbon 14
5730 years
Carbon 15
3 seconds
Cobalt 60
5 years
Cobat 57
271 days
Radium
1600 years
Iodine
8 days
No of half lives elapsed
Fraction remaining
0
1
1
1
2
1
3
1
4
1
5
1
n
1 n
/2
/2
/4
/8
/16
/32
where n= number of half lives.
Classwork
1.
How long will it take 2g of Radium sample to decay to 0.5g.
Find the number of years that it would take Carbon 14 to decay to 1/8 of it’s original
2.
sample.
3.
If 300 atoms of radiation iodine remain after 40 days of decay, find the original
number
of the atoms given that iodine has a half life of 8 days.
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4.
A sample of thoron gas undergoes radioactive decay. If the original mass was 64g,
what
was the radioactive mass left after 208 seconds? (half life of gas is 52 seconds)
DECAY CURVE
A decay curve is an exponential graph displaying the decrease of radioactivity with time.
It could be a plot of no of atoms or mass or activity vs time
Activity or count rate – the average number of decays per second.
SI units- Bequered (Bq).
MAGNETISM
Properties of Magnets;
1. All magnets have two poles. These are the north pole ( N pole) and the south pole ( S
pole).These two poles can NOT exist independently.
2. All magnets obey the Law Of Magnetic Poles which states that “Like poles repel and
unlike poles attract”.
3. All magnets attract magnetic materials. These include iron, cobalt, nickel and alloys
like alcomax, alnico and steel.
4. A freely suspended magnet always comes to rest with its north pole pointing towards
the earth’s north pole and its south pole pointing towards the south pole.
Magnetic And Non-Magnetic Materials
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Magnetic materials are those which can be attracted by magnets while non-magnetic
materials can not.
Magnetic materials are used to make magnets because they can acquire magnetism. They can
be divided into two groups. These are Hard Magnetic materials and Soft Magnetic materials.
Hard magnetic materials are difficult to magnetise and demagnetize. They are used to make
permanent magnets. Examples include steel, alcomax alnico etc.
Soft magnetic materials are easy to magnetise and demagnetize. They are used to make
temporary magnets. Examples include iron, cobalt and nickel.
Induced magnetism
When a piece of an iron bar is brought very close to some iron filings, there is no attraction
between them.
However if a magnet is brought close to the iron bar it is seen to immediately attract the iron
filings.
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The iron bar behaves like a magnet if and only if it is still attached to a permanent magnet.
When the magnet is removed the iron fillings quickly drop away. This is because iron is a
soft magnetic material. If a steel bar is used the iron filings will stay attached to the steel bar
for a little longer after removing the permanent magnet.
Magnetisation
There are two methods of magnetisation. These are Stroking and use of Electricity.
Stroking method
The steel rod is stroked from end to end about 30-20 times in the same direction by the same
pole of the magnet.
The pole induced at the end of the rod where stroking begins is the same pole as the stroking
pole. In the diagram above end B will become the South pole. If the rod was stroked with the
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north pole then end B will become the North pole. The poles can also be identified using the
law of magnetic poles.
Electricity method
A steel rod is placed inside a solenoid (a cylindrical coil wound with 500 or more turns of
insulated wire) which is connected to a direct current(dc) supply. The switch is then closed
for a few seconds. The rod will be found to be magnetized. The polarity of the magnet is
given by the right hand grip rule [if the fingers grip the solenoid in the direction of the
current, the thumb points to the North Pole].
In the diagram above P is the _______________ pole while Q is the ______________ pole
Demagnetisation
Electrical Method
The magnet is placed inside a solenoid which is connected to an alternating current supply.
While the current is on, the magnet is slowly removed from the solenoid to some 2-3 metres
away from solenoid.
Other Methods
Magnets can also be demagnetized by heating and hammering as well as poor storage.
Magnetic Saturation
All magnetic materials are assumed to be made up of tiny magnets called magnetic domains.
When the domains are haphazardly aligned then the material does not exhibit the properties
of a magnet.
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If some of the the domains are aligned in the same direction, then the magnetic material starts
acting like a magnet. If all domains are aligned in the same direction then Magnetic
Saturation has been acquired as shown below.
Magnetic saturation is the point beyond which the strength of the magnet can NOT be
increased.
Magnetic Fields
A magnetic field is the region within which a magnet exerts its magnetic force.
Magnetic field lines
Magnetic filed lines or lines of force are used to illustrate the magnetic field around a magnet.

They begin at the N-pole and end at the S-pole

They do not cross

They are concentrated at the poles.
Field around a single magnet
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Field between unlike poles
Field between similar poles
X refers to a point where the net field is zero. This point is called the neutral point.
The magnetic field around a magnet can be detected using using a plotting campus as well as
iron filings.
Using a plotting campus
Lay a bar of magnet on a sheet of paper. Place a plotting compass at a point near one of the
poles of the magnet.
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Mark the position pointed by the arrow of the ploting compass. Move the compass so that the
beginning of the arrow is exactly over the position you marked. Mark the new position
pointed by the compass arrow. Continue the process until the south pole of the magnet is
reached .Join the dots to give one line of force and show the direction of the field or force by
putting arrows on it.
Iron filling method
A plain paper is placed above a magnet and iron fillings are sprinkled on top of the paper.
The iron fillings should form a pattern of the field lines of force.
Electromagnets
An electromagnet is a temporary magnet and its magnetism can be switched on and off. It
consists of an insulated wire wound around a soft magnetic material. This is then connected
to a direct current supply.
The strength of the electromagnet can be increased by either

increasing the current in the coil

increasing the number of turns in the coil

bringing the poles closer to each other.
Electromagnets are used for;

Lifting scrap metal

Tape recording

Relay /reed switch

Electric bell
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Magnetic shielding /screening
When a short iron bar is placed in a magnet field, the field appears to be drawn towards the
bar and concentrated through it. The magnetic field passes through the bar but around it since
iron is a soft magnetic material. If an iron ring is placed in a magnetic field, the field does not
pass inside the ring,
Thus iron rings/boxes iron boxes can be used to protect equipment that can be affected by
magnetic fields. This is known as magnetic shielding/screening.
ELECTROSTATICS [Static Electricity].
Static electricity refers to charge that is not moving i.e. stationary charge.
An insulator can be charged electrically by rubbing it while a conductor cannot.
Types Of Charge



There are two types of charge. These are Positive [+] and Negative [-].
The SI unit of charge is the Coulomb (C)
Negative charge is acquired if excess electrons are gained and positive charge is
gained if electrons are lost.
NB: Positive charge arises as a result of a deficiency of electrons.

All charges obey The Law Of Electric Charges which states that “like charges repel
and unlike charges attract”
Electric charges can exist independent of each other.

Electrostatic Charging
Methods of electrostatic charging include
(i)
(ii)
Charging through contact
Charging through induction
Charging Through Contact
When a polythene rod is rubbed with a cloth it becomes negatively charged. Electrons flow
from the piece of cloth into the polythene rod. As a result the cloth attains a positive charge.
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On the other hand an acetate rod becomes positively charged when rubbed with a piece of
cloth. Electrons flow out of the acetate rod into the cloth which then becomes negatively
charged.
The rods and cloths described above became charge through contact.
Charging through induction
Charging through induction can be achieved in two ways- by earthing as well as through
separation of charges.
Charging through separation of charge.
This can be illustrated by placing two metal spheres A and B next to each other so that they
are in contact.
A charged strip is then brought close to the metal spheres, but not touching them.
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This causes a separation of charges in the two spheres. All negative charges are attracted
from sphere A to B.
On being separated, the two spheres are found to be ;
A- Positively charged
B- Negatively charged
Charging through earthing
A charged strip is brought close to a neutrally charged metal sphere. See (a) below.
This causes a separation of charge within the sphere itself. See (b) below.
Earthing the sphere causes the negative charge to be repelled by the strip to the ground. See
(c) above.
This leaves the sphere with a net positive charge. See (d )above.
Detecting Charge
Charge can be detected through the use of a Gold Leaf Electroscope.
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When a charged object is brought close to the metal cap, the gold leaf deflects upwards. This
happens because both the stem and the leaf have the same charge and as such repel each
other.
To find out the nature of the charge on the object; the electroscope has to be charged first.i.e
only a charged electroscope can be used to detect the type of charge in an object.
Discharging
Discharging refers to the loss of excess charge.
It takes place through contact or ionization. Dangers of ionization are minimized by earthing.
Lightning Conductor
As clouds move overhead they gain a negative charge. When excess charge has been
accumulated in the cloud it is discharged to the ground through ionization. This is called
lightning. Lightning is dangerous and it’s effects can be minimized through the use of a
Lightning Conductor. A lightning conductor discharges a cloud before it discharges on its
own.
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The lightning conductor should be made from a good conductor of electricity and it should be
taller than the structure it is protecting. When clouds move through the sky they acquire a
negative charge. As they pass above the lightning conductor they induce a positive charge in
the spikes at the tip of the lightning conductor.
Since charge accumulates at sharp points, the positive charge at the tip of the spikes is large
enough to ionize the air molecules around them by attracting electrons from them. These
electrons are repelled down the lightning conductor to the ground.. The resulting positive ions
are attracted by the negatively charged cloud.
Thus an electric wind of positively charged particles moves from the spikes to the cloud
where they neutralize its negative charged.
Electric Fields
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The electric field is a region in which a charged particle exerts its electric force. Electric
fields are illustrated with the help of electric field lines which begin at the positive charge and
end at the negative charge.
Field around single charges.
positive charge
negative charge
Field between simmilar charges.
Field between 2 unlike charges.
Field between 2 positively charged plates.
ELECTRICITY
Electric Current, I
Current is the rate of flow of electric charge. Conventional current flows from positive to
negative but the flow of electric charges is from negative to positive.
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current 
I
charge
time
where
Q
t
I = current
Q = charge
t = time
The SI units of current are Amperes(A) or Coulomb per second (C/s).
Current is measured with an ammeter. The circuit symbol for an ammeter is
ammeter is always connected in series with other circuit components.
. An
Potential Difference (pd) or Voltage,V
This refers to the electrical energy needed to drive a charge between two points in a circuit.
voltage 
electricalenergy
charge
V
E
Q
Where V = voltage
E = electrical energy
Q = charge
The SI units of voltage are Volts(V) or Joules per Coulomb (J/C).
NB: One volt is the energy needed to drive a coulomb of charge around a circuit.
Voltage is measured with a voltmeter. The circuit symbol for voltmeter is
voltmeter is always connected in parallel with other circuit components.
. A
Electromotive force(emf)
This is the electrical energy required to drive a charge round a circuit by a power supply. A
voltmeter is connected across the power supply in order to measure the emf.
Resistance, R
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Resistance is the opposition to flow of current. SI units of resistance are Ohms (Ω). An
ohmmeter can be used to measure resistance.
Resistivity
The resistance of a conductor is

indirectly proportional to the cross sectional area(A) of the conductor . R α

directly proportional to the length (l) of the conductor. R  l
1
A
Combining the two

R α
l
A
R  ρ
l
A
Where
R = Resistanceof the conductor
l = length of the conductor
 = resistivity of the conductor
A = cross-sectional area of the conductor.
Resistivity of any material is constant.
For example the resistivity of copper is 1.8 x 10-8 m and nichrome (an alloy) has a
resistivity of 110 x 10-8 m.
Ohm’s Law
The current (I) through a conductor is directly proportional to the voltage (V) across the
conductor, provided temperature and other conditions remain constant.
V = IR
Where V = voltage
I = current
R = resistance.
V/I Characteristic Graphs
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Ohmic Conductor
Filament bulb
Thermistor
Electrical Energy
I
Q
t

Q = It ……………………………..(i)
V
E
…………………………..(ii)
Q
Using eqn (i) in eqn (ii)
V
E
It
Rearranging the eqn
E  IVt
Where E = electrical energy
I = electrical current
V = voltage
t = time
Electrical Power, P
Power 
Energy
time
but
PHYSICS NOTES: Physical Quantities & Measurement
Energy  IVt

P
IVt
t
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P  IV
Where P = electrical power
I = electrical current
V = voltage
Series Circuits
In a series circuit there is only one pathway for current.
Current in Series circuits
The current is the same at all points in a series circuit
A1 = A2 = A3 and therefore
I1 = I2 = I3
Voltage in a Series Circuit.
In a series circuit there is a potential drop across the circuit components. Thus the sum of the
voltages across the circuit components should give the emf.
VT = V1 + V2 + …
Resistance in a series circuit.
The total resistance, RT for resistors R1, R2, R3,etc which are in series is given by
RT = R1 + R2 + R3 + …
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Parallel Circuits
This is a circuit in which there is more than one pathway for current.
Current in parallel circuits
Current divides among the several pathways in a parallel circuit.
AT = A1 + A2
IT = I1 + I2 + …
Voltage in parallel circuits
The voltages across parallel circuit components are equal.
VT = V1 = V2
Resistance in parallel circuits
The total resistance, RT for resistors R1, R2, R3, etc which are parallel is given by
1
1
1
1



 ...
RT R1 R2 R3
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PRACTICAL ELECTRIC
CIRCUITRY
USES OF ELECTRICITY
Electricity is used in
 Lighting
 Machines
 Security
 Communication
 Heating
COST OF ELECTRICITY
Cost of electricity = cost per unit X no of units
No of units = time in hours X power in kilowatts. [ 1 unit is equal to 1 kilowatt-hour.(kWh)]
Example.
If BPC sells electricity at P0.55 per unit, calculate the cost of using two 100 W bulbs for ten
hours.
No of units
Cost
= 2 x 100W x 10 hrs
= 2 x 0.1 kW x 10 hrs
= 2 kWh
= 20 kWh x P0.55
= P1.10
DANGERS OF ELECTRICITY
(a)
(b)
(c)
(d)
Damaged Insulation
An electric shock can occur if a current flows from the electric circuit through a
person’s body to the Earth. This can happen when someone touches the exposed part
of the wire carrying current (live wire).
Overheating Of Cables
When current increases through a conductor, the amount of heat energy lost due to the
resistance of the wire increases. This can lead to explosion, fire or the cables
overheating.
Damp Conditions
Water can conduct electricity. When the body is wet, the resistance of the body
decreases hence more current can flow through the body. One can get a shock if s/he
operates an appliance with wet hands since water can conduct electricity.
Overloading A Socket
When a socket is overloaded with many appliances, the current from the mains
increases which will lead to increased heat produced by cables. This can cause the
insulating material to melt or cause an explosion or fire.
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SAFE USE OF ELECTRICITY
Fuses
This is a safety device made from tin coated-copper wire. It has a low melting point such that
it melts and breaks the circuit when current through it exceeds a certain value called the fuse
rating. This could be due to short circuits or overheating of cables. A fuse ensures that the
current carrying capacity of the wire is not exceeded.
To calculate the fuse rating one has to know the power rating of the device. For example, a
3kW 240V electric fire needs a current of about
Therefore a 13A fuse is recommended.
Fuses and switches are always connected to the live wire so as to isolate the appliance from
the current source when the appliance is not in use or in case of a short circuit.
Earthing
Appliances that are made of metal on the outer case must be earthed as a safety precaution.
This connects the body of the appliance to the ground. When the device is faulty or the ‘live’
wire breaks and touches the metal case, the earth wire will channel the charge to the ground
to prevent any electric shocks.
Double Insulation
Appliances that are made from non-metal outer case are usually double-insulated using a
tough, stiff non-conducting material. This prevents electric current to flow to the user in case
there is a fault. Devices that are double insulated carry the sign below.
3 Pin Mains Plug
Earth wire (green or/and yellow). This is connected to the earth pin.
Live wire (brown). This is connected to the live pin. It carries live current to the circuit.
Neutral wire (blue). This is connected to the neutral pin. It is earthed at the power station.
RING MAIN CIRCUIT
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ELECTROMAGNETIC
EFFECTS
ELECTROMAGNETIC INDUCTION
A change in the magnetic field around a conductor induces an emf in the conductor. The
magnetic field around a conductor can change in several ways including moving the
conductor into and out of a magnetic field or moving a permanent magnet around a
conductor.
In the diagram below a conductor is being moved in a magnetic field.
An emf will only be induced in the conductor if it cuts the magnetic field, i.e. if the conductor
is moving perpendicular to the field as shown by the arrows in the diagram above. No emf
will be induced if the wire moves parallel to the magnetic field or if the conductor is not
moving (stationary).
The direction of induced current is found by using Fleming’s right hand rule. The thumb
represents the motion of wire, the first finger represents the direction of the magnetic field
and second finger represents the direction of the induced current.
NB. All three fingers should be perpendicular to each other.
In the diagram above when the conductor is moved upwards the current flows from ___ to
___ and when it is moved downwards the current flows from ___ to ___.
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If the conductor is coiled, then the direction of the induced emf is given by Lenz’s law which
states that the direction of induced current is such that it opposes the change causing it.
In the diagram above the north pole of the magnet is being moved away from end Q of the
solenoid. According to Lenz’s law this will induce a south pole on end Q of the solenoid.
The outward motion of the magnet will then be opposed since unlike poles attract. The
direction of current in the coil can then be determined using the Right Hand Grip Rule. The
current moves from ___ to ___.
In the diagram above the north pole of the magnet is being moved into end Q of the solenoid.
According to Lenz’s law this will induce a north pole on end Q of the solenoid. The inward
motion of the magnet will then be opposed since like poles repel. The direction of current in
the coil can then be determined using the Right Hand Grip Rule. The current moves from
___ to ___.
Factors that affect the size of the induced current are,
1. Speed of movement of the wire.
2. Strength of the magnet.
3. Number of times the conductor has been wound.
Simple Alternating Current Generator
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A simple a.c. generator comprises a rectangular coil, slip rings, carbon brushes and a
permanent magnet. When the coil is rotated within the magnetic field, an emf is induced as
the coil cuts the magnetic field lines. Thus maximum emf is induced when the coil is parallel
to the field and zero emf is induced when the coil is perpendicular to the magnetic field. The
induced current reverses direction after every half cycle to create an alternating current.
The output voltage is illustrated below
Transformers
A transformer is used to step down or step up voltage. It operates on the principle of mutual
induction which states that a change in the magnetic field of a coil induces an emf in a
neighbouring coil. The emf is induced because the magnetic fields cut the conductor in the
secondary coil. The induced emf is enhanced by putting the coils on a soft iron core so as to
increase magnetic field.
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The diagram below shows two coils A and B which are placed next to each other. Coil A is
connected to a d.c. power supply while Coil B is connected to a centre zero galvanometer.
When switch S is closed the pointer deflects in one direction and goes back to rest position.
When the switch is opened the pointer is deflected in the opposite direction and goes back to
rest position. When the switch is left closed or opened there is no deflection of the pointer.
Coil A is the primary coil and Coil B is the secondary coil. The voltage in the primary coil is
the primary voltage (Vp) and the voltage in the secondary coil is called the secondary voltage
(Vs).
Step-down Transformer (Vp > Vs)
A step down transformer has more turns in the primary coil than in the secondary coil. (N p >
Ns).
Step-up Transformer (Vs > Vp)
A step up transformer has more turns in the secondary coil than in the primary coil. (Np < Ns).
Transformer equation
The voltages in the secondary and primary coils of a transformer are related through the
expression
secondary voltage
primary voltage

secondary turns
primary turns
Vp
Vs

Ns
Np
Energy loss in a transformer
According to the principle of energy conservation the energy input into a transformer should
be equal to the energy output from the transformer.
Thus the power in the primary coil should be equal to the power in the secondary coil, i.e.
IpVp = IsVs
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However transformers are not 100 % efficient, that is the some of the input energy is not
converted to useful energy but is lost due to several factors including;
i
ii
iii
resistance of the windings. Resistance of a conductor increases with its length
and due to the length of the conductor in the coil some energy is lost as heat.
eddy currents. This are currents which are induced in the soft iron core of the
transformer itself and they cause energy loss due to heat. The soft iron core in
transformers is laminated to try and reduce eddy currents.
leakage of field lines. Not all the field lines from the primary coil cuts the
secondary coil, and as such cause energy loss from the transformer.
Transmission of electrical power
Power stations generate electricity at more than 10 000V. This is then stepped up to more
than 200 000V before it can be transmitted over long distances. When it gets to a town or
village, the voltage is stepped down to a suitable voltage at a substation. This is done to
reduce the amount of energy lost due to the length of the transmission lines.
Magnetic Effects of Current
Magnetic Field around a Current Carrying Conductor
A current carrying conductor has a magnetic field around it. The direction of the field can be
shown with the help of the Right Hand Grip rule [Thumb points in direction of current while
the fingers indicate the direction of the field around the conductor].
The strength of the field can be increased by coiling the conductor. A coiled conductor is
called a solenoid. The strength of the magnetic field around a solenoid can be increased by
1. Increasing the number of turns
2. increasing the current
3. inserting a soft magnetic material into the coil to form an electromagnet.
Magnetic field around single current carrying conductors.
Magnetic field around parallel conductors carrying current in same direction
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Conductors carrying current in opposite directions attract each other. The region labelled X
represents the neutral point. At this point the net field is ZERO because the two magnetic
fields cancel each other out.
Magnetic field around parallel conductors carrying current opposite directions
Parallel conductors carrying current in opposite directions repel each other. This is because
the field between the two conductors add up.
The Motor Effect
Current carrying conductor in a magnetic field.
A current carrying conductor experiences a force in a magnetic field. The direction of the
force can be determined with the help of Fleming’s left hand rule;
First finger – direction of field
Second finger – direction of current
Thumb – direction of the motion.
In the diagram below the conductor will move as indicated. The fields above the conductor
add up while the fields beneath the conductor cancel each other out. Consequently there is a
resultant motion of the conductor towards the side where the field is weaker.
In the diagram below the conductor will move as indicated. The fields above the conductor
cancel out each other up while the fields beneath the conductor add up. Consequently there is
a resultant motion of the conductor towards the side where the field is weaker.
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Reversing the field or the current also causes the direction of motion to change.
Simple DC Motor
A simple DC motor consists of a rectangular coil abcd as shown above. The coil is mounted
on an axle between the poles of a magnet. When current passes through the coil it
experiences a turning effect about the axle. The direction of rotation can be determined using
Fleming’s Left Hand rule.
The turning effect of the coil can be increased by
1. increasing the number of turns in the coil
2. increasing the current
3. Inserting a soft magnetic material in the coil.
In the diagram above the split-ring commutator ensures that the side of the coil that is next to
the North Pole is always in contact with the positive brush, while the side of the coil next to
the South Pole is always connected to the negative brush. This ensures that rotation is always
in the same direction.
Practical electric motors are used to provide kinetic energy for different purposes including
domestic and industrial. Such motors are different from the simple dc motors in that
 the magnetic field in which the coil spins is provided by an electromagnets instead of
a permanent magnet.
 Several coils are used in one motor
 The coils have multiple turns
 They use alternating current.
Moving Coil Loudspeakers.
It consists of coil which is attached to a paper cone. The coil is inserted in a pot magnet.
Varying currents from an amplifier pass through the coil, which causes a force to act on the
coil. The direction of this force can be determined using Fleming’s Left Hand Rule.
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Since the current to the speaker is alternating the coil experiences a to and fro movement
within the pot. This causes the vibrations in the paper cone thus producing sound.
Microphones
A microphone works like a loudspeaker in reverse. Thus it operates like a simple ac
generator. The paper cone picks up sound waves from the air which cause the paper cone to
vibrate and as such causes the coil to move in and out of the pot magnet. This results in a
small alternating current to be induced in the coil.
THERMIONIC EMISSION
Cathode Rays
When certain metal filaments are heated, electrons on their surface may gain enough thermal
energy to escape. This release of high speed electrons from the surface of a hot filament is
known as thermionic emission.
Beams of electrons released during thermionic emission are called cathode rays.
Properties of cathode rays
 They have a negative charge
 They travel at very high speeds
 They are deflected towards the positive plate in an electric field.

They are deflected according to Fleming’s left hand rule in a magnetic field.(flow of
convetional current is opposite to direction of cathode rays)
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Cathode Ray Oscilloscope
Basic structure
The cathode ray oscilloscope consists of three parts. These are the electron gun, the deflection
system and the screen. The electron gun consists of the anode and the cathode. The deflection
system consists of the X-plates and the Y-plates.
Part
Electron gun
Heater/fillament
Cathode
PHYSICS NOTES: Physical Quantities & Measurement
Function
Heats the cathode.
Emits electrons when hot
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Anode
Deflection system
Y-plates
X-plates
Fluorescent screen
Accelerates and focuses electron
beam
Deflects
beam
of
electrons
vertically
Deflects
beam
of
electrons
horizontally
Displays the pattern of movement
of the beam.
Function
The cathode ray oscilloscope can be used among other things to
 measure potential difference.

measure short time periods.

display waveforms of alternating potential difference.
Input voltage is applied across the Y plates.
INTRODUCTORY ELECTRONICS
Circuit Components
Colour coded resistors
Resistors are used in electrical circuits to control the amount of current flowing through the
circuit.
First Band – 1st digit of the resistance
Second band – 2nd digit of the resistance
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Third band – no of zeros.
Fourth band – tolerance.
Diode
A diode is a circuit component which allows current to pass in one direction only.
Circuit symbol
PROPERTIES OF WAVES
Definition Of Terms
Wave
A wave is a disturbance in a medium which carries energy.
Wave front
It can be the position of the crests of a wave shown by straight lines. A wave front is always
perpendicular to the direction of the wave. Think of a wave front as the crest of a transverse
wave or the compression of a longitudinal wave.
Fig 1.10 Wave fronts
When a stone is dropped in a pond, at the point where the stone hits the water surface,
circular ripples are formed which expand outwards. These are water waves travelling in a
circular wave front. If you’ve watch an object floating on the water after it has being
disturbed, you will notice that the object moves up and down in its original position.
.
Displacement-Displacement Graph
This graph can be used to show wavelength and amplitude.
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Fig. 3.10. A dispacement-displacement graph
Wavelength (λ)It is the distance between two (2) similar but successive points on a wave.
It is denoted by the Greek letter lambda (λ) and it is measured in metres (m
From Fig. 3.10, A and C are similar and successive, therefore the distance
between A and C can be the wavelength of the wave or the distance between B
and D.
Amplitude: It is the maximum displacement of a vibrating particle from the undisturbed or
rest position. From Fig. 3.10. a, is the amplitude of the wave.
Displacement-Time Graph
This graph can be used to show period and amplitude.
Fig. 3.20. A dispacement-time graph.
Period (T):
The time taken make a complete wave is called the PERIOD (T).From Fig.
3.20 P and R are similar and as such PR is gives us the period of the wave.
The same applies to QS.
Other Terms.
Frequency (f) It is the number of complete waves made in a given period of time. Also
frequency can be the number of waves passing a point in a given period of
time. It is measured in HERTZ (Hz).
Frequency =
number of waves/vib rations/oscillations
total time taken
Frequency is the inverse of period such that
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T=
1
f
and
f =
1
T
Wave Speed ( ): It is the displacement of a wave per unit time. It is measured in metres per
second (m/s).
The Wave Equation
The relationship between the speed, wavelength and the frequency of a wave is given by the
equation
Wave speed = wavelength x frequency
=λf
Types of Waves
Transverse Waves
These are the waves produced when particle displacement is perpendicular to the direction of
the wave. Fig. 2.1 shows the particle displacement in relation to the wave motion.
Fig. 2.10. Particle displacement in a transverse wave.
They are characterized by crests and troughs. Examples include: Water waves, EM waves
and secondary seismic waves.
Longitudinal waves
These are the waves produced when particle displacement is parallel to the direction of the
wave. Fig. 2.21 shows the particle displacement as a longitudinal wave passes through
matter.
Fig. 2.21. Particle displacement in a longitudinal wave.
They are characterized by compressions and rarefactions as shown below
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Examples include: Sound waves, shock waves from explosions and primary seismic waves.
Classwork
1.
The waves below are traveling across water.
2.
Calculate
i.
Wavelength of the waves.
ii.
Period of the waves
iii.
Frequency of the waves.
iv.
Wave speed
The lines in the diagram below are crests of straight water waves
i
ii.
What is the wavelength of the wave?
If wave A occupied 5 seconds ago the position now occupied by wave F,
what is
3.
the frequency of the wave?
iii.
What is the speed of the wave?
A set of waves has a period of 10 seconds. If their speed is 2 m/s calculate their
wavelength.
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Reflection, Refraction and Diffraction of Waves
Waves can undergo reflection (bounce back), refraction (bend) and diffraction (spreading
out). Water waves traveling from deeper water to shallow water will undergo a change in
speed and the wavelength while the frequency remains the same. The speed and the
wavelength decreases. This is due to refraction.
Reflection of waves
Refraction of waves
Water waves traveling over a straight wave front spread out when they pass through an
opening. Water waves passing over a narrow opening behaves as if they are produced by a
point source (that is they become circular). This phenomenon is called DIFFRACTION.
Diffraction of waves
PHYSICS NOTES: Physical Quantities & Measurement
Diffraction of sea waves as they pass into a
harbour.
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Classwork
4.
In the diagram below light waves are incident on an air-glass boundary. Some are
reflected and some are refracted in the glass.
(i)
(ii)
Which of the following is not the same for the incident and refracted waves?
frequency, wavelength, direction, speed, brightness
Complete the diagram above to illustrare the refracted and reflected waves.
Electromagnetic Waves
These are waves which make up the electromagnetic spectrum. The waves in the spectrum
are continuous.
Components Of The Electromagnetic Spectrum
The electromagnetic spectrum has seven components
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Fig. 1.0 The electromagnetic spectrum
The components of the spectrum arranged in order of increasing wavelength are
1.
2.
3.
4.
5.
6.
7.
Gamma rays
X-rays
Ultra-violet
Light
Infra-red
Microwaves
Radio waves
Properties of Electromagnetic Waves









They carry energy from one place to another and can be absorbed by matter to cause
heating and other effects.
Waves with shorter wavelength have high frequency and carry the greatest energy.
They are transverse in nature
They can travel in a vacuum.
They travel at a speed of 3.0 x 108 m/s in vacuum. This is usually called the speed of
light although it is the speed of all EM waves.
The waves are a combination of travelling electric and magnetic fields which are
perpendicular to one another.
They obey the wave equation [v = λf] such that C = λf where C is the speed of EM
waves and is a constant (3.0 x 108 m/s).
They are transverse in nature
They can be reflected, refracted and diffracted.
Sources, Methods of detection and Uses of EM waves.
wave
Gamma
Rays
Sources
 Emitted
by
radioactive
materials.
 Cosmic rays
 Nuclear
reactions
PHYSICS NOTES: Physical Quantities & Measurement
Detection
 Photographic film
 Geiger
Muller
tube.
Uses






Radiotherapy to treat cancer.
Chemotherapy to treat cancer
Sterilizing food and medical eq
Checking for flaws in metal cas
Gamma photography
As a tracer in plants to stu
minerals.
 In metal factories to control
metal bars.
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X-Rays
 X-ray tubes
 Cosmic rays
 Photographic film
 Geiger
Muller
tube.




UltraViolet
(UV)




 Photographic film
 Fluorescent
materials
(they
glow
when
exposed to UV
radiation).




Cosmic rays,
UV lamps
Mercury Lamps
Electric arc used
in welding
X-ray photography
Radiography
Radiotherapy to kill cancer tiss
Used in security check poin
mines.
 Detection of cracks in metal we
 Astronomy
 Diffraction to find crystal struc

Visible
Light
 Luminous and
non-luminous
objects.
 Eye
 Photographic film
 Light Dependant
Resistor
 Chloroplasts
 Solar cells
InfraRed
(IR)
 All
matter
especially hot
objects.
 Photographic film
 Thermometer
with blackened
bulb.
 Thermistor
 Skin
















Microwaves
 Microwaves
ovens
 Microwave
transmitters
 Cosmic rays
PHYSICS NOTES: Physical Quantities & Measurement
 Photographic film
 Microwave
receivers









Used to check for counterfeit m
Used to detect forged art.
Used to get a sun –tan.
Fluorescent dyes are added
detergents. When exposed to
the sun or disco lights our teet
brightly.
Leads to production of vitami
by the skin in small quantities.
Used to sterilize food
Automatic counting in industry
Astronomy
Used in optical instruments.
In photography.
Sight
Photosynthesis
Spectral analysis
Information transmission
To make LASERS
Astronomy
Used in IR heaters/cookers/gril
Infrared photography.
In remote control units for T
systems, Air-Cons,
Burglar alarms use sensors
radiation emitted by an intrude
used in motion sensors to autom
security lamps.
IR imagers are used to locate p
at night or in thick smoke o
rubble.
Drying paint on new cars.
Astronomy
Mobile telephone communicati
Digital Television broadcasts
RADAR to locate position of s
as well as determine the speed
Cooking with microwave oven
Killing insects in granaries.
Microwave photography
Astronomy
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Radio waves
 Cosmic rays
 Radio
transmitters
 Radio receivers
 Radio and TV broadcasts
 Astronomy
 Two way radio communication
Side Effects of Electromagnetic Waves
Gamma Rays
 Can cause gene mutation
 Can cause cancer and leukemia
 Can cause cataracts
 Can cause sterility
 Can cause severe radiation burns
 Can cause miscarriage or damage to the foetus
X-Rays
 Can cause cancer
 Can cause miscarriage or damage to the foetus
 Can cause radiation burns
 Can cause sterility
Ultra-Violet Radiation


Can cause skin cancer
Can kill retinal cells resulting in blindness.
Visible light

Over exposure can cause fatigue of the cilliary muscles.
Infra-Red Radiation


Can burn the skin or matter
Can cause sunburn.
Microwaves

Have a heating effect which can cause burns.
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SOUND WAVES
Sound waves are produced by vibrating sources. They are longitudinal waves in nature and as
such need a medium in order to be transmitted from one place to another.
Bell-jar experiment
The bell-jar experiment can be used to show if this is possible. An electric bell is suspended
with rubber bands inside a bell jar. The rubber bands reduce sound transmission by the wires
so that sound is only transmitted through the glass.
When the circuit is complete the bell rings. A vacuum pump is then used to remove the air
from the bell jar.
The sound heard decreases as the air is pumped from the bell-jar even though the hammer is
still seen striking the gong. Eventually no sound is heard even though the hammer is still
striking the gong. This happens when all the air has been removed from the bell jar which
shows that sound needs a medium for its propagation.
Relative order of the speed of sound in gases, liquids and solids.
Sound travels fastest in solids, followed by liquids then gases. This is because the particles of
matter are far apart in gases but closely packed in solids.
Material
Iron
steel
Water
PHYSICS NOTES: Physical Quantities & Measurement
Speed (m/s)
5000
4500
1500
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Air(mixture of gases)
Hydrogen
Carbon dioxide
330
1350
280
Reflection of Sound
Reflected sound is called an echo. Multiple reflection of sound may produce an effect called
reverberation. It occurs when too many echoes mix up to produce a dull unclear sound.
Diffraction of Sound Waves
You can hear around corners even if you cant see the speaker. This is because the waves can
bend (diffract) around corners.
Audible Frequency
Audible frequency refers to the range of frequencies which can be heard by an organism.
Each animal species has its own audible frequency. Examples are shown below.
Animal
Human Beings
Dogs
Bats
Dolphins
Elephants
Audible Frequency
20 Hz – 20 kHz
20 kHz – 100 kHz
20 Hz – 200 kHz
20 Hz – 200 KHz
5 Hz – 100 kHz
Ultrasonic Sound (Ultrasound or sonar)
This refers to sound which has a frequency which is above the audible frequency for a
particular organism.For human beings any sound above 20 kHz is ultrasound. This means
that we can not hear sound which is above 20 kHz even though it can be heard by other
animals or detected electronically.
Ultrasound waves can be concentrated to form a narrow beam which has many uses.
They can be used
1.
To study the development of a foetus inside its mother or determining the sex of an
unborn baby without operation.
2.
To clean jewellery and equipment. The equipment/jewellery is placed in a bath of a
3.
special liquid. The ultrasound will shake the dirt off the equipment/jewellery. This is
the technique that is used to clean clothes.
By dentist to clean tartar coating from your teeth, helping you prevent gum disease.
4.
By ships to measure the depth of the sea using expression
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s
2d
.
t
Where s = speed of sound waves
d = depth of ocean
t = time taken by wave to travel distance
2d.
2d = distance travelled by wave
In order to measure the sea depth, ultra sound beams are sent from the ship to the sea
bottom or floor. The time taken for the wave to move from the ship to the sea bottom
and back to the ship is then measured. This time is then used along with the speed of
sound in water to calculate the sea depth.
Example: The ultra sound wave above took 4 seconds to travel to sea floor and back
to ship. If the speed of sound in sea water is 1500 m/s calculate depth, d.
2d
Solution:
s
t
st
d
2
1500 x 4
d
2
d = 3000 metres.
This method is known as echo sounding and can also be used to calculate the
distance between large buildings/structures.
5.
Used for navigation by submarines to locate other submarines.
6.
To locate shoal of fish as shown below in the diagram.
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Noise Pollution
Unpleasant sounds are called noise. An area that has a high degree of noise is said to be
polluted by noise. These situations can be in a densely populated town or part of the town,
airports, studios, road traffic etc. Noise can damage ears, cause tiredness and make someone
lose concentration.
There are ways in which unwanted noise can be reduced. By building quieter engines or
building airports far away from the residential area. In cars exhaust systems can be fitted with
silencers.
At home sound absorbing materials such as curtains, carpets, windows can be used. The
further the noise is, the weaker it is. People who are exposed to high level of noise can wear
ear protectors.
Classwork
1.
A man standing between two hills claps his hand. He receives the first echo after 2.25s. The
speed of sound in air is 330 m/s.
(a)
find the distance between the man and the nearer hill.
(b)
Calculate the time taken by the second echo to reach the man if the distance between
the man and the further hill is 512 m.
2.
A man fires a gun and hears the echo from a cliff after 4 seconds. How far away is
the cliff? (Speed of sound = 340 m/s)
A sonar pulse sent out by a boat arrives back after 3 seconds. If the speed of sound in
water 1500 m/s, how deep is the water?
3
Characteristics of Sound
The notes from a musical instrument can vary in three ways:
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
Pitch

Loudness

Quality
Frequency and Pitch
Pitch of a sound note depends on its frequency. The higher the frequency, the higher the pitch and
the lower the frequency, the lower the pitch.
A high-pitched note has a high frequency but a short wavelength.
Loudness and Amplitude
Loudness of a sound depends on the amplitude of the wave. The larger the amplitude the
louder the sound note.
Quality of a sound note.
The same note on different instrument sounds different even if the frequency is the same. We
say they differ in quality (Timbre). This difference is brought by the fact that no instrument
other than a tuning fork or a signal generator can produce a note of one frequency (a pure
note).
Notes of the same frequency (pitch) but different quality.
Acoustics
When a band is playing in a hall, the sound the audience hears depends partly on how the hall
itself affects the sound waves. That is the acoustics of the hall. A large empty hall, with hard
walls, floors, and ceiling usually sounds ‘echoey’. Sound waves are reflected from the
surfaces and mixes with the original sound making the sound to be unheard and dull. This
may take several seconds before the sound can die away. This effect is called reverberation.
In a hall, some materials such as carpets, curtains and even the audience reduce reverberation
by absorbing the sound. Some halls have specially designed sound absorbers suspended in
ceilings.
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LIGHT
REFLECTION OF LIGHT
Reflection is the bouncing back of light when it falls on an object.
When light falls on an object like a book, it bounces in all directions because the surface is a
bit rough. This is called Diffuse or Irregular Reflection.
When the surface is very smooth, like polished metal surface, light bounces in a regular
manner. This is called Regular Reflection.
Reflection of light at different surfaces
Laws of Reflection

The angle of incidence, i and the angle reflection, r are equal.

The incident ray, reflected ray and the normal all, lie in the same plane.
Plane Reflecting Surfaces
Properties of images formed by plane mirrors
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
The image and the object are equidistant from the mirror.

The image is the same size as the object.

The image is virtual,

The image is laterally inverted

The image is upright/erect
Experiment to determine the position of the image formed by a plane mirror.
Apparatus:
 Pin board

8 pins

A4 plain paper

Plane mirror
Procedure:
1. Attach the plain paper to the pin board with 4 pins.
2. Draw a line at the centre of the plane mirror and label it MM’.
3. Place a mirror vertically along the line MM’.
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4. Stick a pin O in front of the plane mirror. This is the object pin.
5. With the eye in a suitable position, place two pins in front of the mirror such that
they are in line with image I of the object O seen in the mirror [These pins should
be place as far apart as possible to improve accuracy]. Mark the positions of the
pins P and Q and draw a straight line PQ through their positions.
6. Repeat steps 4 and 5 for pins R and S and line RS.
7. Remove the mirror and pins from the pin board. Extend lines PQ and RS beyond
MM’ until they intersect.
8. The image is formed at the intersection of PQ and RS.
Uses of Plane Mirrors.
1. Cosmetic purposes
2. Periscopes
3. Rear view mirrors in vehicles.
4. Decorations
Curved Reflecting Surfaces
Curved mirrors are of two types: concave mirror and convex mirror.
A concave mirror makes a parallel beam of light to converge at a point called the principal
focus of the mirror. Image formed depends on the position of the object.
A convex mirror makes a parallel beam of light to diverge (spread out) and appear to come
from the principal focus of the mirror. Image formed by convex mirror is smaller and upright.
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Uses of Convex Mirrors
 Convex mirrors can be used to give a wide field of view, such as a car driving side
mirrors or a shop security mirror.
Uses of Concave Mirrors
 Concave mirrors can be used to collect light energy, sound, heat radiation, radar and
TV signals.

Concave mirrors can produce a magnified image if the object is too close.
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REFRACTION OF LIGHT
Refraction of light is the bending of light as it travels from one medium to another.
[N.B. Even though the light bends it always travels in a straight line.] ,
When a light ray travels from an optically less dense medium to an optically denser medium,
the rays are bent or refracted towards the normal ( i > r ).
i is the angle of incidence and r is the angle of refraction.
When a light ray travels from an optically denser medium to an optically less dense medium,
the rays are bent or refracted away from the normal ( i < r ).
i is the angle of incidence and r is the angle of refraction.
If the light ray passes through a glass block which has parallel sides, the emerging ray will
be parallel to the ray entering the glass block as seen in diagram below.
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Refractive Index (n).
Light travels at different speeds in different materials. When light moves from one medium to
another its speed changes and this causes it to change direction (refract) at the boundary of
the mediums.
The ratio of the speed of light in a vacuum to the ratio of the speed of light in a given material
is called refractive index (n).
Refractive Index (n) =
Example 1:
speed of light in air
speed of light in a given material
Speed of light in air is 3.0 x 108 m/s and in glass speed of light is 2.0 x 108 m/s
Thus refractive index of glass =
3.0 x 10 8
2.0 x 10 8
= 1.5.
Snell’s Law
Refractive index can be calculated using the angle of incidence i and the angle of refraction r.
The refractive index is given by
sin i
n
sin r
This relationship is known as Snell’s Law.
Example 2: The refractive index of glass is 1.52. If the light ray is incident at an angle of
35º, what will be the angle of refraction?
Solution
n
sin r 
sin i
sin r

0.574
1.52
r = Sin-1(0.3774)
PHYSICS NOTES: Physical Quantities & Measurement
1.52 

sin 350
sin r
sin r = 0.3774

r = 22.2º
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Real and Apparent Depth
A river or a pond appears to be less deeper than it really is.
The bottom of a swimming pool appears to be close the surface.
The same thing applies to the fish swimming near the bottom of a pond, they appear to be
close to the surface.
All this are a result of refraction
The light from the water bottom to the person’s eye is refracted away from the normal at the
surface since it is travelling form an optically denser medium to a less dense medium. To an
observer the rays of light appear as if they are coming from the image of the pebble.
Refractive index can be calculated using the equation
Real Depth
Refractive index, n 
Apparent Depth
Refractive index is a constant for any given material.
water - 1.33, Diamond - 2.42, Glass, 1.5
Classwork
1.
2.
3.
Given that the real depth of a pool of water is 4m and that the refractive index
of the water is 1.33, calculate the apparent depth of the pool.
When light moves from air into glass the angle of refraction r is 43º. Calculate
the angle of incidence i.
Calculate the refractive index of air. The speed of light in air is 3.0 x 108 m/s.
Critical Angle (c) & Total Internal Reflection
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The incidence angle for which the angle of refraction is 90º is called the critical angle(c). It
only occurs when light travels from a denser medium to a less dense medium. The critical
angle is a constant for any given material, e.g. water-49 º, Diamond-24 º, Glass-42 º.
If the incidence angle exceeds the critical angle for any material then Total Internal
Reflection takes place.
If i < c then normal refraction takes place.
If i < c then r = 90 º.
If i > c then total internal reflection takes place. See diagram below
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Critical angle and refractive Index
Critical angle and refractive Index are related through the expression,
1
n
sin c
Example 3: Refractive index of glass is 1.5. Calculate its critical angle.
Solution
1
1

1.5 =
n
sin c
sin c
Rearranging:
sin c =
1
= 0.667
1 .5
c = Sin-1(0.667)
c = 42º
Consequences & application of total internal reflection
Optical Fibres/Light Pipes
Optical fibres are very thin, flexible rods made from a special glass.
Light can be trapped by total internal reflection inside the optic fibre. The light rays meet the
sides of the rod at an angle greater than the critical angle of the glass. The light rays are then
totally internally reflected inside the glass rod.
Surgeons use a device called an endoscope to examine the inside of patients’ bodies. This is
made of bundles of fibre optics.
Optical fibres can also carry telephone calls. In industry they are used to examine hidden
parts.
Security personnel use fibre optics to view inside rooms were hostages are held.
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Reflecting Prisms
Glass prisms are used to change the direction of light rays through total internal reflection.
In periscopes, 45o prisms are used instead of plane mirrors.
In car or bicycle rear reflectors, the direction of the incoming light can be reversed by two
total internal reflections.
Mirages
Mirages are common in hot deserts or even in a hot day in a tarred road. A traveler often sees
a pool of water ahead of him/her which is an optical illusion.
Mirages are caused by the progressive and continuous refraction of light as it passes into
warmer layers of air of changing refractive index.
The rays of light eventually become parallel to the ground, and then proceed to bend upwards
as a result of total internal reflection.
To the observer the rays of light appear to come from the road. This creates an image of the
sky on the road which looks like a pool of water.
LENSES
Lenses refract light and form images. There are two main types of lenses: The Convex
(converging) lens and Concave (diverging) lens.
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Action of a thin converging lens on parallel light beams
Definition of Terms
Principal Axis: A path followed by a light ray as it passes through the centre of the lens and is
perpendicular to the lens.
Principal focus (F): A point on the principal axis at which all the rays seem to converge after
passing through the lens.
Optical Centre(c): The geometric centre of a lens.
Focal length (f): Length between the optical centre and the principal focus. This is a constant
for
any given lens.
Characteristics Of Images Formed By Convex Lenses
This can be shown with the help of ray diagrams. Ray diagrams are used to locate the image
formed by drawing two of the following standard rays.
1. A ray passing through the centre of the lens is not refracted (it passes as a straight
line).
2. A ray parallel to the principal axis passes through F after leaving the lens.
NB:
All rays begin from the top of the object and the bending takes place at the line
passing through the middle of the lens.
Object beyond 2F
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The image is
 Inverted

Real

Smaller than the object

Formed between F and 2F.
The lens is used in this manner in a camera.
Object Between F and 2F
The image is
 Real

Bigger than the object (magnified)

Inverted

formed beyond 2F.
When used in a slide projector or a photographic enlarger.
Object at 2F
The image is
 Inverted

Real

Same size as the object

Formed between F and 2F.
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The lens is used in this way in various optical instruments to provide an upright
image.
Object Between F and C
The image is
 Virtual

Upright

Bigger than the object (Magnified)

formed behind the object
A lens can be used in this manner in a magnifying glass.
Object at 2F
The image will be formed at infinity, similarly, when the object is at infinity, the image will
be formed at F.
Uses of Lenses in Optical Instruments
The camera uses a convex lens to form an image that is real, small, inverted on a piece of
film at the back. The image is formed between F and 2F of the lens. The image is formed on
the film.
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A slide projector forms a real image on a screen of a slide or a film in a cine-projector. The
image is usually smaller than the real object (slide or frame of film), and is further away from
the lens.
Good illumination of the slide is needed in order for the image to be bright. This is achieved
by focusing the light beam by a concave mirror and two condenser lenses as shown in the
diagram below.
A Photographic Enlarger uses a magnified image of the negative to produce a well
magnified print of a photograph. It works the same way as a slide projector.
Simple microscope (magnifying glass)
A convex lens forms an enlarged, upright virtual image of an object placed between F and the
lens. It acts as a magnifying glass as shown below.
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Finding Focal length of a Lens
Method 1
Place a lens in front of a screen. Adjust the position of the lens until a sharp image of a
distant object is seen on the screen. The distance between the image lens and the screen gives
the focal length.
Method 2
A more accurate method of finding focal length is by using the expression
1 1 1
 
f v u
which is known as the lens equation. Where v is image distance and u is object distance.
Place a candle along a metre rule and place a screen at the other end. Place a lens in between
them and adjust its position until the image of the candle is seen on the screen. Measure and
record u and v, then calculate f using the expression above.
Magnification
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magnification 
magnification 
image distance (v)
object distance (u)
magnification 
PHYSICS NOTES: Physical Quantities & Measurement
image size
object size
or
or
image height(v)
object height (u)
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