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National 5 Physics
Electricity and Energy
Pupil Booklet
Electricity and Energy Learning Outcomes
Conservation of energy
energy is transferred between stores. Identification and explanation of ‘loss’ of
energy where energy is transferred.
mass, gravitational field strength and height.
problems involving kinetic energy, mass
and speed.
energy.
Electrical charge carriers and electric fields
ed per unit time.
time.
Potential difference (voltage)
field on a charged particle.
energy given to the charge carriers in a circuit.
Ohm’s Law
-I graph to determine resistance.
onship to solve problems involving potential difference
(voltage), current and resistance.
resistance of a conductor.
Practical electrical and electronic circuits
of current, voltage and resistance, using appropriate meters in
complex circuits.
electronic components including cell, battery, lamp, switch, resistor, variable
resistor, voltmeter, ammeter, LED, motor, microphone, loudspeaker, photovoltaic
cell, fuse, diode, capacitor, thermistor, LDR, relay, transistor.
-channel
enhancement mode MOSFET. Explanation of their function as a switch in
transistor switching circuits.
resistors in series and in parallel circuits, and circuits with a combination of series
and parallel resistors.
Electrical power
time.
roblems involving power, potential
difference (voltage), current and resistance in electrical circuits.
appliance.
Specific heat capacity
ials require different quantities of heat to raise the
temperature of unit mass by one degree Celsius.
energy of its particles.
rature and heat energy.
temperature change and specific heat capacity.
Gas laws and the kinetic model
force and area.
absolute zero of temperature.
-volume, pressure-temperature and volumetemperature laws qualitatively in terms of a kinetic model.
ppropriate relationships to solve problems involving the volume, pressure
and kelvin temperature of a fixed mass of gas.
Energy
Energy cannot be destroyed, but it can be changed from one form into another. All
forms of energy are measured in the same unit: the joule (J).
There are eight types of energy
Kinetic energy
the energy of moving things
Heat energy
the temperature of an object is determined by the kinetic
energy of its particles. Energy stored in this way is called heat
energy
Sound energy
when atoms or molecules are made to vibrate
Light energy
electromagnetic radiation carries energy in photons
Gravitational potential energy
lifting an object in a gravitational field stores energy
Chemical
energy is stored in the bonds that bind atoms together
Electrical
the energy of moving electric charges
Nuclear
energy is stored in the bonds that bind a nucleus together
Energy Transformations
Energy can be changed from one form into another. We say energy is being
transformed. An arrow is often used to indicate an energy transformation
Trolley rolling down a hill
Burning wood
Battery connected in a circuit
Loudspeaker
Potential  Kinetic
Chemical  Heat+Light
Chemical  Electrical
Electrical  Sound
Energy Loss
During an energy transformation, energy can be transformed into a form that is not
useful. For example the energy transformation in a traditional filament bulb is
electrical  light and heat. The useful energy is light but some energy will be lost as
it becomes heat. We say there is an energy loss (the total energy out still equals the
total energy in).
Kinetic energy
Kinetic Energy is the energy associated with a moving object. It is measured in
joules and has the symbol Ek.
The kinetic energy of a moving object depends on the mass of the object and on the
square of its velocity.
Ek = 1 mv2
kinetic energy
in joules
speed in ms-1
2
mass in kg
Example
How much kinetic energy does a car of mass 1000 kg have when it is travelling at 20
m/s
m
= 1000 kg
v
= 20 ms-1
Ek
1mv2
2
= 1  1000  202
2
= 200000 J
Kinetic energy and stopping distances
The stopping distance of a vehicle consists of two parts: thinking distance and
braking distance. The thinking distance increases with speed. Thinking distance =
speed  reaction time.
To stop a vehicle, the brakes do work to transform the kinetic energy into heat.
This work equals the (braking force x the braking distance). The braking distance
must therefore increase as the speed and kinetic energy of the vehicle increase.
Gravitational potential energy
An object which is raised up to a high position is said to have gravitational potential
energy. The work done against gravity to raise it equals the energy transformed into
potential energy.
Imagine a mass of m kg lifted through a height of h metres:
h
Potential energy = mass x gravity x height
gravitational potential
energy gained in joules
Ep = mgh
mass in kg
h is height gained in metres
gravitational field strength
(10 Nkg-1 on Earth)
Example
A chairlift raises a skier of mass 50 kg to a height of 250 m. How much potential
energy does the skier gain?
m = 50 kg
g = 10 Nkg-1
h = 250 m
Ep = mgh
= 50 x 10 x 250
= 125000 J
Principle of Conservation of energy
The total amount of energy remains constant during energy transfers. Energy
cannot be created or destroyed but simply transformed to one of its many forms.
In the last example the skier gains 125000J of potential energy. If the skier was
to ski down the hill, assuming no energy loss all of his potential energy energy
would become kinetic energy at the bottom of the slope.
Example
A lump of ice falls from a plane flying at 350m above the ground. What is the speed
of the ice as it hits the ground? Assume there is no air resistance.
Solution
Ek  E p
1 2
mv  mgh
2
1 2
v  gh
2
v 2  2 gh
Mass (m) on both sides
can be cancelled
v  2 gh
v  2  9.8  350
v  82.8ms 1
Note that this question did
not need to provide the mass
Atoms
Every substance is made up of atoms. Each element is made up of the one kind of
atom, sometimes these atoms are combined together to form molecules.
Inside each atom there is a central part called the nucleus. The nucleus
contains two particles:
protons: these have a positive charge
neutrons: these have no charge.
Surrounding the nucleus are negatively charged electrons.
An uncharged atom will have the same number of protons and electrons.
Consider the element helium, which has two neutrons and two protons in the
nucleus, and two electrons surrounding the nucleus. This can be represented as:
Neutron
Electron
Proton
atom of helium
CIRCUITS
Electric Current
Materials can be divided into two main groups, conductors and insulators. In a
conductor, the electrons (sometimes referred to as charges) are free to move through
the structure but in an insulator they are not.
Electric current is a measure of the flow of negative charge around a circuit
and depends on the amount of charge passing any point in a circuit every
second.
All metals are conductors and, with the occasional exception, all non-metals are
insulators.
I=
Q
t
or
I = electric current
Q = electric charge
t = time taken for charge to pass point
Q=It
Units
Electric current is measured in Amperes, A.
Electric charge is measured in Coulombs, C.
Time is measured in seconds, s.
Example
Calculate the electric current in a circuit if 3 C of charge pass a point in a circuit in a
time of 1 minute.
Ensure that all quantities are stated with the correct units.
I=?
Q=3C
t = 1 min = 60 s
Q
3
I= t
= 60
= 0.05 A
Alternating Current (a.c.) and Direct Current (d.c.)
All power supplies can be grouped into one of two categories depending on the way
that they supply energy to the charges in a circuit.
A d.c. supply produces a flow of charge through a circuit in one direction only.
An a.c. supply produces a flow of charge that regularly reverses its direction
through a circuit.
The direction of the current depends on the direction of the ‘push’ from the supply,
therefore power supplies can provide a direct voltage or an alternating voltage which
would result in a direct current (d.c.) or an alternating current (a.c.).
+
-
+
-
d.c. supplies
cell
battery
power
supply
signal
generator
+
power
supply
a.c. supplies
Mains Supply Frequency
The mains electrical supply in the U.K. is an alternating supply with a quoted
voltage of 230 V and a frequency of 50 Hz, that is it completes one cycle 50 times
per second.
Peak Value and Quoted (Effective) Value of A.C.
A d.c. supply provides a constant ‘push’ to the charges as they move around a circuit
whereas the a.c. supply does not as the voltage is continually varying.
The voltage for an alternating supply varies from zero to the peak value to zero to
the peak value in the reverse direction and so on.
V in Volts
V in Volts
Effective
voltage
Time
(milliseconds)
Varying a.c. supply
Time
(milliseconds)
Steady d.c. supply
The peak value of voltage for an alternating supply cannot be used as a
measure of its effective voltage as the voltage is only at that peak value for a
short space of time. The effective voltage of an a.c. supply is less than the peak
value.
For example, an alternating supply with a peak value of 10 V does not supply the
same power to a circuit as a direct supply of 10 V, in fact it is less, approximately 7 V.
The effective value of current and voltage in an a.c. circuit is measured using a.c.
meters in the circuit.
The peak value of voltage in an a.c. circuit can be measured using an oscilloscope.
Voltage and Potential Difference (p.d.)
The voltage or potential difference (often referred to as the p.d.) of the supply is a
measure of the energy given to the charges in a circuit.
Units
Voltage (p.d.) has the symbol V and is measured in volts, V.
Force Fields
In Physics, a field means a region where an object experiences a force without being
touched. For example, there is a gravitational field around the Earth. This attracts
masses towards the earth’s centre. Magnets cause magnetic fields and electric charges
have electric fields around them.
Electric Fields
In an electric field, a charged particle will experience a force. We use lines of force to
show the strength and direction of the force. The closer the field lines the stronger the
force. Field lines are continuous - they start on positive and finish on negative charge.
The direction is taken as the same as the force on a positive “test” charge placed in
the field.
Electric Field Patterns
Positive point charge
Negative point charge
+ test charge
has a force
‘outwards’
+ test charge
has a force
‘inwards’
These are called radial fields. The lines are like the radii of a circle. The strength of
the field decreases as we move away from the charge.
Electric Field Pattern
Positive and negative point charges
Circuit Symbols
Circuit symbols are used in electrical circuits to represent circuit components or
devices to make them easier to draw and understand.
Some of the circuit symbols that you will need to know are shown below.
A
V
ammeter
voltmeter
resistor
cell
variable
resistor
battery (of cells)
fuse
lamp
switch
Series and Parallel Circuits
Components in a circuit can be connected in series or
parallel. A series arrangement of components is where
they are in-line with each other, that is connected endto-end.
Series
A parallel arrangement of components is where they
are connected across each other where the current
has more
than one path through that part of the circuit.
Parallel
Measuring Current and Potential Difference or Voltage
Electric current is measured using an ammeter which is connected in series
with the component.
Potential difference (p.d.), or voltage, is measured using a voltmeter which is
connected in parallel with the component.
Measuring the
current through
the lamp
A
Measuring the
voltage (p.d.)
across the lamp
V
Current and Potential Difference or Voltage in Series Circuits
The current is the same at all points in a series circuit.
The sum of the potential differences across the components in a series circuit is equal
to the voltage of the supply.
VS
I
IA
C
I
B
IA = IB = IC
V1
V2
VS = V1 + V2
Current and Potential Difference or Voltage in Parallel Circuits
The potential difference across components in parallel is the same for all components.
The sum of the currents in parallel branches is equal to the current drawn from the
supply.
IS
V1
A
IA
I
V2
V1 = V2
IS = IA + I B
B
Electrical Resistance
Resistance is a measure of the opposition of a circuit component to the flow of
charge or current through that component. The greater the resistance of a
component, the less will be the current through that component.
All normal circuit components have resistance and the resistance of a component is
measured using the relationship
R=
V
or
R = resistance
V = potential difference (voltage)
V=IR
I
I = current
Resistance is measured in ohms, Ω.
Potential difference (or voltage) is measured in
volts, V. Current is measured in amperes, A.
This relationship is known as Ohm’s Law, named after a German physicist, Georg
Ohm. For components called resistors, the resistance remains approximately constant
for different
values of current therefore the ratio V/I (= R) remains constant for different values of
current.
A
V
Example
Calculate the resistance of the resistor in the diagram opposite.
Ensure that all quantities are stated in the correct units.
R=?
V=5V
I = 200 mA = 0.2 A
R= V
= 5 = 25 Ω
I
0.2
Ohmmeter
Another way of measuring resistance is to use an Ohmmeter. The symbol for an
ohmmeter is
Ω
To connect an ohmmeter only the meter and the measured device are used. There is
no need for a power supply. E.g. To measure the resistance of a resistor
Ω
Resistors in Series
When more than one component is connected in series, the total resistance of all the
components is equivalent to one single resistor, RT, calculated using the relationship
RT = R1 + R2 + R3
For the following circuit with three components in series,
is equivalent to
R1
R2
R3
RT
The above relationship is true for two or more components connected in series.
Resistors in Parallel
When more than one component is connected in parallel, the total resistance of all
the components is equivalent to one single resistor, RT, calculated using the
relationship
1
1
RT
= R1
1
1
+ R2 + R3
Example 1 Components in series
Calculate the total resistance of the circuit opposite.
R1 = 10 Ω
R2 = 50 Ω
RT = R1 + R2 + R3
R3 = 25 Ω
RT = 10 + 50 + 25 = 85 Ω
10 Ω
50 Ω
25 Ω
Example 2 Components in parallel
Calculate the total resistance of the components above when connected in parallel.
R1 = 10 Ω
R2 = 50 Ω
R3 = 25 Ω
1
R
T
1
R
1
+
1
R
2
+
1
R
=
3
=
1
RT
Note:
=
1
10
5
50
RT
8
50
= 50 therefore
= 8
1
+
+
1
50
1
50
+
+
1
25
2
50
=
8
50
RT = 6.5 Ω
For components in series, RT is always greater than the largest resistance.
For components in parallel, RT is always less than the smallest resistance.
Temperature and Resistance
As the temperature of a conductor increases, its resistance increases.
When a conductor is heated, the atoms vibrate with greater amplitude. This makes
it more difficult for electrons to move through the material so resistance increases.
Electrical Components
Name
Photovoltaic
cell
Symbol
Fuse
Function
Also known as a solar cell, converts light
energy to electrical energy
Thin piece of wire designed to melt (and
break the circuit) when a certain current
passes through it. Used as a safety device
Current can only flow through a diode in
one direction
Can store charge, used in timing circuits
Diode
Capacitor
Thermistor
Temperature dependant resistor.
Temperature increases, resistance decreases
Temperature decreases, resistance increases
(Note that this is different from most
conductors as stated above)
Light Dependant resistor
Light level increases, resistance decreases
Light level decreases, resistance increases
LDR
The Light Emitting Diode (LED)
LEDs operate at much lower voltages and currents then conventional bulbs and will
therefore require a protective resistor in series to limit the current.
The LED is a diode and therefore will only allow current to flow in one direction. To
operate it must be connected as shown below.
+ve
-ve
Voltage Dividers
A voltage divider does exactly as its name suggests - it divides a supply voltage
across two resistors which are connected in series.
The two resistors may have fixed values or one may be a LDR, a thermistor or other
input device.
The supply voltage is divided in the ratio of the resistances in the voltage divider
For the voltage divider shown:
ELECTRICAL ENERGY
In the earlier section on potential difference, it was stated that the potential
difference of the supply is a measure of the energy given to the charges in the
circuit.
The energy carried by these charges around the circuit is then converted to other
forms of energy by the components in the circuit. Electrical components are
devices that change or transform the electrical energy from the supply to the
circuit into other forms of energy.
If energy is supplied to the charges in the circuit, then an electric current exists and
there is an energy transformation in each of the components in the circuit.
Examples
An electric lamp is designed to emit light energy. This happens because the electric
current passing through the filament causes it to get hot; hot enough to glow and
emit light. A lamp therefore transforms electrical energy to heat and light energy.
An electric bar fire works in a similar way. The bar of the fire is made from a length
of resistance wire similar to the filament of a lamp. The resistance wire is designed to
get hot when a current passes through it. It also glows when it is hot, but not as much
as the filament of the lamp.
Energy Units
Electrical energy, like all forms of energy, has the symbol E and is measured in
joules, J.
Power and Energy
To compare different components, it is often useful to compare the rate at which
energy is transformed, that is the energy transformed each second.
This electrical energy transformed each second is known as the power.
E
P= t
or
E=Pt
P = power
E = energy
t = time
Units
Power is measured in watts, W.
Energy is measured in joules, J.
Time is measured in seconds, s.
1 watt is equivalent to the transfer of 1 joule per second.
Example
If an electric fire uses 1.8 MJ of energy in a time of 10 minutes, calculate the power
output of the fire.
Ensure that all quantities are stated with the correct units.
P=?
6
E = 1.8 MJ = 1.8 x10 J
P=
t = 10 min = 600 s
E
t
=
1.8 x 10
600
6
= 3000 W
Power Current and Voltage
Electrical power is also dependent on the potential difference across the component
and the current through it. If 1 volt across a component pushes a current of 1 ampere,
then the power will be 1 watt.
P = power in watts
V = voltage or potential difference in volts
I = current in amperes
P=IV
Example
A 230 V toaster draws a current of 4 A from the mains supply. Calculate the power
output of this toaster.
P=?
V = 230 V
P = V I = 230  4 = 920 W
I =4A
More Power Equations
Using the equation P = I V and Ohm’s Law equation V = I R, we are able to obtain -
V  IR
P  I  ( IR )
P  I 2R
V
I
R
V 
P    V
R
V2
P
R
Example
A component data book states that a 1 kΩ resistor can safely handle a power output of
0.4 W.
a) What is the maximum current it can safely handle?
b) What potential difference would exist across the resistor at this current?
a)I = ?
P = 0.4 W
R = 1 kΩ = 1000 Ω
b)V = ?
P = 0.4 W
R = 1000 Ω
I = 0.02 A
P
2
I =R
=
0.4
4
1000 = 4x10-
I = 0.02 A
2
V =PR
= 0.4 x 1000
= 400
or
V =IR
= 0.02 x 1000
V = 20 V
V = 20 V
HEAT
Heat is a measure of the average kinetic energy of the particles in a substance.
Temperature is a measure of the quantity of heat energy in a substance. Can be
measured in C or Kelvin.
Specific Heat Capacity
The specific heat capacity of a substance is the amount of heat energy required to
change the temperature of 1 kg of a substance by 1 C.
Specific heat capacity is calculated using the formula:
heat transferred
Eh = cm t
change in temperature
mass of material
specific heat capacity
Units
The unit for specific heat capacity is the joule per kilogram degree celsius (J/kg C).
The specific heat capacity shows that the same mass of different materials requires
different quantites of energy to raise their temperature of unit mass by one degree
Celsius.
Example
When a kettle containing 2 kg of water (specific heat capacity 4200 J/kg C) cools
from 40 C to 20 C, calculate the heat given out by the water.
m = 2 kg
T 2 = 40 C
Eh = ?
c = 4200 J/kg C
T = 20 C
Eh = cm T = 4200 x 2 x (40 – 20) = 168000 J or 168 kJ
1
GAS LAWS
Pressure
Pressure on a surface is defined as the force acting normal (perpendicular) to the
surface.
p = pressure in pascals, Pa
F
p=
F = normal force in newtons, N
A
A = area in square metres, m2
1 pascal is equivalent to 1 newton per square metre; ie 1 Pa = 1 N m-2.
Example
Calculate the pressure exerted on the ground by a truck of mass
1600 kg if each wheel has an area of 0.02 m2 in contact
with the ground.
Total area A = 4 × 0.02 = 0.08 m2
Normal force F = weight of truck = mg = 1600 × 9.8 = 15680 N
p=?
F = 15680 N
A = 0.08 m2
p= F
A
= 15680
0.08
= 196,000 Pa or 196 kPa
Kinetic Theory of Gases
The kinetic theory tries to explain the behaviour of gases using a model. The model
considers a gas to be composed of a large number of very small particles which are far
apart and which move randomly at high speeds, colliding elastically with everything
they meet.
Volume
The volume of a gas is taken as the volume of the container. The
volume occupied by the gas particles themselves is considered so small
as to be negligible.
Temperature The temperature of a gas depends on the kinetic energy of the gas
particles. The faster the particles move, the greater their kinetic energy
and the higher the temperature.
Pressure
The pressure of a gas is caused by the particles colliding with the walls
of the container. The more frequent these collisions or the more
violent these collisions, the greater will be the pressure.
Relationship Between Pressure and Volume of a Gas
For a fixed mass of gas at a constant temperature, the pressure of a gas is inversely
proportional to its volume.
pα1
V
p × V = constant
p1 V1 = p2 V2
Graph
0
0
Example
The pressure of a gas enclosed in a cylinder by a piston changes from 80 kPa to 200
kPa.
If there is no change in temperature and the initial volume was 25 litres, calculate the
new volume.
p1 = 80 kPa p1 V1 = p2 V2
V1 = 25 litres 80 × 25 = 200 × V2
p2 = 200 kPa V2 = 10 litres
V2 = ?
Relationship Between Pressure and Temperature of a Gas
If a graph is drawn of pressure against temperature in degrees celsius for a fixed mass
of gas at a constant volume, the graph is a straight line which does not pass through
the origin. When the graph is extended until the pressure reaches zero, it crosses the
temperature axis at -273 oC. This is true for all gases.
Kelvin Temperature Scale
-273oC is called absolute zero and is the zero on the kelvin temperature scale. At a
temperature of absolute zero, 0 K, all particle motion stops and this is therefore the
lowest possible temperature.
One division on the kelvin temperature scale is the same size as one division on the
celsius temperature scale, i.e. temperature differences are the same in kelvin as in
degrees celsius, e.g. a temperature increase of 10°C is the same as a temperature
increase of 10 K.
Note the unit of the kelvin scale is the kelvin, K, not degrees kelvin, °K!
Converting Temperatures Between °C and K
Converting °C to K
add 273
Converting K to °C
subtract 273
If the graph of pressure against temperature is drawn using the kelvin temperature
scale, zero on the graph is the zero on the kelvin temperature scale and the graph now
goes through the origin.
For a fixed mass of gas at a constant volume, the pressure of a gas is directly
proportional to its temperature measured in kelvin (K).
pT
p
= constant
T
p1
p
= 2
T1
T2
Example
Hydrogen in a sealed container at 27 °C has a pressure of 1.8 × 105 Pa. If it is
heated to a temperature of 77 °C, what will be its new pressure?
p1 = 1.8 × 105 Pa
T1 = 27 °C = 300 K
p2 = ?
T2 = 77 °C = 350 K
p2 = 2.1 × 105 Pa
Relationship Between Volume and Temperature of a Gas
If a graph is drawn of volume against temperature, in degrees celsius, for a fixed mass
of gas at a constant pressure, the graph is a straight line which does not pass through
the origin. When the graph is extended until the volume reaches zero, again it crosses
the temperature axis at -273 °C. This is true for all gases.
If the graph of volume against temperature is drawn using the kelvin temperature
scale, the graph now goes through the origin.
For a fixed mass of gas at a constant pressure, the volume of a gas is directly
proportional to its temperature measured in kelvin (K).
V T
V
= constant
T
V1
V
= 2
T1
T2
Example
400 cm3 of air is at a temperature of 20 °C. At what temperature will the volume be
500 cm3 if the air pressure does not change?
V1 = 400 cm3
T1 = 20 °C = 293 K
V2 = 500 cm3
T2 = ?
V1
V
= 2
T1
T2
400
500
=
293
T2
T2 = 366 K = 93 °C (convert back to temperature
scale in the question)
Combined Gas Equation
By combining the above three relationships, the following relationship for the
pressure, volume and temperature of a fixed mass of gas is true for all gases.
pV
= constant
T
p 1 V1
p 2 V2
=
T1
T2
Example
A balloon contains 1.5 m3 of helium at a pressure of 100 kPa and at a temperature of
27 °C. If the pressure is increased to 250 kPa at a temperature of 127 °C, calculate
the new volume of the balloon.
p1 = 100 kPa
V1 = 1.5 m3
100  1.5
200  V2
=
T1 = 27 °C = 300 K
300
400
p2 = 250 kPa
V2 = ?
V2 = 0.8 m3
T2 = 127 °C = 400 K
Gas Laws and the Kinetic Theory of Gases
Pressure - Volume (constant mass and temperature)
Consider a volume V of gas at a pressure p. If the volume of the container is reduced
without a change in temperature, the particles of the gas will hit the walls of the
container more often (but not any harder as their average kinetic energy has not
changed). This will produce a larger force on the container walls. The area of the
container walls will also reduce with reduced volume.
As volume decreases, then the force increases and area decreases resulting in, from
the definition of pressure, an increase in pressure,
i.e. volume decreases hence pressure increases and vice versa.
Pressure - Temperature (constant mass and volume)
Consider a gas at a pressure p and temperature T. If the temperature of the gas is
increased, the kinetic energy and hence speed of the particles of the gas increases.
The particles collide with the container walls more violently and more often. This
will produce a larger force on the container walls.
As temperature increases, then the force increases resulting in, from the definition of
pressure, an increase in pressure,
i.e. temperature increases hence pressure increases and vice versa.
Volume - Temperature (constant mass and pressure)
Consider a volume V of gas at a temperature T. If the temperature of the gas is
increased, the kinetic energy and hence speed of the particles of the gas increases. If
the volume was to remain constant, an increase in pressure would result as explained
above. If the pressure is to remain constant, then the volume of the gas must increase
to increase the area of the container walls that the increased force is acting on, i.e.
volume decreases hence pressure increases and vice versa.