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ELECTRICITY 1:
The usefulness of electrical appliances in the home, safety-fuses & earthing, transferring electrical energy,
power and energy transfer calculations (P = IV = E/t = I2R, E = Pt =
IVt) and pay-back time cost
calculations
Doc Brown's Physics Revision
Notes
Suitable for GCSE/IGCSE Physics/Science courses or
their equivalent
Why are electrical devices so useful?
How do we calculate the energy transfers in an electrical appliance?
What do we mean by a unit of electricity
used?
How do we calculate the cost of running an
electrical device?
It would be a good idea to study sections 2.
and 3. before working your way through this page
2.
Electrical circuits and how to draw them, circuit symbols, parallel
circuits, series circuits explained
3. Ohm's Law, experimental investigations of
resistance, I-V graphs, calculations V = IR, Q = It, E = QV
Important
definitions, descriptions and units
Note: You may/may
not (but don't worry!), have come across all of these terms, it depends
on how far your studies have got. In your course, you might not need
every formula - that's up to you to find out.
V
the potential difference (p.d., commonly called
'voltage')) is the driving force that moves the electrical charge around
a circuit. The p.d. across any part of a circuit is measured in volts,
V.
I
the current = rate of flow of electrical charge in
coulombs/second (C/s), measured in amperes (amps, A).
Formula connection:
Q = It,
I = Q/t, t = Q/I, Q = electrical charge moved in
coulombs (C), time t (s)
R
a resistance in a circuit, measured in ohms (Ω).
A resistance slows down the flow of electrical charge.
Formula connection:
V = IR,
I = V/R, R = V/I (This is the formula for
Ohm's Law)
P
the power delivered by a circuit = the rate of energy
transfer (J/s) and is measured in watts (W).
Formula connection:
P = IV,
I = P/V, V = P/I also P = I2R
(see also P = E/t below)
E = QV, Q =
E/V, V = E/Q, E = energy transfer in joules (J),
Q = electrical charge moved (C), V = p.d. (V)
E = Pt,
P = E/t, t = E/P, where P = power (W), E
= energy transferred (J), t = time taken (s)
Formula connection: Since E = Pt and P = IV,
energy transferred E =
IVt
The usefulness of electrical appliances
e.g. in the home
-
 Appreciate that we often use electrical
appliances because they transfer energy into other useful at the flick of a switch ie very
convenient!
-
Energy is transferred because the
electric charge does work against the circuit resistance(s) - remember: work
done = energy transferred.
-
Electrical appliances are designed to
transfer to do useful work in a circuit when the current flows through the
components of e.g. heating element of a fire or kettle (electrical energy
store to a
thermal energy store), motion in a food mixer (electrical to a kinetic
energy store) etc.
-
Don't forget that no appliance is perfect
(100% efficient), so there are always energy losses.
-
Just think of all the
devices-appliance that run off electricity in the home eg light bulbs, TV,
refrigerator, CD player, radio, oven, mobile phone charger, computers,
battery charger, Hoover, food mixer, microwave, iron, immersion heater,
telephone, internet etc. etc.!
-
Think of the importance of these
devices-appliances in your life - music/TV on demand, food safely stored in
the fridge, light to read by in the evening
-
Try to imagine life without your
domestic electricity and think how wonderful 240V is!
-
Quite simply the convenience and
usefulness of mains electricity to our way of life and standard of living is
incalculable, so don't waste it!
-
Electrical appliances can be low or high
power - convenient for the energy needs required to power most things in the
home.
-
Think of all those everyday tasks now
done more conveniently with electrical appliances, saving your time and
energy.
-
Even with lighting, electric bulbs are
rather better and safer than oil/gas lamps or candles!
-
Powerful electrical machines in industry
are easily run from mains electricity and can do jobs far more quickly than
manual labour.
-
This has allowed the efficiency of
industrial production to be considerably increased.
-
Steam power replaced people and steam
replaced by electrical power - the power aspect of the industrial
revolution!
-
Lifts require a powerful electric motor
and think of the hard work you do in climbing several flights of stairs!
-
Know how to calculate how much energy
is transferred by an appliance and how much the appliance costs to run.
-
You should be able to use
their skills, knowledge and understanding to:
-
Be able to compare the advantages and
disadvantages of using different electrical appliances for a particular
application,
-
You will be required to compare
different electrical appliances, using data provided.
-
For developing countries where
infra-structure lacks a reliable mains electricity supply, battery operated
devices can be used and even clockwork radios have been designed.
-
However, batteries are costly
despite being a convenient supply of stored chemical energy which converts
to electrical energy on demand. They also don't last very long!
-
In the case of a clockwork
powered radio, when the radio is 'wound up' the energy is stored as elastic
potential energy and again released as needed to listen to the radio, for
free! This completely avoids the need for costly batteries and their safe
disposal to avoid pollution.
-
Without mains electricity,
communities in developing countries cannot have the same standard of
material living.
-
You should also be aware that some
energy is 'wasted' or 'dissipated' because electrical appliances are
never 100% efficient when switched on!
-
The waste energy usually ends up
increasing the thermal energy store of the component or surroundings e.g.
from friction of moving parts or heat from overheated circuits.
-
Despite the wasted energy in many
appliances, there are obvious instances where we want the electrical
energy to end up as heat.
-
Electrical heaters is the most obvious
example - you use a high resistance a coil of wire to act as a heating
element in an appliance e.g. electric fire, toaster etc.
-
The thin metal filaments of filament
bulbs need to become very hot to emit useful light.
-
Fuses rely on an 'overheating' effect to protect
an appliance and ourselves from electrocution.
More on the
uses of electricity in the home
including safety aspects
Connections! The electricity supply to your home is a.c.
(alternating current) where the current constant reversing direction
e.g. an oscillation of 50 Hz (50 cycles/second).
The a.c. supply to the ring mains circuits in
your house originates from the
National Grid system.
Alternating currents are produced from alternating voltages in which
the positive and negative terminals of the potential difference keep alternating
(+ <=> -).
The a.c. mains supply in the UK is usually around
230-240 V with a frequency of 50 Hz (50 hertz or 50 cycles/second).
Other devices will use a d.c. (direct current)
supply from cells or batteries, in which the current only flows in one direction
e.g. torch batteries.
A d.c. current is produced by a direct voltage -
potential difference (p.d.) and is either positive or negative, but NOT
both. You can convert an ac current into
a dc current using a diode.
Many electrical appliances in the home are connected
to the ring mains circuit with three core cables fitting into a plug.
The plug (pictures below) is inserted into a
socket which is directly
connected to the a.c. mains supply. Most
sockets have their own switches connected to the live wire of the
ring mains circuit in a house. This
enables the circuit to be broken and isolate any appliance if there
is a risk of electric shock.
The cables consist of a copper wire core and sheathed in an
insulating
plastic covering, each of which is colour coded to clearly indicate its
function (annotated image below).
The colour coding is kept the same for all appliances
so that you know exactly which wire is which!
If wired incorrectly you may blow the fuse or
have an accident - potentially fatal electrocution (see earth wire),
so make sure you know which is which and how to wire a plug safely
irrespective of any GCSE physics exam!
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The function of each of the three wires in a
three core cable.
The live wire
- brown colour
The live wire provides the alternating
current potential difference with a p.d. of +/- ~230-240 V.
The live wire carries the p.d. directly from the mains supply
and this 'live' wire must never be touched if the circuit is
switched on for obvious reasons!
In fact you should never touch or
manipulate any wire if the circuit is live!
The neutral wire
- blue colour
The neutral wire completes the circuit
to the appliance and carries away the current.
This allows the current to flow
in through the live wire (maximum p.d. of ~230-240 V) and out
through the neutral wire (minimum p.d. ~0 V).
The p.d. between the live wire and neutral
wire is ~230-240 V for the mains electricity supply.
The earth
wire - green + yellow bands
The earth wire has a safety function to
protect the wiring and YOU!
It doesn't normally carry a current and its
p.d. should be 0 V.
The p.d. between the live wire and the earth
wire is ~230-240 V.
There is no p.d. between the neutral wire and
earth wire, both are at 0 V.
The earth wire is connected to the metal casing of
an appliance and carries the current away if a fault develops in the
circuit.
If a fault develops and the live wire touches
any conducting part of the appliance, the current will run to
earth through the earth wire and NOT through you if you touch the appliances.
This also might, and should, blow the fuse
because of the surge in current, so the circuit is broken and made
safe.
The
danger of the live wire - danger of electrocution - safety
function of earth wire
Under normal conditions your body has a p.d.
of 0 V with respect to the ground ('earth').
Unfortunately, if you touch the live wire
with the circuit switched on, a potential difference is produced
across your body and the current flows through you to the ground -
'to earth'.
In other words, you will experience
electrocution - potential injury from an electric shock, and, if the
current is large enough, it may kill you!
It doesn't matter whether the appliance is
switched on or not, if the plug is in the socket, there is a
connection to the live wire which always has a p.d. of ~230-240
V!
If there is any low resistance connection
between the live wire and earth wire a sudden huge current
can flow to earth, which is dangerous.
This is the cause of many house fires due to
a faulty connection where lots of heat is produced.
For more on electrical safety see
live wire and fuses notes.
Power
ratings
Most appliances are labelled with a power
rating, which is the maximum power output with which it can
be used safely.
The power rating tells you the maximum amount
of energy transferred from one energy store to another per second
when the appliances is being used.
e.g. a 700 W iron means 700 J of energy
are being transferred (used) every second.
A 3 kW heater transfers to the thermal
energy store of a room at the rate of 3000 J/second.
The power rating is useful information for
the consumer.
The lower the power rating, the less
electricity it uses, saving money - cheaper to run - as long as the
appliance can still do what you want it to do.
e.g. if 500 W iron can do the work in the
same time as a 750 W iron, then the 500 W iron is the more
efficient and cheaper way to do your ironing!
750 - 500 = 250, so 250 J/s is saved to
the thermal energy store of the clothes being ironed.
Whatever the power rating, its the efficiency
of the appliance that is really important - what percentage of
energy input is transferred in doing useful work.
However, beware!, just because an appliance has a higher power
rating, it doesn't mean it is more efficient than a lower power
appliance.
A higher powered appliance might waste
more energy i.e. has lower % efficiency in terms of the
electrical energy doing useful work.
Reminder: Power of appliance = current x
potential difference
P (W or
J/s) = I
(A) x V
(V)
For more see
electrical power calculations
section.
Apart from electrical power
calculations for electrical appliances, this formula is
needed to
calculate a safe fuse rating.
See
Conservation of energy,
energy transfers-conversions, efficiency - calculations and
Sankey diagrams
More on the dangers of the live wire
and earthing appliances for extra safety
With respect to an external electricity
supply, as with the earth-ground itself, your body is at a p.d. of 0
V.
Unfortunately, this means if you touch the
live wire or anything connected to it, a large p.d. of 240 V occurs
across your body i.e. between you and the 'earth'.
Therefore an electrical current will flow
through you, giving you an electric shock, which can be sufficient
to kill you.
Even if the socket switch is 'off' or
appliance is 'switched off' there is still a danger of an electric
shock because the live wire is still at high pd (eg 240 V).
If the live wire is touched you are still in
grave danger of an electric shock because a current can still flow
through you to 'earth'.
Note
(i)
Wearing electrically insulating rubber boots may offer some
protection, but is that what you normally wear!?
(ii) Water is a poor conductor, but
with a high potential difference it can conduct. You should also
remember from your chemistry (electrolysis)
that ions from salts increase the electrical conductivity of
water and you have salt ions in your blood, cells and nervous
system etc.!
(iii) It is the function of fuse
to protect you and the appliance from current surges (next
section).
When things go wrong! The
function of a fuse and how to calculate the fuse
rating for an appliance
How does a fuse work?
In any household or
industrial circuit, you can get sudden surge (increase) in
current. The current surge maybe due to a fault, but even
switching appliances on and off. A current surge due to a fault
can lead to overheating, damaging the appliance or even causing
a fire.
An appliance is fitted with
an earth wire and a fuse in the live wire.
If a fault develops and the
live wire comes into contact with the metal case, then,
as long as the metal case is 'earthed' (connected to the earth
wire) the current surge flows harmlessly from the live wire,
through the case and down the earth wire to earth.
The current surge should melt
the fuse, as long as the correct fuse rating is used, and the
current surge is over the fuse rating (in amperes).
This is why the fuse must
be connected in the live wire!
Once the fuse has melted the
circuit is broken and the live wire supply is cut off. This
isolates the whole appliance so you cannot get an electric shock
from touching the case.
Fuses rely on an 'overheating'
effect to protect an appliance from damage (e.g. so it might be
repaired) and ourselves from electrocution from a high voltage
current running through our body to earth.
If the temperature of a resistor
becomes too high from a current surge causing overheating, the resistance increases and so
does the heat transfer to its thermal energy store.
This may interfere with the
working of an appliance due to the increase in temperature of a
resistor.
The temperature might rise
sufficiently to melt the wire in a circuit component and the break
in the circuit stops the 'device' working.
This is how a fuse works, if a
fault develops and too much current flows, a fuse wire melts from
this overheating effect, this breaks the circuit and makes it safe.
The larger the current in the
appliance the thicker the wire should be to minimise the
resistance and overheating. Generally speaking the fuse rating
increases with increase in cable thickness.
Note:
(i) As well as
appliances, the ring main circuits to the 'plug in' sockets
and lighting are protected with fuses in the same way.
(ii) You can
protect circuits with circuit breakers (sometimes
called ?).
There are several types
of circuit breakers e.g. some work off the magnetic effect
of a solenoid so that a current surge produces a magnetic
field strong enough to make a magnet open two contacts to
break the circuit.
Circuit breakers are
safer than normal household fuses. A wire does not melt, but
the circuit is broken by a fast 'switching off'
action - faster than fuse melts. They also have the
advantage of being reset, which is less trouble than
fitting a replacement fuse. They are however, more
expensive, but safer!
Fuse ratings and how to you choose is the safest to use?
For domestic appliances in
the home the most common fuse ratings in the UK are 3A, 5A, 8A
and 13A.
The fuse should have a
rating of close to, but, just above the maximum safe current that
will run through an appliance.
If a fault develops, and the
current rises a few amps above expected, the fuse must melt and
break the circuit making it safe.
This means you have to work
out the current flowing from the power rating of the appliance
from the formula ...
power (W) = current (A) x potential difference
(V)
P = IV
Example 1. A 2kW electric fire works
of a 230 V ac mains supply of electricity.
Calculate the current flowing in the
appliance and suggest a suitable fuse rating.
2kW = 2000 W
P = IV, I = P/V = 2000/230 =
~8.7 A
Ideally a
10A or 11A fuse
would do, but its likely that in this case the appliance
would be fitted with a 13A fuse.
Obviously, you choose the nearest fuse rating
from what is available.
Example 2. What fuse would you choose
to put in the plug of a 700 W electric iron working off 230V
mains electricity?
I = P/V = 700/230 =
~3.0 A
Ideally a
4A fuse
would be best, but a 5A would be acceptable.
Double insulation
To protect you from electric
shock, all appliances with metal cases should be earthed
i.e. the metal case is connected to the earth wire, using
three core cable as previously described.
An earthed conductor can
never become live.
A metal casing is obviously
an electrical conductor, but if the appliance has plastic casing
(electrical insulator) with no external metal parts that can be
touched, it is said to double insulated.
This means the appliance
doesn't need an earth wire and so is connected with two
core cable - live and neutral wires only.
Power, energy
transfer and electricity cost calculations
-
Know and appreciate examples of energy transfers
that everyday electrical appliances are designed to bring about.
-
Know that the amount of energy an
appliance transfers depends on how long the appliance is switched on and its
power.
-
The quantity of electricity that
is transferred ('used') in an appliance depends on its power and how long
you use it for ie time its switched on.
-
Energy is measured in joules (E
in J) and power in watts (P in W)
-
1 watt = 1 J of energy
transferred in 1 second (1 W = 1 J/s)
-
Since a joule is a very tiny
amount of energy, we often quote power in kilowatts (P in kW).
-
1 kW = 1000 W = 1000 J/s
-
A bulb might be quoted with a
50W rating (50 J/s), an iron might be quoted as having a 500 W or 0.5 kW power
rating (500 J/s, 0.5kJ/s) and a three bar electric fire might have a 3kW
power rating (3 kJ/s, 3000 J/s).
-
However when dealing with large
amounts of electrical energy its more convenient to think and calculate in
kilowatt-hours (kWh).
-
1 kilowatt-hour = the amount of
electrical energy that a 1 kW appliance uses in 1 hour.
-
In fact, in terms of the
electricity use in a house, the term unit on your electricity bill
means a kilowatt hour and the price will quoted as eg '9p per unit',
in other words you will pay 9p for every kilowatt-hour of electrical energy
you use.
-
Three formulae for calculating power,
energy transferred
and other things too!
-
If unsure about units of potential
difference (p.d. in V), current in amperes (amps, A) or resistance in ohms (Ω)
then read the first section of
Ohm's Law and calculations using V = IR
-
 (a)
power P (W) = current I (A) x
potential difference V (V)
-
P = IV
-
P in W or J/s, I in amps A, V p.d.
in volts.
-
The more energy transferred in a
given time, the greater the power of the device.
-
The p.d. V tells you how much
energy each unit of electrical charge transfers (V
= E/Q, J/C, see section 3 for
E =
QV calculations).
-
The current I tells you how
much charge passes a given point in a circuit per unit time
(coulombs/second, C/s).
-
This means both p.d. and current
affect the rate at which energy is transferred to an appliance from the
electrical energy store to another energy store.
-
Examples of calculations using P = IV
-
Q1 A 2 kW electric fire is connected to
a 240 V supply.
-
Q2 The current flowing through an
electric motor is 12 A.
-
Q3 What p.d. must a power supply have,
to produce a power output of 2 kW from a machine through which 12.0 A flows?
-
(b) power = current2 x
resistance
-
P = I2R
-
P in W or J/s, I in amps A and p.d. in
volts, R in ohms Ω.
-
(this is useful if you don't know the
p.d., but, you must know the resistance instead)
-
Examples of calculations using
P = I2R
-
Q1 A current of 20 A passes through
a resistance of 10 Ω.
-
Q2 A machine needs to deliver a
power output of 8.0 kW from a power supply of p.d. 240 V.
-
What current will flow the
machine?
-
Don't forget to change kW into W.
-
P = I2R, I =
√(P/R) = √(8000/240) =
5.8 A (2 sf)
-
-
-
Q3 A 2.0 kW electric fire has 4.0
A running through this heating appliance.
-
(c) Energy transferred by device
= appliance power x time
-
The total energy transferred by an
electrical appliance depends on the power of the appliance (in J/S = W)
and the time it is used for ... giving the simple proportionality
formula ...
-
E = Pt (but
here focussing on its 'electrical' connection)
-
rearrangements: P = E/t
and t = E/P
-
Application: power of appliance =
electrical energy transferred / time used
-
See
power
rating notes
-
Formula connection: Since P = IV,
energy transferred E = IVt
-
(calculation examples
to do, copy to
electricity 3 too
with E = QV)
-
When electrical charge moves through
a potential difference energy is transferred as work done against the
electrical resistance (p.d.).
-
The energy of the charge comes from
the power source (dc battery, ac mains electricity) which raises the
potential energy of the electrons.
-
The charge, (usually electrons),
'falls' through the p.d. across the components of a circuit,
giving up its electrical potential energy to another energy store e.g.
thermal, or other form of energy e.g. sound or light.
-
The energy transferred in an
electrical device can be calculated from the formula:
-
You can use two different sets of
units
-
(1st) The usual and familiar J, W and
s.
-
E is energy
transferred in joules, J
-
P is power in watts,
W = J/s
-
t is time in seconds,
s
-
Examples of calculations
-
Q1 An 800 watt oven is used for
one and a half hours.
-
How much energy in MJ is
transferred to the thermal energy store of the oven?
-
800 W = 800 J/s, time = 1.5 x 60
x 60 = 5400 s
-
E = Pt = 800 x 5400 = 4
320 000 J = 4 320 kJ =
4.32 MJ
-
-
-
Q2
An electric heater transfers
1.5 MJ of energy every minute.
-
Calculate the power of the
electric fire in kW.
-
5.0 MJ = 5.0 x 106 J,
time = 5 x 60 = 300 s
-
E = Pt, P = E/t =
1.5 x 106/300 = 5000 W =
5.0 kW
-
-
-
Q3 A rechargeable battery can
deliver a total of 8.0 MJ of energy to a device.
-
If the device delivers a power
output of 25 W, to the nearest hour, how long can it be used for?
-
P = 25 J/s, E = 8.0 x 106
J
-
E = Pt, t = E/P =
8.0 x 106/25 = 3.2 x 105 s
-
1 hour = 60 x 60 = 3600 s
-
3.2 x 105/3600 =
89 hours
-
-
-
Q4 The p.d.
across a resistor is 24.0 V. If a current of 3.0 A is flowing, how
much energy is transferred in 5 minutes?
-
time = 5 x 60 = 300 seconds.
-
E (J) = I (A) x V (V) x t
(s), E =
IVt
-
E = 3.0 x 24.0 x 300 = 21 600
J
-
-
-
Q5 ?
-
(2nd) The practical everyday units e.g. on an appliance or electricity
bill.
-
E is
energy transferred in kilowatt-hours, kWh
-
P is power in kilowatts,
kW (1 kW = 1000 J/s)
-
t is
time in hours, h
-
The power formula triangle for the units of
power in kilowatts (kW),
units of energy in kilowatt-hours (kWh) and units of time
in hours (h).
TOP OF PAGE
Electricity and
magnetism revision
notes index
1.
Usefulness of electricity, safety, energy transfer, cost & power calculations, P = IV = I2R,
E = Pt, E=IVt
2.
Electrical circuits and how to draw them, circuit symbols, parallel
circuits, series circuits explained
3. Ohm's Law, experimental investigations of
resistance, I-V graphs, calculations V = IR, Q = It, E = QV
4. Circuit devices and how are they used? (e.g.
thermistor and LDR), relevant graphs gcse physics revision
5. More on series and parallel circuits,
circuit diagrams, measurements and calculations
gcse physics revision
6. The 'National Grid' power supply, environmental
issues, use of transformers
gcse
physics revision notes
7.
Comparison of methods of generating electricity
gcse
physics revision notes (energy 6)
8. Static electricity and electric fields, uses
and dangers of static electricity gcse
physics revision notes
9.
Magnetism
- magnetic materials - temporary (induced) and permanent magnets - uses gcse
physics revision
10.
Electromagnetism, solenoid coils, uses of electromagnets gcse
physics revision notes
11. Motor effect of an electric current,
electric motor, loudspeaker, Fleming's left-hand rule, F = BIL gcse physics
12.
Generator effect, applications e.g. generators
generating electricity and microphone
gcse
physics revision
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