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A tenminute guide to electrical theory
This article introduces the basic principles of electricity, with
emphasis on domestic electrical systems. Although
some calculations are involved, it's fairly elementary, so if you're a
physicist you probably shouldn't be reading it. The article is aimed
at DIY enthusiasts, householders, and, perhaps, electricians, who have an
understanding of the practical skills involved in electrical wiring,
and want to know more about the basic theory. An understanding of
this theory is important if one wishes to tackle more tricky
wiring applications safely. For example, also on this site is
an article on cable and breaker selection
for demanding wiring applications,
but that won't make much sense if you don't know, for example,
what Ohm's law is.
You can be an electrician without knowing much about electricity. It seems odd,
but it's true. But if you do know the principles, you can do safe and practical
work without memorizing a whole heap of regulations, because they're mostly
derived from standard principles anyway. The key features of electricity are
voltage, current, resistance, power, and
frequency.
An electrical current is the flow of electricity around an electrical circuit.
The flow of electricity follows similar principles to the flow of water in
pipes, as we shall see, with the exception that an electrical system must make a complete
circuit. The circuit will contain a power source of some kind; in mains
wiring the power source is the national electrical distribution system which is mostly outside our control. Of course, the distribution company don't
run wires directly from the power station to our houses: there is all
manner of other stuff between them and us, but that isn't all that
important. For most cases you can proceed as if a small power station
was connected directly to your house.
In domestic electrical work, current is generally measured in amps.
Currents you will encounter in practice range from about 0.5 amps (through a
lightbulb) to about 40 amps (an electric shower). Technically 'amps' is short
for 'Ampères', but the full name is now rarely used. The mathematical symbol
for current, as it is written in calculations, is not 'C' (for current)
or 'A' (for amps) but in fact
'I'. This is just because the symbols 'C' and 'A' are reserved for
other things. You will occasionally come across currents measured
in milliamps ('mA' for short). A milliamp is a thousandth
of an amp. For example, most earthleakage breakers used in
domestic wiring trip at 30 mA, which is about one thirtieth of an
amp.
To get an electrical current to flow, we need a power source, and some sort of
conductor. A conductor is defined as anything that can carry a flow of
electricity. In electrical practice, conductors tend to be copper wire or
copper bars, usually hidden away inside plastic sleeves. The sleeves are
insulators, that is, materials that prevent the flow of electricity. It
is the insulator that keeps the electrical current where it belongs  inside
the cable.
In the UK (and everywhere else, as far as I know), electricity is distributed
around the country in the form of alternating current. This means that
the flow of electrical current changes direction,
usually 50 or 60 times per second.
There are two reasons for this, both historical. First, electrical transformers
(which we need to change voltage, see below) only work with alternating
currents. Second, we generate electricity by spinning wires around inside
magnets (this is a bit of a simplification, of course), and this naturally
produces an alternating current. At the points where the current is about
to change direction, there will
(for a short time) be no current flowing at all. 'Alternating current' is
usually abbreviated to 'AC'.
The fact that current is alternating has little practical impact on domestic
wiring. If you grab a live conductor you'll get a shock which is just as
unpleasant even though, in principle, part of the time no current will be
flowing. One area where the alternating nature of the electrical supply
is apparent, however, is in the use of fluorescent lights. Incandescent
(filament) bulbs generate their light because the filament becomes whitehot. It
cannot heat up and cool down as fast as the alternation of the electrical
current, so the light is fairly constant. Fluorescent lights, on the other
hand, produce a detectable flicker at the speed of the supply alternation. The
light from a fluorescent tube will 'pulse' about 100 times per second (50 times
with the supply current in one direction and 50 in the other). We can't normally see
this flicker, but it does tend to make rotating machines look as though they're
standing still, or going backwards. This is why we are warned not to use
drilling equipment, for example, in strong fluorescent light.
Voltage is a measure of the strength of an electrical supply. A
voltage may exist even when no current is flowing.
In older textbooks you will find terms like 'electrical potential' or
'electromotive force', which gives a better feel for what voltage means.
Strictly, a voltage is only defined between two points. When only one
point is specified, we tacitly assume that the other point is the earth (which
means exactly what it says: the ground beneath our feet). The earth is not a
very good conductor of electricity, but there's an awful lot of it, which makes
up for this to a certain extent. So when I say 'there's 230 volts at this point',
what I really mean is that the voltage difference between this point and earth
is 230 volts (it's a bit more complicated than this in practice, as we shall
see).
Voltage is measured in volts, which is abbreviated to 'V'. So '230V' means '230
volts'. The mathematical symbol for voltage is also 'V'. Incidentally,
although you'll hear electricians talking about '240 volt' mains, in
fact our mains supply voltage has been 230 volts for about ten years,
to make our electrical equipment compatible with that of the rest
of Europe.
To get an alternating current, we need an alternating voltage. So the
electrical mains voltage will cycle from about 325 volts, to zero, to 325
volts, then back to zero, and so on, 50 times per second. This is shown in
figure 1
Figure 1:
The variation of the voltage waveform over time. One complete cycle of
this variation lasts one fiftieth of a second (in the UK)

Why is the maximum voltage 325 volts and not 230 volts as we normally say?
It turns out that this waveform (which varies between high and low voltages)
carries the same amount of energy as a constant voltage about 70% the size.
So when we talk about a 230V AC supply, we mean a supply that would carry the
same energy as a constant voltage of 230 V. This actually means an AC voltage
that reaches 325 volts at certain points, and is zero at others.
Electrical engineers refer to the '230 volt' figure as the 'root mean square'
voltage, for reasons that you'll find in an engineering textbook.
This is abbreviated to 'rms', so you'll sometimes seen the domestic
mains voltage written as '230 Vrms'. Unless indicated otherwise, you can
expect voltages
and currents described in electrical manuals and manufacturers'
catalogues as 'rms' figures, and then ignore this fact completely. The
reason you can ignore it is that — in domestic work — so long
as all measurements of voltage, current, and power
are rms measurements, all the calculations still
give correct answers.
230 volts is quite enough to give you a nasty shock, and sometimes these shocks
can be fatal. In some parts of the world lower voltages are used, for increased
safety. For reasons that will be explained later, it is more efficient (i.e.,
less wasteful of energy) to distribute electricity at a higher voltage, but
increased efficiency is gained at the expense of safety.
We have already mentioned electrical materials which are conductors (that allow
an electrical current to flow easily) and insulators (that don't). In reality
nothing is a perfect insulator or a perfect conductor: most materials have a
certain degree of resistance, and lie on a scale somewhere
between a perfect insulator and a perfect conductor.
Materials with high resistance tend to be
insulators; those with low resistance tend to be conductors.
Even copper electrical
cables have a certain amount of resistance. Resistance is measured in ohms,
which is either abbreviated to '', or to 'R' if your word processor doesn't
have a ''
symbol^{1}.
The mathematical symbol is the letter 'R' as well. One ohm is a lot of
resistance in electrical practice; we normally like our electrical conductors
to have resistances much less than an ohm, for reasons that will be
explained.
You'll not be surprised to learn, I hope, that these important quantities 
voltage, current and resistance  are related. It turns out that the voltage
can be found by multiplying the current (in amps) by the resistance (in ohms).
In symbols this is
V = I R
If algebra puts you off, don't worry, it says exactly the same thing as the
'voltage is current times resistance', but in a shorter format.
In case you're interested, this simple formula is called 'Ohm's law', and is probably
the most important thing ever discovered in electrical engineering. In domestic
wiring, 'V' will nearly always be '230' (volts), so in practice we usually want
to work out current (knowing resistance), or viceversa. We can write Ohm's law
in two different ways:
I = V / R
and
R = V / I
So if we have, say, a lightbulb which has a filament with a resistance of 500
ohms at running temperature, what current flows in it? Since we know that
I = V / R and V is 230, and R (resistance) is 500, then I is 230/500, which is 0.46 amps,
or about half an amp.
It may help to understand these relationships by comparing them to a system that
may be more familiar. Figure 2 shows a water tank
suspended off the ground, connected to a length of pipe. Because the pipe is
open at the end, water will run down in and make a puddle on the floor.
In this system, the height of the water tank is analogous to the voltage. If we
double the height of the tank (from the end of the pipe), this is equivalent to
doubling the voltage. If we do this, all other things being equal, the water
will flow down the pipe twice as fast as before. This is why, if you have a
water tank in your attic, you will usually get a greater flow of water from a
downstairs tap than from an upstairs tap: the height of the water tank above the
tap is about twice as large.
The flow of water through the pipe is analogous to the flow of current. If we
double the voltage, we double the current (if the resistance remains
constant).
The pipe attached to the tank represents the resistance. It is very similar to
an electrical resistance. For example, if we double the length of the pipe, the
flow of water will decrease to about half its previous value. There's twice as
much pipe, therefore twice as much resistance. If we make the pipe thinner,
this will also slow down the flow. This is true of electrical cables as well. A
longer cable has more resistance than a shorter one, and a thin cable has more
resistance than a fat one (but of course it is the thickness of copper that is
important, not the thickness of the insulating plastic). Cable sizes
are expressed in terms of the crosssection area of copper in the live
and neutral conductors, measured in square millimetres (abbreviated to 'mm^{2}' or
'sq mm'). Electrical power rings are very commonly made from
2.5 mm^{2} cable. This means that each of the live and
neutral conductors has an area of 2.5 mm^{2}.
You'll frequently hear this abbreviated to '2.5 millimetre' or '2.5 mil'.
Strictly speaking, this is wrong: the conductors are not 2.5 millimetres
across, they have an area of 2.5 square millimetres. This slang
does not normally cause problems in practice.
Figure 2:
The 'water' model of current, voltage and resistance; see text for
details

The main difference between an electrical system, and the water system shown in
figure 2 is that electrical current must flow in a
circuit. Electricity can't form a puddle in the same way that water can; it has
to be confined to conductors. So in some senses a better analogy might be a
central heating system, where water flows around a set of pipes and radiators,
driven by a pump. In any event, if a circuit is not complete, no current can
flow. This is good, because it means we can uses switches to turn things on and
off. Traditionally a switch is a mechanical contact: pressing it or moving the
lever moves a piece of copper in such a way as to open or close a circuit.
It is now possible to get electronic switching devices that have no moving
parts.
A practical electrical circuit consists of at least the following things: a
power source, some conductors, and an electrical appliance (see
figure 3).
Figure 3:
The simplest possible, practical electrical circuit

In a domestic mains system, the 'power source' is essentially the wires that
bring the electrical supply into the house (and all the power stations, etc.,
that they're connected to). Since we don't have any control over that, we can
usefully think of it as a 230 volt power source without worrying to much about
it^{2}.
This circuit will power the appliance (whatever it is) and, because there is
not even a switch, it will continue to power it forever, or until the power
runs out. Because we are dealing with alternating currents, the flow of current
around the circuit is constantly changing direction (but this does not cause
any problem, as discussed above).
Suppose we want to connect two appliances in this circuit (after all, a house
with only one lightbulb isn't going to be much use). How are we to accomplish
this? There seem to be two basic strategies. The first, called 'series' wiring
is shown in figure 4. The second, 'parallel' wiring, is shown
in figure 5.
Figure 4:
Connection of electrical appliances in series

Figure 5:
Connection of electrical appliances in parallel

There is a place for both these schemes, but in nearly all domestic wiring we
will want to wire things up in parallel. Why? The problem with the series
arrangement is that all the appliances in the system get the same current. This
must be the case, because there is only one set of wires to carry the
current around. Now suppose one appliance is a lightbulb and the other is an
electric shower. The lightbulb wants about half an amp, while the electric
shower wants about 40 amps. There's no way to arrange them so they both get the
current they want. What would happen in practice? Well, the resistance
of the lightbulb is huge compared to that of the electric shower so,
in practice, the current in the circuit will the same as that for
a lightbulb: about half an amp. That isn't going to warm your water
very well.
In a parallel system, all appliances get the same voltage across them. In the
UK this means the 230 volt mains supply. Each appliance will have a particular
resistance, and therefore get a current which is appropriate for its needs.
In practice, we couldn't use the same wires to carry electricity to both a
lightbulb and an electric shower, because the shower would need very thick cables, as
will be explained, and it would uneconomical to wire up a lighting system
using such heavyduty cable.
We've seen how you can connect electrical appliances in
parallel, but what happens if you connect cables in parallel? In other
words, rather than running one pair of wires to each appliance,
why not run two? How would this help? Well, if there are two sets
of conductors running to each appliance, this is exactly the
same as having one set of conductors but with twice as much
copper area. And a conductor with twice the area can carry
twice the current (for reasons I'll explain later). So if we
double the number of cables connecting each appliance, we double
the amount of current they can carry. Another way of looking at
this is to say that if we double the number of cables, they
only need to have half the area, and thin cable is cheaper than
thick cable.
This principle is exploited in the wiring of 'ring' circuits in
domestic installations. Rings are almost always used in wiring power
outlets, and sometime in lighting as well.
In a ring, every socket outlet has
not just one live, neutral, and earth connection back to the
supply, but two; this is because the ring goes all around the
area served and then back to the supply.
This also explains why it is so dangerous to allow a ring to become
broken. In this situation there will only be one set of conductors
serving each power outlet. Some outlets will be on one side of
the break, and some will be on the other. So all will get a supply,
and it isn't obvious that anything is wrong. However, a doublegang
13amp socket can draw a current of 26 amps if two heavyduty
appliances are plugged in, and this may well be too high for a single
run of 2.5 mm^{2} cable, but well within the capabilities
of two such cables. There is a very real risk of the cable
overheating. In normal circumstances it is impossible to plug
in enough appliances to damage the cabling. Why? Because the fuse
or MCB has been chosen to suit the current rating of the cable
(see below). In a ring system, we will choose the fuse or MCB to
suit the capacity of the ring, not a single cable.
The fuse will normally be rated to trip at about 30A, which is
well within the capacity of the ring, but close to, or above,
the capacity of the single cable. So the fuse
won't protect us from plugging in two 13amp appliances:
26 amps isn't enough to trip the fuse, and the cable will
overheat instead.
Power is the rate at which an electrical appliance can consume electrical
energy, or the rate at which a generator can produce it. In the UK we are
charged for our electricity in terms of energy: the more energy we use, the
more we pay. A highpower appliance uses energy more rapidly than a lowpower
one, and therefore costs more to run.
Power is measured in watts, or in kilowatts. A kilowatt is a thousand watts,
and is a more useful figure when dealing with electric fires and heaters. The
abbreviations are 'W' (for watts) and 'kW' (for kilowatts). Note the positions
of the capital letters here. It is technically incorrect
to abbreviate kilowatts to 'KW'
(although plenty of people do, including electricity supply companies).
The mathematical symbol for power is 'P'.
If we know the voltage and current in an electrical appliance we can work out
its power. It turns out that power (in watts) is equal to the voltage (in
volts) multiplied by the current (in amps). In symbols this is:
P = V I
So, taking the lightbulb case again, its current (as we worked out earlier) was
0.5 amps, the voltage is (as ever) 230 volts, so the power is 115 watts (0.5 x
230)^{3}.
I don't think you can buy a 115 W lightbulb, so what current flows in a
100 W lightbulb? We can write the formula above in two other ways:
V = P / I
and
I = P / V
The second of these is what we need: it gives us current ('I') if we know P and
V. So the current in the 100 W bulb is (100 / 230) amps, or about 0.43 amps.
Here's another example. What rating of fuse do I need in a plug that
supplies an electrical kettle? Let's suppose the kettle has a power
rating of 2.5 kW (which is common). Since I = P / V ,
P is 2500 (watts), and V is 230 (volts), we have
I = 2500 / 230 , which is about 10.9 amps. Since plug
fuses are only usually only available in ratings of 3, 5, and 13 amps,
we need a 13amp fuse, this being the next rating up from the
calculated 10.9 amps. A 5amp fuse would probably blow quite
quickly, but we'll come onto that in a moment.
A lightbulb converts electrical energy into light and heat. A filament bulb
is very inefficient, in fact, producing about 50 times more heat than light. In
fact all electrical equipment gets hot in use, including wires. The amount of
energy that goes into heat can always be calculated if we know the voltage and
current, but for electrical cables it's easier to do it a different way.
Since we know that V = I R (from above) and that
P = V I , then
a bit of juggling symbols shows that
P = I^{2} R
or in words: power is given by multiplying the square of the current by the
resistance. (The square of anything is that number multiplied by itself). Let's
take an example.
Suppose an electrical cable had a resistance of 2 ohms. This cable is carrying
a current of 13 amps (which is the maximum allowed for a plugin appliance).
How much power is turned into heat by the cable?
Power is given by the square of the current times the resistance, so in this
case is 13 x 13 x 2, which is 338 watts. That's about the same as three
lightbulbs. So the electrical cable will get about as hot as three lightbulbs.
Apart from being a complete waste of energy (which you're paying for), this may
be enough heat to melt the cable, which would be a Bad Thing (especially if it's
underground). This explains why we need fat cables for highpower appliances
and can get away with thin cables for lowpower ones.
Fat cables have lower resistances, and therefore less energy is
wasted as heat, and they don't get hot enough to melt.
Is it all right to use
fat cables for lowpower appliances? Well, it doesn't compromise safety, but
it's not very costeffective. Thick cables are much more expensive than thin
ones. Another problem is that thick cables are much harder to work with than
thin ones.
Electrical engineers measure electrical energy in kilowatthours.
One kilowatthour, which is the same as 1000 watthours,
is sufficient energy to power a one kilowatt appliance for one hour.
Energy of 1
kilowatthour may be consumed by an appliance
that takes 1000 watts running for
1 hour, or an appliance that takes 1 watt running for 1000 hours,
or an appliance that takes 100 watts running for 10 hours, or
anything in between so long as the time multiplied by the power comes
to 1000.
The electricity bill does not distinguish between highpower and lowpower
appliances, only the total energy. You will normally be charged a certain
amount for each kilowatthour of energy, plus a certain fixed amount, in each
bill. Many supply companies are now offering charging schemes that
remove the fixed amount (standing charge) which
is good news for people who are careful with
electricity^{4}.
Here's an example. Suppose your supply company charges 10 pence per kilowatt
hour. How much does it cost to run a 40amp electric shower for half an hour?
Since power is voltage times current, the shower will consume 40 x 230 watts.
That's 9200 watts, or 9.2 kilowatts. So it would cost 9.2 times ten pence to
run it for one hour, or half that for half an hour. So the total cost is (1/2)
x 9.2 x 10 pence, or 46 pence. This is about the same price as running a
100watt lightbulb for two days.
Three main electrical conductors enter a domestic property, and are distributed
throughout it. These conductors are referred to as live, neutral and
earth.
The live and neutral conductors should be considered as the 'power supply' to
the premises. The voltage between live and neutral will generally be about 230
V AC. In all normal circumstances, current that enters the premises on the
live conductor leaves it on the neutral, and viceversa. The earth conductor
carries negligible current except in fault situations.
Although the live and neutral conductors both carry current, only the live
conductor is at a voltage that could be harmful. The neutral conductor will
normally be at the same voltage as the earth conductor. In fact, at some point
the neutral and the earth will be connected together. This situation is shown
in figure 6
Figure 6:
The origin of 'live', 'neutral' and 'earth' conductors in a domestic
premises

The figure grossly oversimplifies the real situation, of course; we don't each
have an electrical power station in the garden, delivering electricity at 230
volts. In reality the supplier's distribution system will be a complex mixture
of cables, transformers and switchgear, but this need not concern us. In
practice, we can assume that the electricity supply takes the form shown in
figure 6.
Note that the supplier's equipment is connected to earth at one side, and this is
what distinguishes 'live' from 'neutral'. The 'neutral' side is connected to
earth at the supplier's side. Your premises will also have a separate earth
connection, either brought in by the electricity supplier's cable, or attached
to a stake driven into the ground (which is the arrangement shown
in the figure above). The different methods of supplying an
earth are sometimes important, particularly when calculating whether
we need more electrical shock protection than earthing alone can
provide.
From the main cable entering the premises, live, neutral and earth conductors
will be distributed to every electrical appliance using a variety of different
cable types and sizes.
We have seen that electrical current causes a heating effect, and if the
current is large, or the electrical resistance high, this effect can be enough
to cause damage or a fire. Fire, as a result of overheating, is one of the main
risks from sloppy electrical work. However, the tendency of a high current to
cause a wire to melt and break is put to good use in the design of the fuse.
A fuse is a simple device that will limit the current flowing in an electrical
circuit. In practice a fuse normally consists of a piece of wire of exactly the right
length and thickness to overheat and break when the current gets to a
particular level. If an excessive current occurs, we hope the fuse will 'blow'
rather than some other part of the circuit overheating. This is
called overcurrent protection.
For now, the important thing to remember is that
the fuse must be able to withstand a higher current than the appliances to
which it is connected (otherwise it would blow unnecessarily), but a lower
current than the cables which connect them.
This ensures that in the event of a
fault, the fuse will blow before the cable is damaged.
While fuses are still widely used, miniature circuit breakers (MCBs) are now
increasingly replacing them.
On the whole it is moderate
overheating that is the problem in electrical wiring, not
huge current overloads. If you
get a shortcircuit between live and neutral in a power outlet, for
example, the current that will flow will be immense. Without a fuse
it could easily rise to thousands of amps. Now, although this would be
inconvenient, oddly enough it probably wouldn't be all that
dangerous, because the
cable will simply melt right through in a fraction of a second
and break the circuit. There would
be an enormous bang and a puff of smoke and that would be the end
of the problem. It will be the beginning of your hard work,
of course, as you struggle to find which floorboard the
burnedout cable is under, but that's a different matter.
On the other hand, if you ask a cable that is rated for a maximum of
6 amps to carry a current of 13 amps, and you have a 32amp
fuse or MCB, then you get no overcurrent protection at all.
The cable probably won't fail with a huge bang: it
will gradually heat up to about 250 degrees celcius, at which
point the copper will melt. However, it may take tens of
minutes to do so. In the meantime, you've got something that
is hot enough to combust wood clamped to your joists. See the problem?
Probably the most common cause of this problem — apart from
outright stupid wiring or fuse selection — is ring circuits
breaking and thereby halving their current capacities.
You can carry out electrical wiring using common sense and DIY
manuals. However, if you understand a bit about electrical theory then
you can work out how thick cables should be, what size fuses or MCBs
you need, how many power sockets you can run from a 32amp fuse, etc.
This isn't stuff you'll normally find out from DIY guides, because
the publishers think you're too thick to understand. In fact,
if you can multiply and divide, then you can work these things out.
Footnotes
 ...
symbol^{1}
 is the Greek letter pronounced 'omega', which sounds a
bit like 'ohm'. Oh, how we laughed...
 ...
it^{2}
 We can't completely ignore the parts of the electrical system outside the
house, unfortunately. For example, the resistance of the external part has an
effect on the current that will flow in a shortcircuit, and has implications
for selection of fuses and cables.
 ...
230)^{3}
 This
isn't exactly true, but in domestic situations it's close enough not to matter. If you want to know more, look up 'power factor' in a physics textbook.
 ...
electricity^{4}
 In schemes like this, if you halve your electricity
consumption you halve your bill. With a standing charge, the saving is not as
great, because the standing charge does not go down


