A Ten-minute Guide to Electrical.

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A ten-minute guide to electrical

theoryThis 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 thepractical 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 selectionfor 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, andfrequency.

Current

An electrical current is the flow of electricity around an electrical circuit. The flow of

electricity follows similar principles tothe 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, thedistribution 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 'Ampres', 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

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'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

earth-leakage 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 theflow 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 isapparent, however, is in the use of fluorescent lights.

Incandescent (filament) bulbs generate their light because the filament becomes white-

hot. 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

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 'electricalpotential' or 'electro-motive 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).

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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 writtenas '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 allmeasurements 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

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of safety.

Resistance

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, andlie 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 ' ' symbol1. 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 muchless than an ohm, for reasons that will be

explained.

The relationship between current, voltage andresistance

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 vice-versa. 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 / Rand 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 2shows 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.

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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 cross-section area of copper in the live and neutral

conductors, measured in square millimetres (abbreviated to 'mm2' or 'sq mm'). Electrical

power rings are very commonly made from 2.5 mm2cable. This means that each of the

live and neutral conductors has an area of 2.5 mm2. 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

Electrical circuits

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The main difference between an electrical system, and the water system shown in

figure 2is 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 theelectrical 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 it2.

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? Thereseem to be two basic strategies. The first, called 'series' wiring is shown in figure 4. The

second, 'parallel' wiring, is shown in figure 5.

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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 mustbe 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 heavy-duty

cable.

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Ring wiring

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 areacan 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 thissituation 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 double-gang 13-amp

socket can draw a current of 26 amps if two heavy-duty appliances are plugged in, and

this may well be too high for a single run of 2.5 mm2cable, but well within the

capabilities of twosuch 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 thecapacity 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 13-amp appliances:

26 amps isn't enough to trip the fuse, and the cable will overheat instead.

Power

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 high-power applianceuses energy more rapidly than a low-power 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

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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 iscommon). 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 13-amp fuse, this being the next rating up

from the calculated 10.9 amps. A 5-amp 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 = I2R

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 plug-in 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 13x 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 high-power appliances and can get away with thin cables for low-power

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 low-power

appliances? Well, it doesn't compromise safety, but it's not very cost-effective. Thick

cables are much more expensive than thin ones. Another problem is that thick cables are

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much harder to work with than thin ones.

Energy, and your electricity bill

Electrical engineers measure electrical energy in kilowatt-hours. One kilowatt-hour,

which is the same as 1000 watt-hours, is sufficient energy to power a one kilowatt

appliance for one hour. Energy of 1 kilowatt-hour may be consumed by an appliancethat takes 1000 watts running for 1 hour, oran 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 high-power and low-power

appliances, only the total energy. You will normally be charged a certain amount for

each kilowatt-hour 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 electricity4.

Here's an example. Suppose your supply company charges 10 pence per kilowatt

hour. How much does it cost to run a 40-amp 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 100-watt lightbulb for two days.

Live, neutral and earth

Three main electrical conductors enter a domestic property, and are distributed

throughout it. These conductors are referred to as live, neutraland 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 vice-versa. 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

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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.

Fuses and over-current protection

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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 anexcessive current occurs, we hope the fuse will 'blow' rather than some other part of the

circuit overheating. This is called over-current 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 moderateoverheating that is the problem in electrical wiring, not

huge current overloads. If you get a short-circuit 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 beginningof your hard work, of course, as you struggle to find which floorboard

the burned-out 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 32-amp fuse or MCB, then you get noovercurrent protection at all. The cableprobablywon'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.

Summary

You can carry out electrical wiring using common sense and DIY manuals. However, ifyou 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 32-amp 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

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... symbol1

is the Greek letter pronounced 'omega', which sounds a bit like 'ohm'. Oh,

how we laughed...

... it2

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 short-circuit, and has implications for selection of fuses

and cables.

... 230)3

This isn't exactlytrue, 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.

... electricity4

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

Copyright 1994-2013 Kevin Boone. Updated May 14 2010