(and all that)

An introduction to electrical circuits

By David C, 2014

Take the battery out of a car and attach a piece of wire to the terminals.

Well, actually, don’t do this. The action would hurt you very badly, from what I have read, possibly even kill you. No, when I say go do something, I actually mean imagine yourself going to do something, as I am now. I’m imagining myself attaching a wire to a car battery in such a way that I don’t get hurt.

We know that a car battery makes electricity and that a wire conducts electricity, and that the whole point of having a wire connected to a battery is to get electricity from the battery to someplace else.

So, what if I have a piece of copper wire, and I attach one end to the battery and the other end to a light-bulb: how come the light-bulb doesn’t glow until I run another length of wire back to the battery? If a battery is like a gas bottle releasing electrons into a wire instead of compressed gas into a cooker, how come I need to send used-up electrons back into the bottle?

*

The first battery I know of was a dead frog in Italy, about 200 years ago. Well, to be honest I’ve also read about batteries made in Baghdad about 1600 years before that, but those earlier batteries don’t help my story at all so I’ll pretend that they don’t exist. The first battery in the world (ahem) was a dead frog in Italy, in 1781.

To be a little more precise, it wasn’t a whole frog, just the legs that had been cut from the rest of the frog by a surgeon named Luigi Galvani in order that he could better understand how frogs worked. This is an important element in the story: Galvani wasn’t a physicist and wasn’t looking for electricity, he was a surgeon, a fellow who wanted to learn more about anatomy.

The legs, still moist and in good condition following the dissection, were attached to the table by a brass clamp. Signore Galvani began to slice into the muscle with an iron knife, and as he did so, his knife brushed against the brass clamp that was holding the legs in place. The legs twitched.

Yep, the legs of a dead frog twitched. Creepy, to be sure, although not entirely unique. Frogs legs had been observed doing this sort of thing in earlier times, for example twitching in response to flashes of lightning on stormy nights. The limbs of dead animals were also known to twitch when given a shot of electricity from a Leyden Jar, a kind of bottle for storing large quantities of electricity. Yes, it was already well known that a shot of electricity from somewhere would cause the muscles of a dead animal to contract, and that the legs of a frog moved particularly well because of their great length and low weight. So it wasn’t really the fact that the legs were twitching which bothered people (although it bothers me as I write this), it was the fact that the legs were twitching in the absence of electricity.

It was as if the frog had its own supply of electricity, built into the muscle and still stored there even though the rest of the frog was gone.

This is creepy stuff. Was electricity the long suspected spiritual force that kept animals alive and which wafted off to some other world when the animal died, or hung around in the air as some ghostly after-effect? I can imagine – rightly or wrongly – that Mr Galvani was treated with a certain level of suspicion by his neighbours and may not have had too many invitations to dinner where he lived.

But Galvani was a highly respected man at the university where he taught surgery, and if he suggested that there was such a thing as ‘animal electricity’ then the idea was not to be snorted at. Perhaps if the legs of a dead frog could be made to twitch on the operating table then maybe an entire dead man could be made to walk again by somehow releasing its stored electricity, or replenishing it with electricity from elsewhere. If that’s the case, you’re only a few nightmares away from Frankenstein’s monster.

I actually wrote those words in an early draft of this essay, not realising until a few days later just how literally true they were. Some fifty years after Galvani’s famous frog dissection, Mary Shelley obtained a book written by Galvani that described his ideas of animal electricity. It included a description of the frog dissection which had started him on this line of research. Miss Shelley actually had this book with her as ‘light reading’ on that famous holiday weekend when she created the story of Frankenstein. How cool a connection is that?

Well despite 150 years of bad copycat literature based on Shelley’s beautiful novel, we know that dead animals don’t generally walk around in response to lightning. Hmmm, well, electric shocks are used to reactivate stopped hearts, but that’s a digression I don’t need to go into right now. I want to focus on the questions raised by Galvani’s discovery: What is it about a frog’s leg, an iron knife and a brass clamp that causes a flow of electricity?

*

Alessandro Volta had an idea. He’s another Italian university professor of the day and a friend of Signore Galvani. He set up a copy of the frog leg experiment, and confirmed that it worked, and then set about changing things to determine what in particular was going on.

The first thing to note was the importance of the two metals. It wasn’t sufficient to touch the frog leg with just a knife or a clamp but by both, and these items had to be made of different metals. An iron knife touching an iron clamp doesn’t make a muscle twitch.

Attention then shifts to the frog’s leg. How necessary is the leg in generating electricity? Could it be replaced by other things?

Signore Volta explored this possibility and found that he could get the same effect from a jug of salty water. To be sure, the jug wasn’t twitching, but it was sending a steady flow of electricity into the two metals, which could be verified by the simple electroscopes of the day. So it seemed that the wonderful life force that Galvani had discovered was actually something to do with the salty water in the muscle tissue rather than the tissue itself. It was more to do with metal wanting to rust than with dead animals wanting to walk.

Shall we say that the muscle in a frog’s leg is a powerful chemical reaction poised and ready for action, normally activated by a small electrical impulse from the frog’s brain. If there is no brain there is no impulse, but as long as the nerve fibres leading into the muscle are still in good condition then that powerful knee-jerk reaction is still possible and could happen if an electrical impulse came in from any source.

That small electrical impulse comes from the metals trying to rust. Iron really wants to rust in the salty environment of the frog’s leg but it can’t. What it can do instead, however - and do so quite easily - is to push electrons onto the zinc and copper atoms in the attached brass clamp. These atoms have no particular interest in gathering electrons themselves but quite happily pass them on to other places further away, like the tissues at the other end of the frog’s leg.

This results in an abundance of electrons in the salty water where the brass clamp touches the frog leg, enough to trigger the knee-jerk response that caught everyone’s attention. The electrical impulse travels down the nerve fibre to the other end of the muscle, where electrons are released into the salty water in the vicinity of the iron knife. This makes it possible, at last, for the iron to interact with the salts and to rust.

In effect a train of electrons has found it easier to take the long road to its destination rather than take the more difficult short path. As is the case in all batteries, a chemical reaction has been separated into two parts: a part where electrons are being thrown away and a part where electrons are being absorbed. If a metal wire connects these two parts, then a current will flow through the wire. Plain and simple.

*

That answers the question I raised at the beginning of this essay: electrons will flow out of a battery only if there are other electrons ready to flow back in from the other side. Electrons are not pushed out of a battery like compressed air pushed out of a gas tank, they are trying to flow from one side of the battery to the other, and the only way they can do this is to go the long way, through the wire. Disconnect the wire from the inlet end of the battery and the electrons lose interest.

*

My next two questions are, how long will the battery operate for, and how brightly will the light-bulb glow? I ask both these things at the same time because both of them depend on how quickly the electrons zoom around the wire, from one side of the chemical reaction to the other.

A typical car battery can push somewhere between 1,000,000,000,000,000,000,000,000,000,000 and 2,000,000,000,000,000,000,000,000,000,000 electrons from one side of the battery to the other side before its salts are used up. That’s a number with thirty zeroes behind it. If the electrons travel very quickly, then the journey resembles a lightning bolt and everything melts.

Of course, it makes more sense to have the electrons travel slowly. I could scoop electrons out of the battery a couple of thousand at a time and have a battery that lasts a lifetime. But the light from the bulb will be very dim, like that from a glow-worm.

So how slow is too slow? How do I determine such a thing?

*

There’s a formula which helps with this sort of calculation, a formula you should get to know if you’re ever going to do anything with electrical circuits.

Some people call it Ohm’s law while others simply call it the electricians’ rule, in recognition of the fact that electricians use it all the time. In fact, because of its down-to-earth practicality, the electrician’s rule is probably the most frequently used formulae ever created.

I = currentV = VoltageR = Resistance

Personally, as a teacher, I prefer to write the formula like this...

...because then I can see how the speed of the electrons depends on the forces that speed it up and slow it down.

Written as a fraction, you can see that the speed at which electrons travel round a circuit is a trade-off between the push (V) from the battery and the friction (R) in the wire.

I = currentV = VoltageR = Resistance

If we say that the push from a battery is 24 Volts and arbitrarily say that the resistance throughout the circuit adds up to 6 Ohms then the ‘speed’ at which the electrons travel will be

How fast is that in kilometres per hour?

That’s a really difficult thing to explain right now so I’m going to avoid that question completely and hope you won’t remember it for a very long time. Just accept for now that 4 amps is a very strong current and the electrons therefore are probably moving very fast.

A quick search on the internet actually surprised me. A current of even 1 Amp is very big. Most everyday currents are measured in milliamps. A single amp will kill you under the right circumstances, the websites all say. So whatever you do while reading my essay, don’t go out and connect a wire to a car battery. The outcome will not be very nice. Your parents will be angry at me.

*

The ‘amp’ measures how quickly electrons are whistling around an electrical circuit, and was created at a time long before anyone really knew what electricity was, or even which way round it was going. Does the electricity go from the negative terminal to the positive, or the other way round? No-one really knew. All they could say was that if an amp’s worth of electricity was passing through a circuit – in whatever direction – spectacular things would happen, and if you doubled the current, the spectacular nature of those things would double.

We now know that an amp is about 6 trillion-trillion electrons, all travelling in the same direction at once, all leaving the battery in the same second. That’s six with eighteen zeroes behind it, a number so vast that there are few things on Earth that can match it, not even the US financial debt. 6,000,000,000,000,000,000 American dollar bills stacked in a pile would reach not just as far as the Moon but would reach right out of the solar system, requiring more paper than there are trees on Earth to provide it.

That’s a lot of electrons. And yet at least that many electrons are on the march through the light bulbs and ovens and microwaves and TV sets of our houses at any given second in time. We may think that human migration in the twenty-first century has reached an all-time high, or that money is changing hands faster in our age than ever before, but if we really want to know what it is that is moving the fastest as a result of our human busy-ness, it’s electrons. Think of how many electrons are on the go in all the household appliances and street lamps in all the cities and towns of the world. We are champions at moving electrons!

*

The electricians are already screaming at me from the sidelines. “Voltage is NOT a force,” they are saying, “and current is NOT a speed, and resistance is NOT friction!” They’re quite right, of course. I’m bending the truth quite a bit to make it easier for me to teach and for you to learn. However, Voltage is enough like a force that I can pretend (for now) that it is. You can’t have a voltage without a force. One necessarily goes with the other.

Same argument for current: Current is not exactly a speed but it’s enough LIKE a speed that I can use the terms interchangeably most of the time.

As for resistance, it’s so much like friction that it barely matters that it’s defined in different units. When you think of electrical resistance in a wire, I want you to think of electrons going clunk-clunk-clunk down a turbulent river filled with boulders. The motion of the electrons consists mostly of sliding from one rock to the next. Each time an electron hits a boulder or scrapes past it, it causes the rock to vibrate. That means that the rocks – in theory at least – are warming up as they absorb energy from the electrons. We don’t see heat being generated in rocky rivers but we do see it generated in electrical wires: attach a wire to a battery and the wires warm up, sometimes frighteningly fast. How quickly they do depends on how rough the journey down the wire is, and how hard the battery is pushing. If both numbers are high then the wire will melt.

We can see proof of that in another formula that you should become familiar with.

In a circuit where the current is 4 amps and the push from the battery is 24 volts, the energy leaking out of the battery every second is 4x24=96 Joules. That’s a lot of energy. What comes out of the battery goes into the circuit as heat. Another formula allows me to work out how much heat is being generated in a circuit like this.

Without going into too much detail, the formula tells me that a copper wire absorbing 96 joules of energy every second from a car battery pushing electrons at 24 volts will be hot enough to melt in a matter of seconds.

P = PowerV = Voltage I = Current

Well, maybe this won’t happen because I haven’t taken into consideration how much heat will radiate off into the air around the wire before it melts. Maybe the wire won’t actually melt but it will get very, very hot in a very short period of time.

This kind of explains why we have electrical circuits in the first place. A wire carrying a very high current will get hot and will act like a heater. If it gets really hot it will glow, in which case I’ve just reinvented the light-bulb.

But there are better ways to warm up the house than pumping electricity into an unprotected piece of wire. Perhaps if I made the copper wire longer, the resistance would be greater and the electrons would move more slowly, which means there would be less friction in the wire, which therefore means there would be less heat. That’s a good idea, except that there are ways of calculating just how much wire you would need to bring the current down to a safe level, and the numbers tend to be very big. To bring the current from a car battery down to say, 1 amp, you’d need a copper wire about 80 metres long. Even at this length I have a wire that’s too dangerous to touch and which will singe my carpet if I leave it in operation too long.

This is all very upsetting. How am I supposed to get electricity out of a 24-volt car battery without melting the wires or setting fire to something? There’s just too much heat!

*

Meantime, back in 1781, Il Signore Alessandro Volta is wondering what to do with his jug of salty water. The only reason he created this thing was to investigate his friend’s claim that dead animals kept a secret store of biological electricity, and he had proven instead that it was salty water that stored electricity. The frog leg was just a twitchy part of the circuit. He’s still got this apparatus in his laboratory – the jug, the water and the loop of wire half submerged in it – and he’s wondering if there’s anything else he can apply it to. This assembly causes electricity to flow. Surely that’s of interest to other people. Er, right?

*

Before the days of the twitching frog and the saltwater jug, the only way to make electricity was to rub your hands against certain waxy or powdery materials. The best way to do this was to grind the material into the shape of a ball and spike it onto the axle of a spinning wheel so that you could crank the handle with your feet and make the ball spin rapidly between your hands. The static would get into your fingers and run up your arms into your clothes, and when you walked away from the spinning wheel you could crackle and sparkle in front of people, and shock them when you touched them. You could put on a real show if you wanted people to respect you.

An even better trick was to accumulate the charge in a metal container and store it there in large quantities until someone came to your house. Then you could touch the container with a metal spike on the end of a long wooden pole and point it at people, and if you did it just right you’d hear a loud crackle, see a flash of lightning shoot from the stick to something metallic or wet, and people would drop to their knees and beg for your mercy. And if any of this sounds at all Harry Potterish, just remember that it all started with static electricity in the Middle Ages and ended with Galvani’s twitching frog leg and Volta’s jug of salty water.

So what is electricity, then? More importantly, what was electricity in the eyes of someone who lived in the 1700s? At this time, electricity was being extracted from all kinds of materials, from hardened wood sap to chunks of sulphur rock, and now it seemed even from the limbs of a dead animal.

Ben Franklin in America – the man with the kite in the 1750s – was able to show that all these different kinds of electricity were one and the same, and all that was happening was that SOMETHING – some strange invisible liquid - was flowing from a place where there was too much of it, to a place where there was not enough of it. He didn’t know what was actually flowing, and had no reason to suspect that anyone ever would. So he just called it ‘electricity’ like everybody else, and said that too much of it was a positive charge and not enough of it was a negative charge. Whatever this invisible stuff was, it came out of certain materials and was absorbed by certain others. It was weightless, odourless, colourless and yet could kick like a mule if you let it.

Looking back with historical hindsight we can see that Volta’s jug of salt water was as important a development in the history of science as the radioactive rocks analysed by Madam Curie a hundred-and-something years later. It was energy seemingly coming out of nowhere, an endless supply of it. And yet no-one at the time could have cared less because the idea of energy - even the word ‘energy’ - hadn’t even been invented yet.

What could you do with electricity in the 1790s? Light a house? No-one would think of this possibility for nearly a century. People in the 1790s used candles to light houses. Who needed a light-bulb?

What about electrical heating? You’ve seen from my demonstration that you can melt metals with it or make things very hot. But Volta’s jug was hardly in the same league as a modern car battery. Besides, you’d need copper wire to make electrons move that fast, and in the 1790s most electricity was still being conducted by wet bits of string. No-one had a reason for making copper wire before the invention of batteries, so there was no place to go and buy it. So what possible advantage could there be to a fizzing jug of water in comparison to a burning log in the fireplace? These were simply not questions being asked this early in history because no-one had reason to think of them.

Signore Volta could easily have just poured the water down the drain and put the jug back in the cupboard, but he didn’t. Perhaps if he could make the electric current just a bit stronger, he might be able to do something useful with it.

He tinkered with a number of improvements, first of all linking several jugs of water together so that the trickle of electricity from each could combine into a much stronger current. Later he dispensed with the jugs completely and replaced them with slabs of cardboard soaked in salty water, and sandwiched them between plates of copper and zinc. The whole thing looked no doubt like a multi-layered hamburger and stood about half a metre high. People called it Volta’s electric pile, which over time abbreviated to Voltaic Pile, a device that sounds like it could bend space into four dimensions but in fact generated just one volt of electricity for about an hour before the moisture dribbled out of the cardboard and made a smelly mess on the table.

There’s a painting of Volta some years later showing this ‘electric pile’ to Emperor Napoleon, who had just succeeded in annexing that part of Italy into the French Republic, thereby making the Italian invention a French one. I have to wonder what Napoleon made of this dripping stack of metal and cardboard plates that could make attached objects spark and crackle. Could he have seen it as a brilliant new invention, or simply a peculiar plaything for bored professors? I can imagine him thanking the good scientist politely and walking away and wondering why universities employed people like this. That’s what I’d be thinking if I was in his shoes.

*

Perhaps Napoleon would have been more impressed if he could have seen a light-bulb come to life when attached to Volta’s soggy pile. But light-bulbs would not be invented for at least another 90 years. Imagine: it took more time to think of adding a light bulb to an electric circuit than to add a steam locomotive to a railway line!

But light bulbs are not easy to make. Thomas Edison and his staff worked for years on the problem, going through many, many different materials that glowed very nicely when electrified but which would burn out in a matter of seconds due to their own heat.

Edison’s people had to stop asking the obvious question “What material will resist burning?” and start asking the less obvious question “How do I stop ANY material from burning?” When his people switched their attention to this question, the light bulb became inventable.

Take a piece of material and put it inside a glass bottle and suck the air out. Things only burn when they are exposed to air. No air, no burning. Well, that oversimplifies things dramatically, but you get the basic idea. Light bulbs only last as long as they do because they have no air in which to burn.

The filament of a light bulb is a very short piece of wire designed to squander energy on a huge scale. It needs to slow electrons down dramatically so that the energy of friction makes the wire hot enough to glow, not just a sombre orange red but a dazzling pure white.

Think of how hot ordinary materials have to be in order to glow white hot. Take a hunk of iron and put it into a furnace. To begin to glow at all it has to reach 700 degrees Celsius. To reach white heat it has to reach nearly 1100 degrees. That’s the sort of heat you get on the underbelly of a spaceship during re-entry. Are light bulb filaments as hot as all that? I’ve no idea, but I’m never going to touch one.

(update after consulting the internet: light bulbs reach over 2000 degrees Celsius, definitely hotter than a space shuttle re-entry).

*

If I could I would put a light-bulb into a time machine and TARDIS it back to Signore Volta so that he could show people what electricity really could achieve. But even that would be a waste of effort because the batteries of the time were just too weak to do anything very impressive. Modern light bulbs require 230 volts to make the kind of light we are used to. Volta’s soggy cardboard pile generated about a single Volt, which means just 1/230 th of the force required to make the bulb glow properly. Il Signore Volta would have had to close the curtains and look very closely to see any light coming out of that bulb.

The problem is always to do with the strength and durability of the battery. It would take a generation of further tinkering by other scientists to make a battery which didn’t leak or rust or run down so quickly, which could be carried easily from place to place. And even so, the amount of force these new batteries produced never get much bigger than the 1 volt of Volta’s original cardboard-and-metal pile.

You can see, then, how the ‘volt’ got set to the value it still has today. One volt of electromotive force meant essentially the force of one generator. To get two volts of force you needed two generators. Twenty volts could be extracted from twenty generators. The word ‘volt’ really just told you how many generators you needed to connect together.

And that’s how the word ‘battery’ got associated with electrical generators. To do anything interesting with electricity, you had to have a stockpile of these things working in unison, spread across your laboratory table or perhaps packed into a neat box under it; a ‘battery’ of generators.

Now people could have serious fun with electrical circuits. Humphrey Davy in the UK had the biggest, most powerful battery in the world in the 1830s and he used it to give public demonstrations once a month, demonstrations that probably involved great thunderbolts of lightning arcing noisily between metal rods, witnessed by a breathtaken audience. The wonderful thing about Davy is that he didn’t describe the phenomena as anything more or less than what it really was. No supernatural demons or forest spirits in his explanations, or incantations in ancient tongues to pagan gods, Davy simply explained his magic in terrestrial terms, as electricity going from one place to another, noisily and ferociously.

But Davy was much more than a showman. He was a serious, pious man who wanted to pull back the fabric of the universe a little bit and see how it worked. Most of the time he could be found in his laboratory with his assistant Michael Faraday (another genius), the two of them putting vast amounts of electricity into things just to see what might come out.

For instance, there was the time they put electricity into a vat of soda water and found a hitherto unseen metal forming on one of the electric plates. It needed a name so he called it Sodium. Then on another occasion he applied electricity to a material called potash. Guess what came out? Another unknown metal, which he called Potassium. In all, about a dozen new elements were discovered by Sir Humphrey Davy and Michael Faraday. No one person (or pair of people) before or since has discovered so many elements on the Periodic Table.

We should remember that in any new discovery, usually two things emerge: one is the new product you were looking for, and the other is the PROCESS you used to get what you were looking for. Often it will be that the process you developed turns out to be more important than the thing you made from it, because that process can then be applied to other things as well.

Electroplating became a big deal in the industrial revolution because it meant that a thin layer of costly silver could be coated onto a knife or fork or spoon made of common old iron. Not only does it look better, it doesn’t rust when you dip it into your soup.

These pedantic and pretty applications of electroplating no doubt helped pay for the more serious uses of the process: for example, you could protect ships from the corrosive effects of seawater by coating them with a layer of atoms that have no interest in rusting, a process called galvanising, in honour of you-know-who.

Galvani’s name is remembered in other ways. When my Mum sees me lying on the couch and speaks of “galvanising” me into action, she is unknowingly (or perhaps knowingly, I’m not sure) describing me as a dead animal that has to be brought back to life with an electric shock; not too wrong a description, really.

Electroplating may have been a big deal in the industrial revolution, but the idea itself may have not been so new as I’ve described. Remember those original batteries I didn’t want to talk about at the beginning of this essay? The ones found in Baghdad that date back to 200AD or thereabouts? Cylindrical copper plates were found inside, which our experts today think might have been used for electroplating.

*

It’s been so long now since I asked my question that you probably don’t even remember me asking it. It was several pages back, remember, when I attached a 20-metre length of copper wire to a 24-volt car battery and watched the wires singeing my carpet and asking ‘How does anybody get electricity out of a battery without melting or setting fire to something?’ The heat generated by a flow of electrons is just too great, even at the best of times.

Well, I think I have an answer. Watch what happens when I attach an ordinary light-bulb to a 20-metre length of copper wire and connect it all to a 24-volt car battery.

Remember from my story that light-bulbs have to get very hot to work properly, and that this requires that they be very strong resistors. The light-bulb shining over my head right now has a resistance of 100 ohms, much more than the resistance in the wire and deliberately so because that’s how you squeeze energy out of a train of electrons: resistance.

So adding a light-bulb to a 20-metre length of copper wire increases the total resistance from 6 ohms to 106 ohms. Watch what happens to the current.

Can you see that the light-bulb is doing the wire a favour? It’s slowing the current down to the point where it will no longer harm the wire. Now instead of taking a minute to reach melting point, the wire needs quarter of an hour, which realistically means the wire has seventeen times as long to radiate that heat into the atmosphere. Under those conditions, it won’t really heat up at all, at least not by more than a few degrees.

I’m having a genuine moment of discovery as I write all of this. NOW I can understand why there is a market for electrical components called RESISTORS that are especially designed to waste energy. Why would anyone pay for a component that throws away good energy? Simply put, resistors are there so that you can slow electrons down and stop your circuit from overheating.

At the same time, you can make your battery last longer. In a circuit where the electrons are moving seventeen times slower, you can draw power for seventeen times as long. This 24-volt car battery would have been drained in 15 hours by the copper wire alone, but adding a light-bulb to it extends its lifespan to 11 days!

*

This is great news. But maybe the news is just a little too great because the current has slowed right down to a trickle, just one-seventeenth of what it used to be. Now instead of getting 96 joules of energy out of the battery per second, I’m only getting 5.5.

5.5 joules of energy per second, also called 5.5 watts, is not an awful lot. Even if all of that power is going to the light-bulb then it’s glowing with the ferocity of a lighted match. Even if it does last for 11 days, the light of a matchstick is not going to be very useful.

So what options do I have for making the bulb glow more brightly?

Maybe I could reduce the length of the copper wire so that there is less friction in it. That would make the current go faster and that means more energy would be dropped off at the light-bulb.

Don’t get too excited, however. Even if I could somehow remove the copper wire completely, I’d be dropping the resistance in the circuit from 106 ohms to 100 ohms, an improvement of just 6 percent. That means a six percent increase in power going to the light-bulb, a herculean increase in power of just one quarter of a watt!

There has to be a better way. How about wandering down to the hardware store and buying a much smaller light-bulb, the kind you’d get in a torch? Those tiny bulbs have resistances of just 5, 10, or 20 ohms. Less resistance in the bulb means faster current which means more power.

Okay, so let me see what happens when a 10-ohm light-bulb is connected to a 24-volt battery by a wire that has 6 ohms of resistance in it.

Altogether there are 16 ohms of resistance.

24/16 = 1.5 amps

1.5 x 24 = 36 watts

This looks great, but how much of this power is going into the bulb as light and how much of it is going into the wire as waste heat? That depends on the fraction of resistances provided by both parts. The light provides 10/16ths of the resistance so it gets 10/16ths of the power in the circuit. 10/16ths of 26 watts is about 22.5 watts. Nearly half of the power drawn from the battery is wasted, but at least we’re getting a good supply to the light-bulb.

Maybe I should try some other light-bulbs, ones with bigger or even smaller resistances.

If you draw a graph of the performances of the various-sized light-bulbs, you’ll see that the performance doesn’t get consistently better in either direction; bigger resistances or smaller resistances. Bigger resistances just slow the current down too much so that the power supply becomes tiny.

At the other extreme, tiny resistances allow bigger currents, but most of the power gets wasted in the wire.

The best performance comes from a hypothetical light-bulb resistance of 6 ohms.

Under those circumstances we get a light bulb using exactly half of the power coming out of the battery: 24 watts.

Will the wire still heat up and melt? It might because it’s also absorbing 24 watts of power from the battery. That’s a quarter of what I calculated at the start of this essay when all I had was a 20-metre length of wire connected to the battery. Theoretically it should take four times as long to overheat: four minutes, maybe, instead of one. I wouldn’t want to put my hand on it, but it may be good enough to work. At least I can say (with some finality) that this is the best I’m ever going to get from this circuit. If I really want to run a light off a battery then maybe I should use a smaller battery like...like a torch battery. Hmmm... Maybe that’s why torches were invented.

For 100 years between 1750 and 1850 the story of electricity was the story of an invisible electrical fluid that somehow flowed through metals and liquids but didn’t flow through other things.

By that stage, however, people were beginning to suspect that electricity was made of hard stuff, not liquid; tiny particles that made up the chemicals from which electricity came.

Electrons are funny things. They are incredibly light, which means that they can move very quickly when they’re pushed. Their low mass means they can stop in an instant if they have to, or turn sharp corners at high speed that would have bulkier creatures like us skidding round in broad arcs. They have essentially no inertia. They are the lightest mass-carrying objects we know of.

Ask an electron what it thinks of gravity and its answer will be interesting. An electron experiences as much gravitational pull from the centre of the Earth as we humans experience from the centre of the sun. Do you feel any lighter when the Sun is directly overhead? That’s what an electron feels about the Earth.

But here’s the strangest thing of all about electrons: they do not seem to have any physical size. They are not just very, very small, they are no size at all; just pin-pricks in space that somehow carry mass and electric charge.

At this extremely small level, and I mean very, very, very, very, very, very, VERY small level, nothing we can talk of makes sense. We can say that an electron is a dimensionless point in space, but only if we acknowledge further that that point has to lie within a region defined by its wave form. In a sense, the electron is an infinitely small butterfly that can be anywhere inside a butterfly net. We can’t see the butterfly but we can see the butterfly net, and that will have to do.

The existence of the electron was not proven until 1897 even though it had been suspected for a very long time before that, simply because of the association electricity has with chemistry: theories just made a lot more sense if atoms were trading electrical particles instead of oozing electrical water.

1897 isn’t really that long ago. My grandparents were already alive at this time, and probably so were many of your great-grandparents. I can imagine my great-grandfather reading of the discovery in his morning newspaper: “It says here that the electron has been discovered.” To which my great-grandmother responds, “That’s nice, Dear. More tea?”

The discovery of the electron would not have changed the world very significantly outside of the universities and schools where science was taught. But within those nerdist enclaves of learning, it was a very, very big deal.

Well, to some scientists more than others. Some would have argued that the final proof of the existence of charge-carrying particles was unnecessary because electricity had been harnessed and put to good use for over fifty years by this time without anyone knowing or caring about these particles. Did it really matter how big or small they were?

Well, there are some things you confirm by experimentation and other things you are caught off-guard by. One of the surprises was the charge carried by the electron: it was negative instead of positive, the complete opposite to what people had assumed for the previous 150 years.

How could this possibly have happened? Who got it wrong in the first place?

Ben Franklin in the 1750s had two electrically-charged objects in his workshop and joined them together and observed that the combination of the two made both disappear. It was proof that electrical charges came in opposites, and that a ‘positive’ charge could mean too much of something and a ‘negative’ charge could mean too little of something. But which was which? I get an impression of the bespectacled Mr Franklin holding the two objects in his hands, and sweeping his eyes back and forth from one to the other and saying after a while, “That one”. And so the object in his left hand became the positive charge and the one on his right became the negative charge, and electricity flowed from left to right.

And that’s how it was for the next 150 years. Generation by generation, textbook by textbook, teachers and students followed Franklin’s suggestion until people forgot that it was merely a suggestion and treated it as an unchallengeable fact.

Well, this is where we should say “Oops” and try to correct the situation. “Electrons have the opposite charge to what we have been saying for 150 years, which means that the current is actually going in the opposite direction to what we assumed. The arrows in our textbooks for 150 years have been back-to-front. What we said was all back-to-front.”

But does it really make any difference which way the arrows are pointing? The effect is the same whether we assume that an electron moves to the left or the empty space left behind by a moving electron moves to the right.

I remember my own physics teacher comparing it to watching kids climb over the seats in a bus, from the back seat to the front seat. Is it the kids climbing towards the front of the bus or is it emptiness climbing over the seats towards the back? If the seats were as small as electrons, you could easily be mistaken.

The outcome has been that the world has decided (without asking me) to perpetuate the mistake rather than to correct it. So another hundred years have gone by with the mistake perpetuated; “current goes from positive to negative” the books still say, implying that electrons swim upstream like salmon instead of bounce downstream like rocks.

As a teacher I find myself in a strange situation because of this. I know the mistake is harmless but knowing it’s a mistake makes me uncomfortable when I teach. I am now obliged in the 21st century to mark a student’s homework wrong if the arrows in his electrical circuit diagrams go in the right direction and tell him to turn the arrows round the other way and perpetuate the mistake. We ‘correct’ correct homework by de-correcting the correctness of it.

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This is the first of two reasons why I didn’t want to tell you how fast the electrons are travelling in a 4 amp current, all those pages back, near the beginning of this essay. For one thing, the electrons are going in the opposite direction. Current goes from positive to negative while the electrons go from negative to positive.

Then there’s the other reason.

Sigh.

You see, the truth is, electrons do not zing around a circuit in the way that you might think they do. Electrons cram into a wire at one end and cause electrons to fall out the other. These are not the same electrons.

If you pushed your way into a crowded football stadium you would probably be responsible for some poor chap being pushed out the other side. Seen from above the roof of the stadium, it might look as though you had rushed from one side of the stadium to the other – changing clothes along the way – to fall out the other side. Electrons all look the same so they don’t have to change clothes to fool us into thinking that a single electron is moving through a circuit at extraordinary speed. Truth is, electrons move very slowly through a circuit - measured in millimetres per second – even though the current can be close to the speed of light. What we see as electrons moving is actually a shock wave of electrons crashing into each other and pushing each other out of the way.

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We’ve come a long way in this essay now, some 7000 words so far as I write them, and it may seem that we have covered all of the important stuff about electrical circuits.

But let me challenge you with some fundamental questions:

ONE: Why is it that electrons travel at the same speed around the circuit instead of rushing up to the light-bulb and slowing down only when they get to the light-bulb? That’s where most of the resistance is, so surely that’s where the speed is the slowest.

Well, think of electrons as cars cruising down a motorway. There’s a rough bit of road up a head: earthquake damage, so there’s lots of potholes and orange cones. All the cars going through it have to slow down. That causes a traffic jam that backs up cars all the way back to the battery. But remember that cars don’t come out of the battery any faster than cars going into the battery from the other side, so the slow-moving traffic goes right through the battery all the way round to the other side of the light-bulb. Conclusion: ALL electrons in a circuit travel at the same speed, whether they are going through the congested bit of the circuit or not.

TWO: Why does the resistance of the wire get added to the resistance of the light-bulb?

As a student, many years ago, I had the idea that electrons would be moving so slowly because of the light-bulb that they should have no trouble slipping through the rough bits in the wire. Therefore there should be no further decrease in speed. The speed of the electrons should depend on only the biggest single resistance in the wire, not the resistances of everything added together.

The conclusion is wrong because the picture painted is wrong. These are not cars cruising down a motorway but electrons rock-hopping down a river in which the stepping stones are copper atoms. Atoms are sticky. An electron jumping off one atom to get to the next has to overcome a wee bit of electrical pull by each atom it touches, and that costs energy. Outcome: the resistance in the wire is important too. All resistances in a circuit add up to determine how quickly the current flows, no matter how small those individual resistances may be.

THREE: - and this is the biggie – What kind of energy is being carried around the circuit? It starts off as chemical energy in the battery and ends up as heat in the wire and in the light-bulb, but while the electrons are carrying it, is it kinetic energy or potential energy or something else?

We know from school that moving items have kinetic energy so it makes sense for us to visualise the electrons as having kinetic energy as they go round the circuit, and they lose it a bit at a time as they collide with atoms in the wire and in the light-bulb. BUT HERE’S THE PROBLEM: if electrons lose kinetic energy as they go, they ought to be slowing down, but they’re not!

We have to acknowledge that electrons travelling at constant speed neither gain nor lose kinetic energy. Although the electrons certainly do have kinetic energy, it doesn’t feature anywhere in these calculations because it doesn’t change. The energy being passed to the atoms in the wire and in the light-bulb is potential energy.

How can that be? Potential energy is like energy stored in a rock held at a certain height above the ground. What sort of height exists in an electrical circuit?

Well, let’s look closer again. What does ‘height’ actually mean? It means that there’s a force down below somewhere that is pulling on that rock, and if we let the rock go it will release some of that height-energy.

Well in a circuit, it’s not gravity which is pulling the electrons ‘down’ the circuit but electrical attraction. Electrons are falling towards the positive terminal on the battery as if it were gravity pulling them down towards the centre of the Earth.

In that case I can think of the circuit as a river of water starting high in the mountains and flowing downhill towards the positive terminal of the battery. The battery, therefore is a pump which pushes the water back up to the mountain-top.

I can even draw a picture of it, and give it a fancy title like... oh let me see... the “electric potential” graph of the circuit? In that case the potential difference between any two parts of the circuit is simply how far downhill the river has fallen between those two parts.

We can see that the water flows gently downhill when it’s in the copper wire but sort of goes over a cliff when it hits the light-bulb. Then it flows gently again down to the base of the battery.

Graphs like this help engineers to see where the energy in a circuit comes from and where it is most quickly gobbled up. In this case, it’s the light-bulb.

So do we ever get to know just how quickly electrons drift around a circuit, given that they’re not really going around the circuit but are simply colliding into one another and doing it in the direction opposite to what was taught for 150 years? Actually, no.

Well, a really determined scientist could find out and tell us, but we would probably just say “uh-huh” and get back to whatever we were doing before we asked the question. The truth is that the actual kilometres-per-hour speed of an electron in a circuit is just a factoid of no particular use in electrical science. It would be like an engineer at a hydroelectric power station asking how quickly water passes through a turbine. What matters is how much STUFF goes through per second because STUFF carries momentum and momentum makes wheels turn. That can happen just as easily if a lot of STUFF is moving slowly as a little bit of STUFF moving quickly. STUFF per second – i.e., current - is what matters, not velocity.

And the difference between force and voltage? Voltage is how much energy is carried by each electron, how much clout it has if you let it fall down a wire to the bottom of the circuit. Even now, as I write these words, my imagination cannot make a clear distinction between this and force. All I know is that the two concepts go hand-in-hand. Maybe it means how high the battery mountain is when electrons are dropped into the wire. A high voltage doesn’t mean a strong push, it means a high mountain. Go figure.

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I feel as though I want to finish this essay with a reference to something else that comes from all of this Victorian-era electrical research.

Humphrey Davy’s clever assistant Michael Faraday took over the running of his boss’s laboratory when the older man retired and continued tinkering with electricity. One day he put a metal spoon into a jug with an electric current running through it and placed it between a couple of powerful magnets. This wasn’t an accident, by the way. Michael knew exactly what he was looking for. The spoon began to spin round inside the jug as if a ghost was stirring tea, and kept spinning for as long as the electrical supply was switched on. If you think a dead frog can change history, then wait til you hear what a spinning spoon can do.

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