The Physics of Electrical Power

Factual Questions
1

An intuitive understanding of electrical power has eluded me for a while even though I work with it and can make useful things happen with it.

I understand current: coulombs per second. I apply voltage to a wire and move the charge to create current. More charge per second equals higher current. I get this.

I don’t get power: joules per second. That is, I don’t understand the underlying concept of what is happening in the circuit.

The best analogy I’ve seen so far is a belt around two pulleys. Applying force to move the drive pulley = applying voltage to make the charge move. One side of the belt goes one way, the other returns to the source. I also can see an analogy to power where I move the belt and the driven pulley moves right away (practically speaking) and energy is transferred from the input pulley to the output pulley.

I think I’m OK up to there but what is it that is being transferred? I know it’s Watts, I know it’s Joules per second but I still don’t really get it. Is it fair to say that something is being transferred from the source to the load at the speed of light? Is there a concept like moving charge which I can visualize to help understand what actually happens when I apply voltage to a conductor and make something happen at the other end?

2

Yes, but that somehting is the charge. Nothing physical gets transferred. I’s a change in energy level/state that gets transferred. It’s not an actual particle unless you get into real deep level quantum mechanics and someone starts talking about virtual photons. But such people are clearly mad anyway and shouldn’t be listened too.

Newton’s cradle

Not sure what level to start at here.

Your conductor is made up of atoms. You can think of them as a solid nucleus with electrons whizzing aorund it like hyperactive planets. That’s completely wrong but you can think of them that way for most practial purposes.

You generate an electrical charge by dislodging one of those electrons so it goes flying off. The trick is that it doesn’t go flying off into space. Instead it only goes flying until it strikes another electron. Then it transfers its energy to the new electron, just like one ball in Newton’s cradle tranferring its energy to the next. That next ball then goes fying off to hit the next one and so forth.

In this way the charge gets passed from one end of your conductor to the other. But the individual electrons stay approximately stationary. This is analogous to the way that the force applied to one end of Newton’s cradle gets transferred to the other end at the speed of sound sound despite the fact that individual balls stay stationary.
Another way I’ve heard it described is like a single file of soldiers reaching from cost to coast. Then you give an order for each soldier to push the man in front when he himself is pushed. As a result the whole line shuffles foward an inch or so but the push itself will travel the whole beadth of the country. And when you give an order to about face and do thesame thing travels back.

In the same way, alternating current can carry a charge from one side of the country to the other oscilating sevral times a second, but no individual electron has to actually cross the country several times a second. It’s the charge, the “push”, that is being transferred from your generator to the motor or whatevr. It’s not something physical.

3

Think of the current as a whole mob of little Coulombs belting around the circuit. (Don’t try and think of electrons and the speed of light – you’ll just get totally confused – the electrons don’t actually move, they passed on the energy. Let’s stick to Little guys each known as Coulomb.)

Each of those Coulombs is holding some boxes each with a diamond in them. You might like to think of that box as a vault with a jewel, or a volt with a joule. Both will work. Joules a measure of energy.

Let’s use a battery of 6 V. The number of Coulombs which go through the battery every second is the current. I = Coulombs/sec.

As they go through the 6 V battery, each of them grabs 6 vaults as it goes through - each with a joule in them. Volts equals the number of Joules given to each coulomb = joules per coulomb.

The number of joules the battery hands out every second is its power. So if you have a 6 V battery with a current of 2 Coulombs going past every second (2 Amp), then the battery is handing out 12 joules every second - the power.

P = V I and Watts = volts x amps = (joules/coulomb) x (coulombs / sec) = joules / sec.

The current drawn through any battery is determined by the resistance of the circuit.

So off the coulombs trot around the circuit. They meet these thugs (commonly known as Resistance) to whom they hand over their joules to bribe the thugs to let them through.

Ohm’s Law: V = IR or I = V/R

The more resistance you’ve got the less current can get pushed out by a battery - less coulombs get out every second. Less current.

If there are three resistors, each of 1 Ohm, each coulomb will hand over 1/3 of their load, that is 2 volts at each. Can you imagine what would happen to the poor little Coulombs if they didn’t have any vaults left to bribe the Resistors? So they carefully divide their volts evenly among all the Ohms.

The coulombs give up enegry (joules) at the resistance. They must give up all their energy before they get back to the battery. That’s why the sum of the voltage across the Resistors must equal the voltage delivered by the battery.

You will find that this imagery also works when you want to look at series or parallel circuits. I can even get it to work in alternating currents – but certainly not without a whiteboard!

And now for my finale: what happens if the coulombs mess up and don’t give up all their joules to Resistors before they get back to the battery?

They get bashed up. It’s called assault in battery.

4

I wrote that at the same time as Blake was writing his reply. It wasn’t directed against him - just that I couldn’t do both directions at once. And he did the electrons version so much better than I could!

5

How long have you been saving that one? :stuck_out_tongue:

Very nice. I was OK with the Newton’s cradle part. I think it’s the concept of the Joule as a unit of energy that has been dogging me. I never saw volts as equal to Joule/Coulomb. That makes more sense to me.

6

I refined it over 25 years of teaching senior physics. Never managed more than a groan at the punch line, though. Each year I hoped for a real laugh! Get on to magnetic fields, with F + BIl, and I have Bill being a really forceful guy, until he gets paralytic, then he’s useless. Vectors and all that.

Had the kids act them all out, as well.

7

I agree–this is a great analogy. It can even be extended to AC. In this case, the drive pulley is rapidly turned clockwise/counter-clockwise. The secondary pulley at the far end will mimic this. In an AC circuit, this rapid reversal happens 60 times a second (for 60 Hz AC).

Now picture what would happen if someone put their hand on the belt at the far end, trying to brake the belt with friction. It wouldn’t matter if the belt traveled in a constant direction (analogous to a DC circuit) or rapidly switched back and forth (analogous to an AC circuit). Either way, the friction between the belt and their hand would heat their hand up. In similar fashion, it doesn’t matter if electrons in a circuit move one way (DC) or alternate back and forth (AC). They will cause a light to light up either way.

Whether it’s an electrical circuit, or a belt and pulleys, the answer is the same. Energy.

It makes no sense to say that the belt itself is being transferred, because work is done at the far end as soon as the drive pulley is turned, and before the section of belt at the drive shaft ever makes it to the far end. Similarly, it makes no sense to say that electrons are being transferred in a circuit. In fact, once you learn that the drift speed of electrons is only on the order of a few inches per minute, it is apparent that the only meaningful thing that is being transferred is energy.

And in the case of an AC circuit or a pulley being turned back-and-forth, the electrons and a given section of the belt never really go anywhere. They just reverse direction rapidly. Again, the only thing that is transferred from the electrical source to the electrical load (or the drive pulley to the secondary pulley) is energy.

8

Yes, as a matter of fact Drift Speed is what got me thinking about all this as I only recently learned just how slow electrons in a circuit travel. I had to repair a piece of coax cable which led me to wonder why an 8-ohm cable is 8 ohms no matter what length I make the cable yet I don’t measure 8 ohms (or anything) if I put my meter across it. Reading up on that led me to drift speed somehow.

My next goal is to learn about B and H fields and all that good stuff that didn’t get covered in school. :slight_smile:

9

Oh, my goodness. This is really too difficult to let drift by.

Charge is physical. Transferring charge in a wire, carrying a current, means moving electrons. They’re real actual particles. There is quantum mechanics woven throughout the universe and embedded in every key on my keyboard, but you can ignore it while typing, and you can treat electrical current in a wire as electron flow while ignoring it too. Plenty of people deal with quantum mechanics without being mad. I don’t want to start a debate about whom shouldn’t be listened to(o?).

10

For anyone who shares my curiosity, I found this site to be very helpful. I guess my question was about a Poynting field. I didn’t know that term before (still reading about it) to know that’s what I was looking for but it’s very interesting.

11

But you have to admit . . .

. . . it helps.

12

Best explainations ever:

For your question specifically:
http://amasci.com/elect/poynt/poynt.html

Electricity in general:
http://amasci.com/ele-edu.html

There is really good stuff there.

13

The energy in an electrical circuit is actually transferred by an electromagnetic wave which travels outside the wire. The wire is basically just the guide for this wave.

In order to calculate the energy transferred by this wave you have to calculate the Poynting vector which is equal to the cross product of the E and B fields. Outside the wire the vector is longitudinal and points to the load; at the surface of the wire it’s perpendicular and represents the power flow into the wire for the ohmic heating.

14

What? Why? If you drink water in New York city where it is carried many miles in an underground tunnel, the water was transferred from upstate, wasn’t it? The trip does not have to be completed in the time it takes you to fill your glass to make this true, does it? Electrons are not very interesting in the sense that they all act the same as one another in every sense the user of electrical power might care about. And, they are available very quickly anyplace in the circuit without regard to the transit time from other points in the circuit, in the same sense that drinking water comes out of the tap right now no matter how long it takes to travel through the pipes from its origin.

Whether you think electrons are a “meaningful thing”, I don’t know. In a thread about “the physics of electrical power” that someone posts because they “don’t understand the underlying concept of what is happening in the circuit”, I think electrons are meaningful things. But why would the magnitude of drift velocity make them not meaningful?

15

Right. This explains, incidentally, why the velocity factor (the fraction of c at which an electric signal propagates along a conductor) varies depending on the insulating medium surrounding it. This velocity is the speed of light through that insulating material because the electrical energy is really being transferred by virtual photons. For free air, it’s about 99% c; for typical plastic insulations it ranges between 50% and 80% c.

16

Very correct, except they’re real photons. Virtual photons mediate the electromagnetic force. The number of real photons in an EM wave, per a given volume, is proportional to the square of the electric field vector.

17

Yes, but as Ring states, the energy of the circuit is not carried by the movement of the electrons, which move on the order of a few inches per minute; instead the energy of the circuit is carried by an EM wave that travels outside of the wire (where no electrons are present) at a fraction of the speed of light, far faster than the movement of the electrons.

Well, water flowing through a pipe is indeed another analogy for a DC circuit. Just as a water pipe is already filled with water, so water comes out of your tap as soon as you open it, a wire is already “filled” with electrons.

The analogy breaks down, however, when you consider an AC circuit in which, on average, the electrons don’t go anywhere. They just oscillate back and forth. What’s more interesting than the movement of the electrons, however, is the behavior of the EM field.

18

Agreed. I used his material extensively when I taught this material years ago. I particularly liked his analogy for capacitors.

19

Interesting. Are there practical applications where this makes a difference?

I find this endlessly fascinating and thank everyone for the great information. I wish now I could’ve worded the OP better regarding the level of information I was looking for but didn’t know enough to frame the question properly.

Apropos of nothing Harvard has a neat little collection of demonstrations to set up that illustrate more advanced concepts than I usually come across.

20

Antenna design and feedline impedance matching , for one. At the simplest case, if you’re making a basic wire antenna and you want it to be exactly 1/4 wavelength at 100 MHz, the length will be about .75 m for a bare wire but if you’re using PVC insulated wire, which has a velocity factor of about .8, the length will be .6 m instead.