# Question on the constant current in electric circuits. [ Not homework ]

1. Feb 23, 2009

### Nanyang

Hi I'm new here and have this question I would like to ask. Sorry if I posted in the wrong section! My level of education is not high so please forgive me for this simple problem, though not simple to me.

Q: Why is it that in, for example, a series electric circuit that the electric current is constant?

I thought about this for very long (a year) when I am free and now, I kind of gave up trying to think of a solution independently.

note: this is not a homework

I thought of it and replied him saying:

Note: I used div and grad to put my points forward, but I mostly self learned that and thus is not an excellent user of this mathematics. So do forgive any ugly mistakes made and if possible, correct it so that I can learn.

So do correct me where I'm wrong and hopefully help me understand why the current is constant in a series circuit.

Last edited: Feb 24, 2009
2. Feb 23, 2009

### HallsofIvy

Think, first, of direct current- electrons moving in one direction through the wire. If one section of current were greater than in the next, there would be a "build up" of eletrons where the faster moving electrons ran into the slower electrons: a "traffic jam".
That can't happen in a resistance only circuit. It can happen, I believe, on a capacitor where charge can build up.

3. Feb 23, 2009

In terms of "free electron theory"each electron accelerates between collisions and the current carried by each separate electron will indeed vary as it makes its way around the circuit.Remember,however ,that the same theory deals with the huge numbers of electrons we get with typical currents and the effects average out to a constant current.Free electron theory is useful up to a point but at a more advanced level we have to start using quantum theory.
May I say that although I have not absorbed the points made in your analysis you are clearly a very deep thinker. Well done.

4. Feb 24, 2009

### Nanyang

Thanks for the replies!

I don't know much about capacitors or inductors so my question is based on having a potential source (maybe some charges at some point) and a closed metal wire loop.

I thought about what you said and thought that:

When the faster ones run into the slower ones, the previously slower ones become the now faster ones and the previously faster ones become the now slower ones... so it's like a longitudinal wave? Hence for some points the electrons get closer together (contraction) and some points further apart (rarefaction), so the charge density is not constant, therefore the current is not a constant.

Hmm... could it be possible that texts are referring to the total charge flow as a whole being constant... and not talking about the current flowing through two or more arbitrary chosen points on the circuit being the same?

Hmm...I thought of that before, but I'm not sure if there are experiments to confirm, at a very precise level, that the current is not a constant for two arbitrary points on the wire.

But texts (and teachers and people) always say that the current is constant like a 'miracle', no mention of averaging (at least for those I read) So I'm looking for an explanation for this 'miracle'...

Again, thanks for the replies! Would be great if there were more opinions from other people on this matter...

Last edited: Feb 24, 2009
5. Feb 24, 2009

### Staff: Mentor

Hi Nanyang,

Consider conservation of charge. If you look at a small segment of a wire than any current that flows in to the segment must either flow out or increase the charge of that segment. One of the implications of the "small circuit" assumption of circuit theory is that charge does not accumulate in any circuit element, therefore if the charge of the segment is not changing then the conservation of charge implies that the current entering is exactly equal to the current leaving.

6. Feb 24, 2009

### Nanyang

Does this assumption also hold for practical circuits in 'real life'? I mean like a battery and a wire.

If it isn't true, then is the 'averaging' effect mentioned by Dadface and also that the electric field of the voltage source is very small hence making it seem almost like a constant electric current?

In other words, is the ammeter (those used in ordinary school labs) not accurate enough to measure the tiny variations in the current, if the assumption that charge cannot accumulate at a point is not true for practical, 'real life' circuits.

7. Feb 24, 2009

### Staff: Mentor

Yes, it holds very well which is why your electronic appliances work. In practice it works well for any circuit that is smaller than about 1/8 of a wavelength of the highest frequency involved, which is why it is called the small circuit approximation.

8. Feb 24, 2009

### alxm

Well, if I remember my physics right, it's true in some cases, but only for highly energetic electrons. In general, it's assumed electron transitions occur so fast that the nuclei don't have time to 'react' and change their position/momentum. This is the basis of the Franck-Condon principle.

9. Feb 24, 2009

There will be tiny current fluctuations at each point in a wire but an ammeter cannot measure these because it measures the current through the whole cross section of the wire.
alxm,it is wonderful what you can pick up in these threads and I have never heard of the Frank Condon principle.I have just googled and I am going back for another look.

10. Feb 24, 2009

### cabraham

A helpful reference you can explore is to search for "Johnson noise" and "shot noise". Electrons moving through conductive media do incur collisions, and the dc value is only an statistical average. Noise components are always present. The magnitude of said noise increases with bandwidth. The higher bandwidth the circuit, the less these variations average out. Hence, a very low BW network has low Johnson & shot noise.

Claude

11. Feb 24, 2009

### Nanyang

Thanks a lot everyone :)