Why would voltage decrease over a resistor?

[member 392791]

The thing that amazes me from reading this thread is how people who have studied physics for 20+ years can still argue about the most fundamental of concepts. That is a true testament to the rigor of physics :)

 

[sophiecentaur]

The thing that amazes me from reading this thread is how people who have studied physics for 20+ years can still argue about the most fundamental of concepts. That is a true testament to the rigor of physics :)

Good point. Mind you, they will argue just as much about fishing, football, politics . . . . .

 

[member 392791]

Only the difference is that those things are more subjective, whereas physics has one true answer

 

[sophiecentaur]

Here we go, 2nd hit on google, with pictures:
http://www.astrophysik.uni-kiel.de/~hhaertel/PUB/voltage_IRL.pdf
Sorry, I don't think I can find an article in peer-reviewed journal because frankly, it has all been sorted out a century ago, now it's kid's textbook level stuff.

And again, I'm not suggesting any kind of "alternative approach to electricity", oh no, certainly not. I'm just saying that there is a qualitative picture of the process, based on a simple model, to complement quantitative methods using conservation laws.

It's a bit like colliding billiard balls. Ordinarily one solves the problem by applying energy and momentum conservation. The forces are not easily quantifiable and do not appear anywhere in the equations used to solve the problem. Nevertheless, if the question was "why did the ball change direction" the answer would be "because of the force acting on it" in line with the Newton's 1st law.

And btw, this picture, while simplified, is quite adequate for many tasks.Yes, the interactions between electrons and crystall lattice are not exactly like a pinball machine, and the processes giong on in the battery are not as simple as constant external force acting on charge carriers but the net effect is pretty much the same. So you won't get the voltage of a lithium cell or the resistivity of copper accurately. No big deal. You still get all the curcuit laws out of it.

Talking about potential and charges, do you agree that voltage between points A and B (in the absence of magnetic field) is $V_{AB} = \frac{1}{4πε_0} \int_v \rho(\textbf{r}) \left( \frac{1}{|\textbf{r}-B|} - \frac{1}{|\textbf{r}-A|} \right) d\textbf{r}$ ? This just goes to show that voltage is completely determined by charge distribution alone, be it an isolated charge in electrostatics or resistor in circuit or anything else. Thankfully, we do not need to compute this integral, but saying that the charge has nothing to do with voltage is just wrong, there is a clear causal link.

And finally, where, in your opinion, did the 1KV/m electic field came from in my example of 1mm 1Ω resistor?

Regards, DK

---- edit ----

Rainer Müller, "A semiquantitative treatment of surface charges in DC circuits", Am. J. Phys. 80, 782(2012)

I think most of you guys have missed my main point. There is no doubt that charges are involved in electric current through 'matter'. There is also no doubt (is there?) that Maxwells equations hold in free space - so there is an effective current without the need for electrons to me moving about. That is all well established stuff. But that was not my point.
My argument was against the statement that it is Charge imbalance that causes a current to flow. Now, if you want to say that it is surplus charges at each end of the resistor that cause the current, you surely (?) need to be able to describe some sort of quantitative relationship between those charges. There is not one. The surplus charge imbalance are a result of the Potential Difference and its value can be calculated in terms of the Capacitance involved. The Current in the Resistor is governed by the PD across the resistor and the energy dissipated per Coulomb is equal to that PD.
The PD is the common factor (independent variable) between two quantities (dependent variables) that are not directly related to each other at all. (Any combination of Q and I is possible) If there's no direct relationship then I cannot see how anyone can claim a causal relationship i.e."Current depends on the Charge difference" (or words to that effect).

This stuff is ancient knowledge and not in modern papers. Old research papers will not be available on line. However, there are a million textbooks out there and I challenge anyone to find that inaccurate idea in any book that's aimed at serious students of Physics. For those who do not 'do' theory, perhaps they could look at Spice (or some other simulation) and try to simulate some circuit in which such a relationship could be shown (when the appropriate variables are controlled).

What was it that set up the original Charge distribution in the situation described? Surely it was energy put into the system and established the Potential Energy situation. If there had been no energy input (and that applies to a circuit and to an 'electrostatic' setup) there would be no charge imbalance. This is not just a 'chicken or egg' argument. There is a inherent order of cause and effect.

That would come from the PD and the length of the resistor . But that assumes a straight resistor. If it were horseshoe shaped then the Field (volts per metre) would be irrelevant. The PD alone would be what determines the current. This is a case where Field is just not as useful as Potential.

 

[sophiecentaur]

Only the difference is that those things are more subjective, whereas physics has one true answer

Not sure about that. We may be making progress in the right direction but it is only a matter of Faith that we can ever aspire to the Truth. The answer that works near enough so that we can't detect significant error, is all we can demand.

 

[Naty1]

mpatryluk...
in case you are still around...and I would not blame you based on the discussion so far if you gave up...
I assume you are starting out with electrical circuits, and if so the discussions so far probably haven't helped much.

I don't understand 3/4 of the drivel posted so far...sophiecentaur being the exception.
I would paraphrase his comments as saying "Such a model [posted by others] of charge distribution, integrals, Gauss' law,etc, are unnecessarily abstract in a circuit analysis like this." At least that's what I think. I'll stick with what I posted already, but here are some additional ways to think in more concrete terms...maybe less abstract than I posted...

why voltage changes along a resistor:

think of voltage as the difference in electric potential energy of a unit charge, one electron, say, transported between two points. [That potential difference comes from some source, say, electro chemicial [battery] or maybe a dc generator. For a chemical viewpoint, you can look up stuff like 'redux reactions' or 'battery', say via Wikipedia.]

These individual electrons are what move along in lock step in a typical conductor...and resistor...loosly bound electrons, called 'conduction electrons', 'valence electrons' or whatever, in a conductor, more tightly bound electrons in a resistor...'More tightly bound' means a stronger local bond to an atom or other material structure...so it takes more potential [electrical energy] to dislodge them.

[An insulator, like ceramic or rubber or plastic has really tightly bound electrons and will not let them move easily...electrons can't move, so they resist any current flow because their electrons 'stay in place'. Circuit designers like insulators because they don't waste power! ]

think of circuit electrons in this simplified analogy as maybe cars lined up on ahighway...as you move one, then two, then three, as moving along in a resistor, it takes more and more work to overcome friction, analogous to individual electron attraction in a typical resistor...So as you move your voltmeter further and further apart over the length of a resistor to measure voltage, you encounter more and more displaced electrons, each with a tiny electric potential difference, and they each add up.

But this has nothing to do with any 'distribution of charge'...the same number of electrons entered one end of the resistor as emerged from the other end...each moves along like a line of cars on the highway...individual electrons 'drift' from atom to atom rather slowly, but as one enters, another leaves at a distant point, pushed along by the potential difference of all the intermediate electrons.

So while electric current is really fast overall, but not light speed, individual electrons in a typical circuit bump along at a only few meters per second...it's called 'electron drift velocity' like cars stuck on a highway moving slow, like 10mph in heavy traffic, yet one enters and one exits miles apart giving the appearance of rapid transport.

Hope that helps...

 

[Delta Kilo]

What was it that set up the original Charge distribution in the situation described? Surely it was energy put into the system and established the Potential Energy situation.

This is an extremely vague statement which does not provide any description at all of the physics behind it.
How is "Potential Energy situation" established exactly? What is the physical mechanism?

This is not just a 'chicken or egg' argument. There is a inherent order of cause and effect.

There is a n inherent order of cause and effect, but it is in reverse to what you seem to be implying. The formula for the voltage I gave above is not limited to steady-current state. Shall we look at transients in RC circuits then?
There the causal link is clear: charges determine the electric field (voltage, if you like) -> electric field exerts forces on the electrons -> current flows -> charge distribution changes gradually over time.

That would come from the PD and the length of the resistor .

Sorry but this is tautology. PD is just another characteristic of electric field. It describes it, it does not cause it to appear. Where did the PD come from then?

Like in mechanics one can solve problems using Newton's laws ans forces or use Lagrangian and principle of least action. The two approaches are equivalent. Some problems are better suited for one or the other. In some cases forces help you to understand the picture qualitatively while quantitative answer comes from Lagrangian.
Your position seems to be like dismissing the forces as completely irrelevant.

 

[sophiecentaur]

@DK: I clearly haven't been writing my ideas clearly enough. I was trying to be general. rather than vague. The charges got there because some work was done on them. That was all I meant by the "potential Energy Situation". (I have made several posts here and I assume that, if someone is going to challenge one of them, they could read -or at least skim - the others, for context.)
Of course there is a direct relationship between Energy and Field. It's just that there are times when it's more useful to consider one than the other. In the case of electrical circuits it is common (pretty well universal) to use Volts. Discussions of the operation of some components will often use fields (Antenna theory, as an example) but I don't t think you could give me examples where Fields are used for overall circuit calculations. That paper about charges and fields around a circuit was interesting and 'confirming' but it doesn't actually suggest that we should alter the way we do our analysis . Nor does it say anything about what's 'really' happening. On that matter, I don't see that we have any serious disagreement.

My main reason for getting into this was to challenge the statement (way back - and I've forgotten who it was who actually made it) that the Charges are the prime cause of current flow. Which charges are at work inside a transformer or a radio receiving antenna? All the theory I have been taught says that there are emf's involved, which induce currents. No charges move through space between primary and secondary windings or between transmitter and receiver. However you want to describe the way of a battery works, it would be very inconvenient if you were to say that you should treat the way a resistor works when connected to a battery differently from when it is connected to a transformer. Is this not why we use Volts in most analysis. I just realized that the notion of a Current Source is sometimes used, in which case you could say, I suppose, that the Coulombs per Second are what drives its load - but even then, it's not Coulombs that are used, it's rate of charge flow.

I (and you, also) will continue to use PD as the 'explanation' for the driving cause of what goes on in electrical circuits. We all know that, because it's the pragmatic way. So, although there are alternative ways of 'looking at' the situation, they won't affect what goes on in practice.

 

[rcgldr]

My main reason for getting into this was to challenge the statement (way back - and I've forgotten who it was who actually made it) that the Charges are the prime cause of current flow.

It was proably my post, and I did not mean to imply it was the prime cause, or that is should be used as a basis for studying circuits. I was just trying to offer an alternate explanation for voltage drop across a resistor, using charge (density) diferential at the terminals of a battery, as an alternative to voltage, hoping that it might seem a bit less abstract to the OP.