Wanted: B Level Explanation of Conduction and Resistance

[anorlunda]

Students seeking “deeper” understanding of basic electricity, frequently come with one of the following misconceptions.

1. Electrons are like balls, they start with potential energy and gain kinetic energy. They deliver their energy to the far end of the wire by filling a bucket.

2. Electrons are like pods filled with energy. The pods burst as they go through a resistor, and they are all used up by the time the wire reaches ground.

I am seeking a B level explanation of conduction and resistance that is not based on analogies. In the QM and relativity forums on PF, analogies are strongly discouraged for very good reasons. Here in the EE forum, we have not been very strict regarding analogies or pop-sci answers to these questions. I would like to put us on more solid ground.

The water analogy is very clever, it can analogize R, L, C, diodes, and batteries. But it can not show $\Delta{V}\cdot{I}$ power losses, and students are likely to use the water analogy to think that energy is delivered when water fills the bucket at the far end.

Going the next level down to fields (i.e. Maxwell’s Equations), is not much help. Maxwell’s Equations help us understand the propagation of EM wave fronts, but they do little with regard to material properties, resistance and conduction in a wire. Also, as soon as we bring in fields here on PF, someone brings up Poynting's Law, which blows student's minds away and IMO impedes learning for B level students.

The Drude Model seems to be the only candidate.

The simple picture of electrons bouncing from Wikipedia (see below) may serve as the B level answer. Wikipedia's little derivation of Ohm's law (https://en.wikipedia.org/wiki/Drude_model#DC_field) could be the I level answer, and (https://en.wikipedia.org/wiki/Free_electron_model) could be the A level answer.

But I really dislike the Drude Model too. It seems to play into misconception 1 above treating electrons like ball bearings in a pinball machine. But the Drude Model also seems to me like yet another analogy to a Japanese Pachinka board. (Actually a pinball machine with active bumpers rather than passive pins is a better analogy than Pachinka.)

With the Pachinka analogy, one visualizes the idea of feeding one ball into the top and getting no current, no power until that ball exits at the bottom. To avoid that misconception, one would have to start with the board flat and fully populated with balls, then tilt the board to apply the field. To visualize the Pachinka board in a closed circuit, one would have to show a mechanism to lift balls from the bottom back to the top.

Even then, the Drude model helps not at all to explain the $\Delta{V}\cdot{I}$ power losses. Nor does it explain how the electrons come to be free from the atoms in a metal. (A personal note, as a power engineer, I'm bored with just V and I. I think the interesting story is power and energy.)

For those reasons, I really dislike the Drude model as not being helpful to students with those common misconceptions. What other B level or I level model could we give that are not analogies and not pop-sci?

Perhaps I am on a fool's mission in this thread. Perhaps there is no other model. Perhaps I should be putting effort into making an animated cartoon that tries to show the Pachinka correctly in a closed circuit. Perhaps I should be rude, saying "You must study fields, and QM and the properties of crystal lattices before asking that question." But I would be very happy to be rescued from that if another PM member can suggest a better B level answer than Drude.

By the way, here's more interesting Drude trivia from WIkipedia that both adds and subtracts from my confidence in the model. https://en.wikipedia.org/wiki/Drude_model#Accuracy_of_the_model

 

[lekh2003]

This is a difficult mission you have embarked on. Analogies are the bridge between laymen and physicists. It will take time to wear down on our own personal analogies to actually think about what electrons, conduction and magnetism are. I am unable to find an explanation, maybe somebody else will.

 

[darkwood]

You can imagine electron flow like a hosepipe full of a line of ball bearings, when you push a new ball bearing into one end of the hose you get one that falls out almost instantly at the other end, there has been little movement of any given electron (ball bearing) but the reaction (charge) along the hose was almost instant.

This analogy can also show what happens for AC as well as DC, AC the ball bearing is pushed in at each end sequentially and if you were to observe any of the electrons they would only be vibrating left and right about their original position, where as DC continues to push the bearings in at one end and we see a somewhat slow migration of any given electron in the direction of flow.

PS this is my own analogy to explain what happens while maintaining a simple concept, it has worked well for my apprentices over the years, I have yet to see a better analogy IMHO but I assume it's an each to their own idea of a good analogy so might not suit everyone.

 

[Paul Colby]

I don't know if I can articulate this well but isn't current flow more of a collective field phenomena than a motion of individual charge carriers? It's a collective phenomena because charge carriers in one part of a circuit influence carriers in distant parts of the circuit through the average E/B field strengths. For certain, scattering phenomena like that captured in the Drude model describe energy lose. Shot noise is best viewed as individual charge carriers crossing a potential boundary etc. But these aren't the bulk of the physics.

 

[jim hardy]

You can imagine electron flow like a hosepipe full of a line of ball bearings,

That one works. It was explained to me as a Pea Shooter, something familiar to every kid in the 50's. We'd all stuffed peas into a soda straw so the concept clicked immediately.

The water analogy has its value but i prefer hydraulics - a pump transmits power to a load someplace via incompressible fluid in pipes. But hydraulics is not in most kids' experience base.
Water analogy reminds us of playing with the garden hose as kids and results in the mistaken idea that electricity is somehow attracted to earth.
Hydraulics though is a closed system just like a circuit. So it avoids that pitfall.

Anyhow you can become very competent at circuit analysis with those analogies and Kirchoff's laws. I agree that too much highfalutin math too soon discourages promising talent.

I'll have to look into the Drude model - first i'd heard of it.

 

[RonL]

Knowing a little about welding and carbon arc search lights, I would think a simple explanation based on a single cell battery, a conducting wire, can show current flow up to the point the wire turns red, then explain the blue flash when the wire is removed from contacting the battery terminal.
As I see it on a microscopic level, the blue flash is energy (resistance) vaporizing copper atoms of the wire (millions) and electrons being energetically ripped from the atoms (trillions), we see the flash because of the close proximity of the electrons during this short time. At the speed of light this makes for a short event.

No analogies to this, but I'm sure someone can improve the wording, assuming my thoughts are correct.

 

[OmCheeto]

Knowing a little about welding and carbon arc search lights, I would think a simple explanation based on a single cell battery, a conducting wire, can show current flow up to the point the wire turns red, then explain the blue flash when the wire is removed from contacting the battery terminal.
As I see it on a microscopic level, the blue flash is energy (resistance) vaporizing copper atoms of the wire (millions) and electrons being energetically ripped from the atoms (trillions), we see the flash because of the close proximity of the electrons during this short time. At the speed of light this makes for a short event.

No analogies to this, but I'm sure someone can improve the wording, assuming my thoughts are correct.

It can definitely use some wordsmithery, but I consider your observations valid.

 

[Paul Colby]

You can imagine electron flow like a hosepipe full of a line of ball bearings, when you push a new ball bearing into one end of the hose you get one that falls out almost instantly at the other end, there has been little movement of any given electron (ball bearing) but the reaction (charge) along the hose was almost instant.

The problem with this analogy is that it does not supply a viable explanation (model) for the speed of propagation of signals. If one applies a short pulse to a wire or transmission line, like a coaxial cable, the propagation of voltage and current is determined by a solution of an electromagnetic boundary value problem and has nothing directly to do with electrons bouncing around. The OPs post requested a more physics based model. Looking at current flow as ball bearings in a pipe would seem to move in the wrong direction IMO.

 

[darkwood]

The problem with this analogy is that it does not supply a viable explanation (model) for the speed of propagation of signals. If one applies a short pulse to a wire or transmission line, like a coaxial cable, the propagation of voltage and current is determined by a solution of an electromagnetic boundary value problem and has nothing directly to do with electrons bouncing around. The OPs post requested a more physics based model. Looking at current flow as ball bearings in a pipe would seem to move in the wrong direction IMO.

I never mentioned the positive/negative charge status in my analogy so fail to see how I get it backwards or that my analogy got is somehow backwards, yes I agree with you in that the OP is after a more complex analogy that covers and explains the wider picture but here lies the problems with analogies, they are designed to allow you to perceive the hard to perceive in a language your mind can interpret, they are not trying to explain the fundamental working of the quantum world which I'm sure you will agree is baffling to the most intellectual of minds so in respect we may need several analogies to cover the various aspects of this subject, we are not trying to explain how it works in reality, we are merely making it easier to understand in a language we can visualise with everyday life.

This is why the OP cannot find one overlying analogy to cover the wide subject, by the nature of what an analogy is it limits itself to specific areas and will be found to break down when you expand on the subject matter and ask other questions.

PS - I dare say that if anyone can find an analogy that can show all the varied aspects of a subject in a language we can easily understand then they have probably shown a better understanding of the subject matter than we currently have ourselves on the quantum level.

 

[rbelli1]

This is why the OP cannot find one overlying analogy

But the OP is looking for a beginner explanation that is not an analogy.

BoB

 

[Paul Colby]

But the OP is looking for a beginner explanation that is not an analogy.

Define beginner is the question I would ask. The mathematics behind a complex system may be described without mastering it. The only point I'm attempting to interject here, is a view that what are called voltage and current in a system, such as a circuit, at a top level is the result of a classical boundary value problem. From there, one must provide the physical description of the materials the comprise this system which provides these boundary conditions. On a micro scale this descriptions involves charge carriers and such which involve various levels of detail, some of which are substantial but these can be added without invalidating the top level explanation.

Too often simple and limited pictures are offered to make things simple. This can become a hurtle later or an impediment as the problem domain changes. For example, the rubber sheet analogy for space-time curvature is a good example of a pleasing picture which is wrong enough to hinder people who wish to go beyond it and actually understand gravity.

 

[rbelli1]

Define beginner is the question I would ask.

How about what is the simplest meaningful non-analogy explanation? Is that something that would be even in the ballpark of beginner?

BoB

 

[Paul Colby]

How about what is the simplest meaningful non-analogy explanation? Is that something that would be even in the ballpark of beginner?

BoB

Teaching engineering is different in many ways than teaching physics not that I can claim to do either effectively. There are different goals in mind. I think the most important thing is to convey is that their is no one complete answer to nature because all things are not yet known. I would also point out that there are really good approximations one may use to solve real world problems which ignore or approximate nature well enough for useful work. Basically, it's very important in life to be able to ignore the full complexity of nature and work with simpler rules provided we keep in mind the limitations. For example, a mechanical engineer may work his entire life using continuum mechanics and ignore atoms all together. Likewise, one may do basic electronics without ever mentioning electrons or charge carriers. You can even commit the heresy of dispensing with current and using perfect and partial conductors and substitute tangent H fields for current instead. I'm not recommending this as a world view but it's worth mention that if one wants to put in the work, one may do it. Doing this provides an excellent opportunity to discuss limitations to (basic) circuit theory like when is a wire no longer a perfect conductor.

As far as the solid state physics required to understand current flow in a conductor I personally love the Drude model but understand it's just a model. The misconceptions mentioned by the OP are a direct result of flawed picture building. People form or worse, are given pictures they consider complete. Actually they should understand from the get go pictures are necessarily incomplete.

One of the things that I alway felt added to my understanding is to provide numbers like what is the real drift velocity of electrons in a wire and how does this compare to the propagation of signals in a circuit. How much force is there between all the free negative charges in a wire and positive charges. How big is an atom. Understanding the scale of things is really important.

 

[ZapperZ]

The problem here is to what degree of complexity does one want to have such an understanding of electrical transport?

The Drude model is adequate for many instances. Ohm's law that is so widely used can derived exactly from such a model. Not only that, even if one turns on a weak-coupling limit for electron-electron interaction, we then get the Landau Fermi Liquid Theory in which the many-body interactions can be renormalized, so that we can transform the complicated one many-body physics into the simpler many one-body physics. When we do that, we get back the Drude-type description, but with quasi-electrons as our particles.

At some point, being "uncomfortable" or "unsatisfactory" with one set of model/theory versus another is not a physics question, but rather an emotional, personal-taste question, because if these descriptions are accurate enough with empirical measurement, then it is useful enough to be valid.

Zz.

 

[nsaspook]

My 2c. For me one of the most important ideas to explain is that current is the same in both wires in the simple battery/lamp circuit system. The wires are filled with electricity (current electricity) but electricity is not energy because the 'energy' is a property of the entire system, not its isolated parts. I normally use the bicycle chain analogy as a method to help beginners understand basic circuit electrical principles like conduction and resistance. Once you get past these basic principles using 'tension' in the links, gear ratios, chain loops, etc ... most people begin to see the electrical circuit as a type of special mechanical device that uses 'electricity' for work.
https://www.physicsforums.com/threa...d-electricity-in-general.876462/#post-5505531
https://pdfs.semanticscholar.org/56d2/230c4f9fdb8409f897220aedc959ff4f365d.pdf

Once the basic mechanics are understood, you can then dig deeper into the details of what is electrical 'tension' and how it's transported/transformed in the electrical circuit (a system) using charge and fields.

 

[jerromyjon]

I don't know, but I think perhaps some compartmentalization is in order. Like temperature is relevant is some respect, and velocity follows, and volume, and then circuit. That might not be the right order, haven't thought it all through yet.

 

[ZapperZ]

Keep in mind that one may come up with whatever "model" that one wants, but that model MUST produce quantitative agreement with what we know about the behavior of a standard conductor.

We know Ohm's law, but there is also the resistivity dependence on temperature, etc... ANY model must be able to produce quantitative agreement with such empirical observations. Otherwise, it is a handwaving argument with no physical justification. Remember, physics just doesn't say what goes up must come down. It must also say where and when it comes down. Just having a mental picture in our head that appears to "make sense" is insufficient.

This is why we still cling to the Drude model. It has the simplest picture at the most naive level that can reproduce many of what we know and use.

Zz.

 

[nsaspook]

I don't see much of a problem using the Drude model for conduction and Resistance as it explains in simple terms the material effects on the conductor of electrical energy redistribution in the circuit. As long as the person understands why the electron is moving at that location in the circuit and how that force arrived at that location. People seem to understand the Drude electron mechanical behavior quickly but it's usually the deeper energy/power transport relationships of the circuit that confuse.

https://forum.allaboutcircuits.com/threads/how-does-electrical-current-flows-through-high-resistance.144501/#post-1225706

 

[Paul Colby]

but it's usually the deeper energy/power transport relationships of the circuit that confuse.

Isn't it the case that these energy/power transport phenomena in a circuit are in large measure independent of the physics described by the Drude model. The Drude model describes (approximates) the physics that yields the field boundary conditions on and in the wire. The energy transport is then described by the resulting boundary value problem.

 

[mjc123]

Just to point out that OP's link to "Poynting's Law" actually directs to Poyning's Law, or the Statute of Drogheda of 1494. Try this:
https://en.wikipedia.org/wiki/Poynting's_theorem

 

[Paul Colby]

Yes, but isn't the ideal helping or at least not impeding B level students becoming A level students? I defer to people with experience teaching the subject. Just sounds like bad policy to give students a model which describes one part of the physics which doesn't other important parts of the physics yet suggest it does include it. Just saying.

 

[anorlunda]

The energy transport is then described by the resulting boundary value problem.

That's true, but it isn't B level.

As long as the person understands why the electron is moving at that location in the circuit and how that force arrived at that location.

That's part of the difficulty. B students start asking the question about a resistor as if it were a rectangular block of a solid (as in the Wikipedia Drude Model illustration in the OP), but then jump to a closed circuit, and the subject being discussed gets blurred.

In another thread @sophiecentaur recently commented on electrons being introduced into the lessons at too early a stage. It is a reminder that the topic of this thread is not physics or models, but basic level education.

It may be useful, but unrealistic, to withhold mention of electrons, charges, and fields from basic electricity courses. It also unhelpful to insist that there are only three levels (QED, fields, Circuit Analysis) to study electricity that are accurate, internally consistent, and not analogies. Alas, we can't get away with either one of those ploys. The B-level student's questions just keep coming.

I'm coming to the conclusion that mere words won't work. Only an animated video might have a chance.

 

[Paul Colby]

That's true, but it isn't B level.

What's wrong with; when charges in wires move, they generate electromagnetic fields. These fields interact over the entire circuit in a way that's all consistent with a series of somewhat complicated equations first collected together in one spot by James Clark Maxwell in the 1860's. For simple circuits where things are changing slowly enough, we can summarize the important bits in Maxwell equations into some pretty simple looking "circuit laws" ... and so on. Then one may explain "slowly enough" then one can explain resistors and the Drude model.

It fine to leave out the scary bits till later in their training but at least they will say, oh that's what he was talking about.

 

[nsaspook]

It may be useful, but unrealistic, to withhold mention of electrons, charges, and fields from basic electricity courses.

I don't think that's a good idea. I was lucky with a fairly rigorous electronic education before I joined the military (Navy 70's) but even their basic course starts with electrons, charges, and fields for a Technician-Level Understanding.

http://www.tpub.com/neets/book1/chapter1/1a.htm

 

[Dale]

The problem that I have with all of this is that ideally an analogy should be simpler than the thing itself. But no analogy I have ever seen is simpler than Ohms law itself.

I actually think that it is better to refuse to give analogies and to require the students to address the concepts directly. Analogies are always limited in applicability and (in this case) fail to simplify things even where they are applicable.

 

[Dale]

It also unhelpful to insist that there are only three levels (QED, fields, Circuit Analysis) to study electricity that are accurate, internally consistent, and not analogies.

Hmm, why do you think that is unhelpful. I would start the first lecture of a circuits class with that discussion. I would tell the students which topics belong with which class and the assumptions/simplifications used. With that “bigger picture” in mind then I would let them know in advance that many questions may be out of scope for this class and would need to wait for later classes. I think that would be very helpful.

 

[anorlunda]

Hmm, why do you think that is unhelpful. I would start the first lecture of a circuits class with that discussion. I would tell the students which topics belong with which class and the assumptions/simplifications used. With that “bigger picture” in mind then I would let them know in advance that many questions may be out of scope for this class and would need to wait for later classes. I think that would be very helpful.

There are two contexts, in a classroom and here at PF. I agree with you that a strategic lecture at the start of a basic class would have enormous benefit. An inspired lecture that others could copy would be wonderful.

Educators: does such a lecture already exist?

The second context is here at PF. I get the impression that most who ask these question and bring their misconceptions, have studied basic electricity and circuits, but plan going no further in their education. Yet they yearn to know what is "really" happening inside Ohm's Law. @sophiecentaur points out that most of them don't have enough calculus to study Maxwell's Equations. In that context, it is unhelpful to point out higher levels of study; because they won't do it. I intended this thread to address this second context, answering PF questions.

 

[ZapperZ]

I intended this thread to address this second context, answering PF questions.

Based on the responses that you have already received, has that issue been addressed adequately?

Again, there is a never-ending level of complexities that one can delve into in terms of electrical transport. One can invoke the Boltzmann transport equation, which is purely "classical", consistent with the Drude model, or one can make it really complicated and invoke the purely quantum mechanical Kubo formulation, which will turn even a seasoned solid state physicist nutty.

If all someone wants to know is the simple picture of electrical conduction and the origin of resistivity, I do not see why using just the Drude model is a problem. After all, that's what we teach students in solid state physics, and it is in Chapter 1 of Ashcroft and Mermin. If someone is more interested beyond that, then point him/her to Chapter 3 of Ashcroft and Mermin on the topic of the failure of the free-electron model.

Zz.

 

[Dale]

I get the impression that most who ask these question and bring their misconceptions, have studied basic electricity and circuits, but plan going no further in their education. Yet they yearn to know what is "really" happening inside Ohm's Law.

If their yearning exceeds their learning then I think that the best approach is to inform them of that fact.

Realistically, if it is a casual desire then they will not be able to satisfy it, and if it is a deep desire then they will need to acquire the necessary background first.

 

[sophiecentaur]

I don't think that's a good idea. I was lucky with a fairly rigorous electronic education before I joined the military (Navy 70's) but even their basic course starts with electrons, charges, and fields for a Technician-Level Understanding.

http://www.tpub.com/neets/book1/chapter1/1a.htm

You have brought in a very relevant point. Basically, Technicians are 'Trained' to perform certain functions and the training is aimed at being a cost effective way of producing people who will be able to work the technology. The services want people who can 'do the job' and I don't feel that recipients of many courses get a good deal out of them. Electrons and Photons are brought in in an effort to 'explain' the inexplicable (inexplicable with their levels of knowledge). It just demonstrates how difficult a subject Physics is when many of the educationist fail to understand the limits of the simple models they are using. I assume that, as you had a rigorous electronics education, you appreciate that electrons only need to be considered when you're inside some components. From many of the comments in your posts, I also assume that your previous education, rather than the 'training' in the military accounts for your ability to give 'good' answers.

Hmm, why do you think that is unhelpful. I would start the first lecture of a circuits class with that discussion.

I have to ask who would be actually in this class, what would their level of knowledge be and where would the whole course be preparing them for? This thread has not decided the answer to that question so we can never come to a conclusion.

 

[Dale]

I have to ask who would be actually in this class, what would their level of knowledge be and where would the whole course be preparing them for?

I was envisioning an intro to circuits class. So it would be freshman and sophomore engineering students, assuming some calculus and physics (possibly concurrently with this class depending on the curriculum).

 

[sophiecentaur]

I was envisioning an intro to circuits class. So it would be freshman and sophomore engineering students, assuming some calculus and physics (possibly concurrently with this class depending on the curriculum).

OK. So that means they are likely to get a better version of things later on. The problem is when they don't and end up with a 'mechanical' picture in their minds which is never corrected. Whatever the situation, they should all be given an immense caveat about treating electrons as primary school objects and that you only get 'right answers' to electronics problems with Maths and not with arm waving about little pebbles moving around a wire. It has been my experience that many (probably most) students want to stick with the naive model, rather than moving on and learning to use a bit of problem solving.
I have endless gratitude for Mr Scales who was totally dismissive of the electron model when he taught us A level electricity. As one of his laziest students, I would not have gone for the Maths if he had given me the option.

 

[nsaspook]

You have brought in a very relevant point. Basically, Technicians are 'Trained' to perform certain functions and the training is aimed at being a cost effective way of producing people who will be able to work the technology. The services want people who can 'do the job' and I don't feel that recipients of many courses get a good deal out of them. Electrons and Photons are brought in in an effort to 'explain' the inexplicable (inexplicable with their levels of knowledge). It just demonstrates how difficult a subject Physics is when many of the educationist fail to understand the limits of the simple models they are using. I assume that, as you had a rigorous electronics education, you appreciate that electrons only need to be considered when you're inside some components.

When I started my education electrons in tubes were still very common so we learned the basic rules of tube operation in a way that was consistent with a physics based model of particles, fields, acceleration and energy.

I think one of the basic misunderstanding in the beginning starts with the idea of electric current (a moving electron) as the electrical KE energy media in a circuit. Any simple educational model or analogy must build a foundation that clearly explains that is a confusing simplification of how the circuit works even in a simple battery and lamp circuit. IMO we need a basic fields based approach from the beginning in circuits as explained in books like this.
http://onlinelibrary.wiley.com/doi/10.1002/0471433934.fmatter/pdf

Field phenomena are often felt to be the domain of the physicist. In a sense this is correct. Unfortunately, without a field-based understanding, many electronic processes must remain mysteries. It is not necessary to solve difficult problems to have an appreciation of how things work. It is only necessary to appreciate the fundamentals and understand the true nature of the world.

 

[sophiecentaur]

When I started my education electrons in tubes were still very common so we learned the basic rules of tube operation in a way that was consistent with a physics based model of particles, fields, acceleration and energy.

I think one of the basic misunderstanding in the beginning starts with the idea of electric current (a moving electron) as the electrical KE energy media in a circuit. Any simple educational model or analogy must build a foundation that clearly explains that is a confusing simplification of how the circuit works even in a simple battery and lamp circuit. IMO we need a basic fields based approach from the beginning in circuits as explained in books like this.
http://onlinelibrary.wiley.com/doi/10.1002/0471433934.fmatter/pdf

I think you have missed my point here. That link is not really about "basic" Physics; a lot of it is more advanced than the basics that most people ever grasp. Virtually none of it is needed for the sort of circuit theory and calculations that get cars and computers designed. My Dad explained about Valves and the flow of electrons - whilst they are in a vacuum but he had more sense than to go into solid state behaviour. (I was probably only about 14 at the time). Your point about KE of electrons in a metal is well made. The thing that bothered me most about the triode valve was how the Anode Volts went DOWN when the current went up!
I guess that a lot of the arguments here are based on personal experience. Either people think their education was good or they feel it was 'badly aimed' / just plain bad - depending.

 

[DrDu]

I would not regard the streaming liquid picture to be merely an analogy. After all, the electrons form a liquid, namely the Fermi liquid.