# Proof of Ohms law

• posted

Has anyone ever proven Ohms law from first principals?

I mean is there any way to take the laws of electrostatics, and from the derive E = IR?

Just Curious

-Thanks

• posted

I have heard that Richard Feynman did stuff like that. Working backwards from the standard model of Quantum Mechanics. Interesting, but only demonstrates consistency.

What level of proof are you interested in? Conservation of energy (which also cannot be "proven" if you set the bar high enough)?

• posted

I don't have the exact answer, but can point you in the right direction. It doesn't really come from electrostatics. The relationship between voltage and current is a property of the device or material being measured. Metals happen to have an extremely linear voltage-current function, so that if a resistor is made from a metallic element, it will obey Ohm's Law.

Why metals behave this way is covered in an elementary solid state physics test, under "Drude Theory of Metals," to sufficient accuracy to probably answer your question. Other things are almost linear, like the carbon-composition resistors, but their resistivity changes slightly with voltage. And of course lots of things have profoundly nonlinear curves, e.g., diodes.

• posted

Well, it hasn't been declared unconstitutional, so there you go. SCNR :-)

Seriously, you could go all the way back to Maxwell's equations but it will be hardcore math. That's what one of our professors did.

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Regards, Joerg

http://www.analogconsultants.com/```
• posted

YES, but just how deep do you want to go.

Resistance is a derived quantity so the formula be should be written R = E/I Voltage ( V or E) is defined as Energy/ unit charge and Current (I) is defined as rate of flow of charge or Coulomb/second

• posted

It can be proved from maxwell's equations(and chances are any book on electromagnitism will drive it). Also there are a few assumptions that are made.

Heres the general idea:

J = -ne*v is the current density for a material with charge moving on average with speed v.

but v = - (e/m)E*tau

So J = g*E where g is called the conductivity. i.e., it depends on the material only and not the applied field E.

Hence there is a relation between the voltage and current(density) and it says they are proportional(For the assumption on the average velocity).

If you apply it to a "rod" or "wire" then you get the macroscopic version which is ohms law.

The main idea here is that applying an electric field produced a motion of charge.. e.g., a velocity of charge and hence v is a function of E. But current is just the motion of these charges and hence ultimately I is a function of E. For many materials its simply proportionate because v is proportionate to E. Its not always the case and of course fails for sufficiently large fields and even depends on frequency(which isn't taken into consideration for this simple analysis). (although the concept can be applied in those cases too by using it as a linear approximation)

• posted

No.

No.

A linear resister is *defined* as that which obeys ohms law. There is no material that is absolutely linear.

Proof is meaningless in science, as is truth. One can only derive approximations based on some arbitary axioms, which may or may not be true.

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Kevin Aylward
ka@kevinaylward.co.uk```
• posted

haha.. arbitrary huh? yeah right...

• posted

Yes.

The point of (physics) science is to discovery the smallest set of axioms that will predict the most experimental results. Whether or not those axioms are "true" or not is not really relevant. of course, if than axioms are contradictory, i.e. false, that is relevant. There is no guarantee two sets of axioms, that contradict each other, will not produce exactly the same predictions. Indeed, for example, check out special relativity and the lorentz ether theory.

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Kevin Aylward
ka@kevinaylward.co.uk```
• posted

Not likely.

Ohm's law ". . .was originally established by experiment. . .", according to Maxwell in 1876, and ". . .must still be considered a purely empirical law, as it has not hitherto been deduced from the fundamental principles of dynamics."

From the Scientific Letters and Papers of James Clerk Maxwell.

Chuck

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• posted

That's sort of circular. Maxwell's equations lead to "Ohm's law" only if you assume that carrier velocity is proportional to field strength in certain materials. So you get Ohm's law by assuming Ohm's Law.

Maxwell didn't actually know what a charge carrier is. He died in

1879.

John

• posted

Really? Where the hell did you get that idea? Not relevant huh? So predicting reality is not relevant?

Those theories were created to try and be relevant. A theory doesn't have to be 100% correct to be useful.

Seems to me like you don't understand what science really is about. You assume because we cannot know exactly that it means its arbitrary. Arbitrary is essentially random... and do you really think that if we pulled out the axioms we have from thin air that they would have been useful as that?

It seems also you have no clue about mathematics. Sure axioms are taken for granted but they usually are based on intuition and people hell of a lot smarter than you seemed to have gotten it right. Do you seriously thing that if our axioms of mathematics were arbitrary that all of mathematics would have held up? Its true you can build up a mathematical basis only from a consistant set of axioms but I doubt if these axioms were completely arbitrary that they would fit with reality so well... or at least what seems to be so well.

You don't seem to agree that science has any useful purpose and has had any useful success... But just look around... or do you think the same results could have been achieved with any other set of "arbitrary" axioms?

• posted

Then how about this rationale: Ohm's law has been applied several gazillion times and it always worked. The number of events where it reportedly hasn't jibed were zilch, I assume. Now in the medical world that would be considered bullet-proof clinical evidence.

```--
Regards, Joerg

http://www.analogconsultants.com/```
• posted

No conductor exactly follows Ohm's Law, so it isn't a law. Lots of conductors are seriously nonlinear. It only works for materials where it works, again circular.

There are solid conductors that have bulk negative resistance.

John

• posted

Ohm's law is a 'rule of thumb' as opposed to a 'law of nature'. It works because people build resistors out of stuff that approximately follows ohm's law for limited ranges. That makes it much easier to predict current when given a voltage.

One can easily think of a counter example. For example, given any macro object, I can always find a voltage range that causes ohm's law to fail. So, it is not a law in any real sense.

The OP was simply asking if there was some kind of more general law that could be used to derive ohm's law. Since it isn't true in any real sense, deriving it from true statements about electrostatics is probably not possible.

Regards, Bob Monsen

• posted

Well, that would be further proof 'cuz that's how some tax laws are :-)

```--
SCNR, Joerg

http://www.analogconsultants.com/```
• posted

Yes there is a more general law... its called maxwell's equations(even though they are based on the real "laws" such as faraday, ampere, etc.

What you need to realize is that all laws have hypothesis. Its true that his law isn't a law in the sense of gravity but for the most part it is a theorem of electronics. It is derivable from first principles as I demonstrated in my "proof". The first principles are those basic concepts that are learned by every physics student like velocity, momentum, voltage, etc... Ohms law is a macroscopic vew of these laws applied to an ideal material.

If you don't understand or no one told you, physics is all about idealizations and approximations. Nothing is perfect!!! NOT EVEN GRAVITY!! You really think that someone behind the "scenes" is computing the gravitation formula for every interaction? Its simply an explination that works and as far as the law is concerned, there has never been anything to contradict it.

In fact ohm's law is a law in the sense of linear approximation as every material exibhits it in some respect since all we are deal with is the motion of electrons and what makes them move. When they break this behavior it's just another equation that needs to be added to make them complete, but fundamentally its the same thing. If say the voltage is increased beyond a point so that now the electrons are not flowing proportional to the voltage then a new "law" needs to be used as ohm's law is applicable only to the case when the speed is proportional to the voltage. But even in the case when its not it can still be approximated locally as proportional(not the best way but done all the time in science).

Re-read my "proof" or go find a book on EM and you'll see that it is from first principles. I did not go into all the detail as its just an outline. (I did explain why it conceptually should come out that way though)

If you think that Ohm just pulled it out his ass then you have a great deal to learn about science. If you think it was all emperical then you would half right. True he discovered it by observation but again, you have a lot to learn about physics if you think that was all. (that is only 1 of the principles of science) Anyone can observe and come up with some explination... only scientists do it right(not that the other methods are necessarily wrong).

Also, it seems you do not understandt he concept of a theorem and the hypothesis that go along with it. Ohm's law is to be applied only to materials that exibit certain properties. Now they are somewhat circular when you get down to it but ultimately everything is.

The hypothesis is simply "If the speed of the electrons flowing in a material is proportional to the applied voltage then ohms law applies" meta-logically identical to "If a numer is even then its square is even". Obviously if the hypothesis is violated then the conclusion won't necessarily hold... it might though, so your idea of a counter example isn't really a counter example because it doesn't satisfy the hypothesis. (although in physics there are many cases that such things happen and physics needs to be "updated" to explain them, this case is not one of them since it's hypothesis is sufficient for its conclusion in all cases(see the derivation to understand why)).

Again, I'll go ahead and outline the idea

E = k*v I = l*v

hence I = l/k*E or that I is proportional to E. All it is is mathematics with a few physical hypothesis. Ohm's law might have started emperically but is fundamentally mathematical. (its really no different than most mathematical theorems)

In in reality the constant of proportionality isn't constant but this is the case in just about everything... even the constant in gravity isn't constant... but it's close enough and if it does change we gotta deal with that when it happens. With ohms law its we simply use circular logic and say if the resistance is constant then it obeys ohms law(this is just what I said earlier in different terms).

Jon

• posted

I was experimenting with a positive temperature coefficient heating element a while back. If you look at the resistance versus temperature graph for a typical PTC heating element, the device's resistance versus temperature follows a mild negative slope up to a certain temperature, then as it gets hotter the curve has a knee and changes to a positive slope, and the slope gets steeper at higher temperatures (as long as you don't burn up the heating element lol). This works as long as the element is being heated internally, by an ever increasing current, and you are using that current to measure resistance (versus voltage across the element). Interesting fact is that if you apply heat to the element externally and apply a small current, the resistance continues FALLING as you make the element hotter and hotter. You go past the knee in the graph and insteaded of turning positive, the resistance just keeps dropping lower and lower. I found that with my PTC heating element at say several hundred degrees fahrenheit, the resistance differed by orders of magnitude depending on whether that heat came from high current within, or was eternally applied and I used small currents to measure resistance. In the latter case, the resistance dropped to a very, very small value. So what is resistance? How do you measure it? You can't. You have to measure other things (current and voltage) and calculate resistance. It's an abstraction. It's only defined in terms of current and voltage. Current and voltage are physical properties.

• posted

Well, obviously,.. sitting in my bedroom on my tod for the last 40 years contemplating the universe, whilst picking fluff out of my navel. oh.. I am an atheist, hell don't exist.

err... did you actually check out, "The Special Theory Of Relativity" and "The Lorentz Ether Theory" ?

Oh dear..you seem to be walking into this one butt first..., to coin a phrase...what part of "...discover the smallest set of axioms that will predict the most experimental results" did you not understand? Maybe I need to rephrase it.

To repeat, I stated that the "truth" of the *axioms* were not relevant. The axioms are just part of a method we use to calculate results. So long as we get the correct answers, it matters little as to the absolute "truth" of the axioms. Indeed, by definition, axioms can not be proved, so its impossible to know if they are the "truth" or not, anyways.

Physics predicts the results of experiments, so just what do *you* mean by "reality"? I would like to know what your expert opinion is as to what actually constitutes a definitiion of "reality".

I have little idea why your phrase here has any relevance to what I said. Are you are responding to another post?

I haven't really discussed the "correctness" of a theory in this post, I was commenting on a theory's "truth". Correctness is the ability of a theory to predict the correct results. I don't see that I made any claim that the correctness of a theory had to be 100%, indeed I stated "most correct predictions". Surely, the only rational interpretation of this phrase is that there is no presumption of complete correctness?

Seems to me that I understand these issues a little deeper than you are giving credit for. Seems to me that you have misread what I wrote.

Assume what what means?

Not in the sense that I am using the term. Shall we say then, "somewhat" arbitrary, in as much as that axioms are not necessarily unique, and we are free to chose any consistent set of axioms and models at will.

There is an interesing quote on this:

"The universe is what we say it is. When theories change the universe changes." James Burke - PBS "Connections" series.

As I noted, they are arbitrary, as it is quite possible to have two sets of contradictory axioms that predict absolutely the same experimental results. Indeed, despite having contradictory axioms, two different theories can be mathematically identical.

But I do actually speak from a higher authority on this matter...

"Physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world." - Albert Einstein

So, apparently, old Albert take the view that axioms are somewhat err.. arbitrary. Well, I suppose it's that two great minds think alike sort of thing. Would you now like to retract your comment below?

Well, I am certainly not an expert of mathematics in the wider scheme of things, but I do dable a bit.

However, I was not really discussing math here per say, I was discussing physics axioms and models, for example, conservation of momentum, conservation of energy etc. In fact, if you might take the time to investigate these issues, one might well be lead to the conclusion that even these basic axioms are actually "defined", that is they form a tautology set, as indded noted by thy lord Einstein.

For example, if we take F=ma. well mate.., try and define force and mass independently from each other.

You mean that there are people smarter than me? Amazing.

Now, again, you are discussing mathematics, not physics per say.. For starters, most of mathematics, probably 99.999999%, has no relevance to "reality" at all. In actual fact, mathematicians chose axioms pretty much at will nowadays and see where it leads them. Why don't you actual do a bit of research on this and see what your modern mathematician does in these here modern times. I think you might be truly surprised at how modern math men arbitrarily chuck away any axiom, and invent new ones as matter of standard procedure. Its all the rage, really. Pointless, but all the rage.

Indeed, arguably, it was this fee spirit approach that, led in part to non Euclidean Geometry, which, amazingly, actually ended up having some applications in this particular universe, to wit, the aforementioned General Relativity. If some dude hadn't decided that the parallel line through a point axiom was not cricket we would no doubt all be floating around in space as Einstein would have been simply unable to invent Gravity as warped space to hold us dudes firmly on to the ground.

Physics is based on arbitrary models, you know, Einstein's "free creations" alluded to above. Models are not unique. There are many equally vaild models of "reality".

Tto continue on that point, for example, from,

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