# Proof of Ohms law

Discussion in 'Electronic Basics' started by noone., Feb 5, 2008.

1. ### noone.Guest

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

2. ### CharlesGuest

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)?

3. ### Bearded OccamGuest

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
the carbon-composition resistors, but their resistivity changes
slightly with voltage. And of course lots of things have profoundly
nonlinear curves, e.g., diodes.

4. ### JoergGuest

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.

5. ### Norman WebbGuest

noone. wrote in message ...
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

6. ### Jon SlaughterGuest

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

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)

7. ### Kevin AylwardGuest

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.

8. ### Jon SlaughterGuest

haha.. arbitrary huh? yeah right...

9. ### Kevin AylwardGuest

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.

10. ### ChuckGuest

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

11. ### John LarkinGuest

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

12. ### Jon SlaughterGuest

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?

13. ### JoergGuest

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.

14. ### John LarkinGuest

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

15. ### Bob MonsenGuest

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

16. ### JoergGuest

Well, that would be further proof 'cuz that's how some tax laws are 17. ### Jon SlaughterGuest

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

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

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.

19. ### Kevin AylwardGuest

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,
http://www.kevinaylward.co.uk/gr/index.html we have the Einstein model, that
is Graviy is due to curved space, i.e. objects just follow "straight lines".
However, an alternative model, is the spin 2 graviton model, which, treats
gravity as momentum exchange of particles, and produces exactly the same
field equations as noted in the link.

So, what is true "reality". Curved space or Spin 2 graviton particle
exchange?
Oh dear...I am quite stunned here. I don't see how anything that I have said
could possibly have lead to this rather grandiose claim of yours here. It
would seem, to the contrary, that it is yourself that misunderstands what
science is actually about. Understandably, as it seems to me that most, have
a similar to your, rather quite idea of what science is. I actually make my
living from science. Like, I design analogue i.cs., all in the virtual
world. However, I don't care if electrons actually exist in what ever your
particular belief of "reality" is. My circuits work, irrespective of what
anyone claims is the reason. Like mate, have you ever actually seen an
electron?
Er.. yes..I already gave an example. It is "The Special Theory Of
Relativity" and "The Lorentz Ether Theory". The second one is the curved
space v spin2 particles, although this second one, don't actually have  