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Proof of Ohms law

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

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  1. noone.

    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
  2. Charles

    Charles Guest

    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. 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.
  4. Joerg

    Joerg Guest

    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 Webb

    Norman Webb Guest

    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. 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. 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. haha.. arbitrary huh? yeah right...
  9. 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. Chuck

    Chuck Guest

    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.

  11. John Larkin

    John Larkin Guest

    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

  12. 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. Joerg

    Joerg Guest

    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.
  14. John Larkin

    John Larkin Guest

    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.

  15. Bob Monsen

    Bob Monsen Guest

    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

    Bob Monsen
  16. Joerg

    Joerg Guest

    Well, that would be further proof 'cuz that's how some tax laws are :)
  17. 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

    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).

  18. gearhead

    gearhead Guest

    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. 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 seem to be walking into this one butt first..., to coin a
    phrase...what part of " 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

    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, 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
    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
    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
    contradictory axioms, I think...
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