Re: Proof of Ohms law


"Joerg" <notthisjoergsch@xxxxxxxxxxxxxxxxxxxxx> wrote in message news:7WNqj.6431$0w.31@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
John Larkin wrote:
On Wed, 06 Feb 2008 00:35:21 GMT, "Jon Slaughter"
<Jon_Slaughter@xxxxxxxxxxx> wrote:

"noone." <harrytuttle777@xxxxxxx> wrote in message news:foao1t024g6@xxxxxxxxxxxxxxxxxxxxxxx
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
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)


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


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/

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

.

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