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unionised
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"
If we want to consider what Ohm actually said, then his law is:
(Current Density) = (Conductivity) x (Electric Field Strength)
V = IR is actually the macroscopic version of his law.
"
Thanks for digging that out, I'd be grateful if you could supply a reference.
I'm not sure it matters.
If your first version of Ohm's law is right then R is a constant.
If the second version is right then R is a function of the field strength.
The second one is true (by deffinition) but almost useless.
I can equally state that the current is the product of the obtuseness and the square of the voltage. (This serves as the deffinition of
"obtuseness"
Equally, it's the product of the awkwardness and the log of the |voltage|.
(likewise, awkwardness is defined such that this expression is true).
The important aspect of his law is that if you chose the first power of the voltage then, for many bits of wire etc. you get a (nearly) constant value
of R.
The second deffinition, which does no more than state that threre is some relation between current and voltage, serves no purpose.
The first, where R is constant, actually gets used quite a lot.
I think you insult Ohm to say that he gave the second definition.
If you accept that Ohms law requires a direct proportionallity then what I said about it not applying to cells is true.
If you think of R as a variable then what, exactly can you use Ohm's law for?
I think that you have tried to move the goalposts by saying that R is a variable in V=IR- it then becomes true by deffinition. Unfortunately, it also
becomes useless.
How could this version of Ohm's law be used to help design anything? it would all become a "suck it and see" approach
I can't see how changing from current to current density; voltage to field strength and conducance to resistance makes any real difference.
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zoomer
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Unionized, I hope you will take this for what it is, just some information. I do not have any beef with you or anyone else on this board.
| Quote: | Originally posted by unionised
How could this version of Ohm's law be used to help design anything? it would all become a "suck it and see" approach
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In semiconductor design, that's exactly what we do. We know the conductivity (the inverse of resistance) of silicon in gross terms. But as you
point out, exactly determining a resistance beforehand that changes with an environment that changes with the resistance itself is a Catch-22. So we
approximate the behavior, build a prototype, then test it to as many V/I curves as possible, and build a chart of the actual resistance. I used to
have large volumes of nothing but conductance charts for Si+.001%Ga, Si+.002%Ga, etc. (Obviously now they are all on CD). As years go by, more and
more is learned, and computer models get better and better, but they still need to take that first prototype into the lab and characterize the heck
out of it. Most of the time, it's not quite what's expected, and some changes are almost always needed before production.
Z
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unionised
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It's interesting to know how these chips that the 21st century runs on are designed. (though I doubt the book was very interesting).
What I was refering to was the nightmare where, just because you raised the current, there wasn't any certainty that the voltage would rise,
never mind that it would be in proportion.
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sparkgap
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Minor mathematical point of contention, unionised, but this in no way detracts from your main point:
"...There's a mathematical function to describe this called something like "Kronecker's Delta" an infinitely narrow,
infinitely high spike with unit area..."
Nope, what you were referring to was the Dirac delta function, which has the properties you describe. Kronecker delta is a slightly different beast. 
sparky (~_~)
"What's UTFSE? I keep hearing about it, but I can't be arsed to search for the answer..."
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unionised
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OOps! wrong delta.
Glad to know that someone read what I posted.
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zoomer
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Actually, we chipheads were always excited when a new volume came out. WCIS.
It's all buried in the computer models now, though.
This thread has taken many directions, and I must confess to have lost track of the main issue. My apologies, but can you give another example of
such a "nightmare scenario?"
Z
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Twospoons
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Myself, as an electronics engineer for 16 years, I only use 'ohm's law' in linear systems, which includes complex impedance. I
can't use V=IxR to calculate the current through a diode. Its an exponential relationship. I= Isat x e ^ (-kT/V) is not ohm's law. Damn
thats hard to type without superscripting!
It gets worse. There's a facinating little device called a tunnel diode. In this diode the junction doping is so sharp that the electrons are
able to cross the depletion barrier by quantum tunnelling, without ever having enough energy to go over the barrier as required in a normal diode.
They freakishly appear on the other side of the barrier simply because the probability function describing the orbital is significantly non-zero on
the other side, because the barrier is very, very thin. In short, they can - so they do! The net result is that part of the V / I curve for a tunnel
diode has negative slope - it behaves like a 'negative' resistance.
How's that for a 'nightmare'?
Helicopter: "helico" -> spiral, "pter" -> with wings
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12AX7
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Idunno but it provides wonderfully precise triggering in my Tek 475. 
Tim
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unionised
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I'd forgoten about tunnel diodes. They really make a mockery of the idea that V=IR.
This site
http://www.americanmicrosemi.com/tutorials/tunneldiode.htm
shows the V I curve. For some values of I there are 3 different Vs and presumably 3 different values for R.
Zoomer,
Quite a lot of things would count as that nightmare, the tunnel diode is one, how do you model a circuit where for a given cuurent there can be 3
possible values of V. It's not impossible but, compared to just V=IR, it's a nightmare.
[Edited on 7-9-2005 by unionised]
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zoomer
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(Apologies for the dropout, I've been away for a family medical emergency, everything's OK now.)
Gee, here I thought you were going to start with a tough one! 
"Negative resistance" is something of a misnomer. Resistance (a molecular-level analogue to friction) is always positive, because the
reverse would be "amplification," a something-for-nothing arrangement that modern physics laws frown on. N-res refers to the phenomenon
where a material's resistance to electron flow is modified by applied EMF in such a way that the amount of current has an inverse reaction to
changes in EMF, and not a direct correlation as with passive and "positive" semiconductor materials. The point here is that N-res
refers to the curve (the trend of multiple values), and not the instantaneous R value itself at any single point.
There is a difference between the mathematical relationship between V, I & R, and the ability of humans to understand and use that relationship in
complex situations. And in re-reading the thread again I wondered if that distinction is what people have been speaking to all along. The
mathematical relationship between V, I & R is absolute and unchanging regardless of the situation, exactly the same way the length of the three
legs of a triangle are always indivisibly linked. However, applying Ohm's Law is tricky if not impossible when dealing with active
materials (semiconductors, e-cells, etc) and sometimes the only way to know the values for sure is to hook it up and measure it yourself.
unionized, if that's what you are saying then I agree with you 100%.
Z
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IrC
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It is what I had been trying to say.
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