# Insights Ohm's Law Mellow - Comments

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#### Greg Bernhardt

A question from Reddit

The ideal gas law doesn't apply for real gases. Is the ideal gas law then not a law?

#### eltodesukane

Semantics..
Just like Moore's law (which is not a fundamental law of the universe),
or evolution theory (which so many have told me is "just a theory").

#### Averagesupernova

Gold Member
I have actually thought about this a number of times. I look at it from the perspective that ohms is simply a ratio. Sometimes the ratio holds true across a wide range of voltages and currents and with other materials not so much. We can nitpick about this from now until eternity I suppose.

#### LvW

...and we can think about the meaning of the form: V=I*R.
We are using this form to find the "voltage drop" caused by a current I that goes through the resistor R.
However, is it - physically spoken - correct to say that the current I is producing a voltage V across the resistor R ?
(Because an electrical field within the resistive body is a precondition for a current I, is it not?)

#### Dr. Courtney

Gold Member
2018 Award
There are important distinctions between truly general laws and useful summaries that are technically approximations at best and in some ways more definitions of tautologies.

Coulomb's law is a true law of Physics.

Ohm's law is more of a definition of Ohmic materials. Ohmic materials obey Ohm's law. That's like saying "It works where it works" without having real predictive power regarding for what materials it will and won't work before the experiment is performed.

The ideal gas law is an approximation in a limiting case. In that sense, it is a true law of Physics, at least as much of Galileo's law of falling bodies.

#### vanhees71

Gold Member
Well, it's really semantics. I'd not say that Coulomb's law is "true law of physics" although I prefer the phrase "fundamental law". All physics laws are "true" in the sense that they are well tested by observations and in most cases have a restricted range of validity.

That said, I think that Coulomb's Law is, as Ohm's Law, a "derived law" from the fundamental laws of (quantum) electrodynamics. Coulomb's Law is the electrostatic field of a radially symmetric static charge distribution and of course derivable from Maxwell's equations. Ohm's Law is derived from linear-response theory of (quantum) electrodynamics. The electric conductivity is a bona-fide transport coefficient, definable in terms of the Kubo formula. The corresponding correlation function is the em. current-current correlator etc.

#### Averagesupernova

Gold Member
...and we can think about the meaning of the form: V=I*R.
We are using this form to find the "voltage drop" caused by a current I that goes through the resistor R.
However, is it - physically spoken - correct to say that the current I is producing a voltage V across the resistor R ?
(Because an electrical field within the resistive body is a precondition for a current I, is it not?)
We can determine the speed, distance, or rate (MPH/KPH) by knowing 2 of the 3. But, we certainly do not say that the length of the road causes motion of the vehicle. I see it is really no different with ohms law.

#### anorlunda

Mentor
However, is it - physically spoken - correct to say that the current I is producing a voltage V across the resistor R ?
(Because an electrical field within the resistive body is a precondition for a current I, is it not?)
Not true in circuit analysis. That is why I added the last paragraph about 5 levels of study. In Maxwell's equations, we deal with the speed of propagation of fields (speed c in a vacuum). So there we can talk about which came first. In circuit analysis, Kirchoff's laws are assumed to apply instantaneously, so that the V and I appear simultaneously; no first/second. If you want to dig deeper into the physics of what happens first, then abandon circuit analysis, abandon Ohm's law, and use Maxwell's equations. Perhaps I should go back and add that bolded sentence to the article.

#### ZapperZ

Staff Emeritus
2018 Award

Ohm's law can be derived from the Drude model of conduction in metals. This is the statistical classical model of electron gas in a conductor that connects the current density, the applied electric field, and the conductivity. Unfortunately, this origin is never mentioned in the article.

It is from this model that we can see the level of simplification, assumptions, and limitations of Ohm's Law, and thus, can also see when and where it will break down.

Zz.

#### sophiecentaur

Gold Member
It's interesting that, in a thread that is trying to discuss Ohm's Law, no one seems to have mentioned Temperature. Ohm's Law is followed by a conductor when its Resistance (obtained from V/I) is independent of Temperature. "R=V/I" is not Ohms Law, any more than measuring the Stress/Strain characteristic of any old lump of material 'is' Hooke's Law.
In circuits, the 'resistive' components are not just designed to follow Ohm's Law (if they are metallic then they will easily do that); they are designed to have a more or less constant resistance over a large temperature range. That is, in fact, a Super Ohm's Law.

#### vanhees71

Gold Member
The electric conductivity of course is a function of temperature and chemical potential (for an anisotropic material it's even a tensor).

#### sophiecentaur

Gold Member
The electric conductivity of course is a function of temperature and chemical potential (for an anisotropic material it's even a tensor).
Yes. But Ohm's Law specifically refers to Metals at a constant temperature, doesn't it? Your point has been ignored by the contributions to this thread.

#### vanhees71

Gold Member
Well, yes, that's why I wrote this posting :-).

#### ZapperZ

Staff Emeritus
2018 Award
Yes. But Ohm's Law specifically refers to Metals at a constant temperature, doesn't it? Your point has been ignored by the contributions to this thread.
I beg to differ. By invoking Drude model, I have implicitly invoked temperature dependence.

However, to be fair to the OP, Ohm's law in the "practical" sense is often used when the resistance is a constant. Thus, it has already implied that temperature effects are not described within the Ohm's law relationship. I do not see this as being a problem, because this might easily be beyond the scope of this topic.

However, since the OP discussed the "non-derivable" issue, and did not even mention the Drude model, I consider that to be a significant omission.

Edit: I found this post made by me from way back in 2007 on the exact topic:

So this has been discussed A LOT over the years.

Zz.

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#### vanhees71

Gold Member
One should also mention that the Drude model is not the final answer but that the "electron theory of metals" is one of the first examples for a degenerate Fermi gas (Sommerfeld model). The model was extended by Sommerfeld, explaining the correct relation between electric and heat conductivity (Wiedemann-Franz law).

#### ZapperZ

Staff Emeritus
2018 Award
One should also mention that the Drude model is not the final answer but that the "electron theory of metals" is one of the first examples for a degenerate Fermi gas (Sommerfeld model). The model was extended by Sommerfeld, explaining the correct relation between electric and heat conductivity (Wiedemann-Franz law).
Again, we can take this to a million different level of complexities, but this is certainly well beyond the scope of this topic. I mean, just look at Ashcroft and Mermin's text. They started off with the Drude model in Chapter 1, and by Chapter 3, they talked about the "Failures of the Free Electron Model", which was the foundation of the Drude Model.

So yes, we can haul this topic into multi-level complexities if we want, but we shouldn't.

Zz.

#### anorlunda

Mentor
However, since the OP discussed the "non-derivable" issue, and did not even mention the Drude model, I consider that to be a significant omission.
It sounds like you didn't read to the end. The article does mention the Dude model as one of five levels at which you can study electricity. It also says that the scope of the article was limited to circuit analysis.

#### ZapperZ

Staff Emeritus
2018 Award
It sounds like you didn't read to the end. The article does mention the Dude model as one of five levels at which you can study electricity. It also says that the scope of the article was limited to circuit analysis.
I did see your link to it, but if you read your main article, it left the impression that Ohm's law is not derivable, that it is purely phenomenological. That is what I was objecting to.

BTW, the Drude model is not a model for "electricity". It is a model to describe the behavior of conduction electrons. It means that it gives you the definition and the origin of physical quantities such as resistance, current, etc. Charge transport, i.e. "electricity", is more often described via the Boltzmann transport equation.

Zz.

#### David Lewis

However, is it... correct to say that the current I is producing a voltage V across the resistor R ?
Yes, if it's an applied voltage. A voltage drop (symbol V) occurs when current passes through the resistor.
Conversely, with a voltage source, EMF (symbol E) produces the current that passes through the resistor.

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