Why is Ohm's Law only applicable to a limited region?

[anorlunda]

anorlunda submitted a new PF Insights post

Ohm's Law Mellow

Continue reading the Original PF Insights Post.

 

[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]

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]

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]

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]

...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]

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]

There is a major omission in this article.

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]

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]

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

 

[sophiecentaur]

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]

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

 

[ZapperZ]

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:

https://www.physicsforums.com/threads/derive-ohms-law.179056/#post-1392205

So this has been discussed A LOT over the years.

Zz.

 

[vanhees71]

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]

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]

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]

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.

 

[sophiecentaur]

Remember, tho', the Voltage is the Energy supply for the charge flow. If you really want a cause and effect, I would say the Voltage causes the current. But in circuits, a voltage somewhere else can cause current to flow which will result in a portion of the supply volts appearing across a resistor. That's K2.

 

[David Lewis]

And in the former, energy is supplied. In the latter, energy is consumed.

 

[Handy Andy]

Ohms law is based on an ideal world for students. All conductors have a complex impedance based on frequency, temperature, resistance, inductance and capacitance. These vary depending on how cables are run adjacent to each other, even climatic conditions can come into play etc. It isn't an ideal world, even a straight piece of wire has typically 10mH per metre. The complex impedances in a conductor become significant when switching very high currents quickly.

 

[Herman Trivilino]

The relation $R=\frac{V}{I}$ is not Ohm's Law. Rather, it's the definition of $R$.

Ohm's Law is the assertion that over a range of voltages, $R$ is constant.

Like all laws, it has limits of validity. There is no such thing as a law with universal limits of validity. Hooke's Law is an example of a law that can be compared to Ohm's Law when teaching this concept of limited validity.

 

[Dilema]

The article "Ohm's law Mellow" address a very impotent issue, Yet there is no evidence for violation of Ohm's law (within the limit of ohm's law). I think the confusion comes from the fact that textbook do not elaborates on the preliminary assumptions under which Ohm's law valid.

 

[Dilema]

anorlunda submitted a new PF Insights post

Ohm's Law Mellow

Continue reading the Original PF Insights Post.

I disagree to the general Idea that Ohm's Law is not a law, yet I strongly support the importance of this issue which I think boils down to the very basics philosophy of what is a physical law, what are the therms under which it consider violated.
Following the article spirit, I would recommend title like: Ohm's hypothesis or even better - Ohm's convention.
I understood the solar device is given in order to provide real example for violation of ohm's law. But it is not. the rectification profiles comes from a diode like element in the equivalent circulate. Up to date there is no system that violates "Ohm's law" . Note for example that Memristor, Thermistor, Warburg element or any constant phase (CPE) or non-CPE do not violates Ohm's law.

 

[anorlunda]

There are no rigid rules in science about the use of words like law, rule, theory, etc, so we are free to disagree

I view the definition of R as the ratio of V and I. As a definition, it can't be violated by definition (pun intended )

Newton's Laws and the conservation laws are all derivable from the fundamental symmetries of nature. I resist the idea of making Ohms Law comparable with those. But if you want to call it a law, go ahead and knock yourself out. But don't complain if I prefer different words.

 

[vanhees71]

Ohm's Law is derived from many-body theory. It's defining a typical transport coefficient in the sense of linear-response theory. It's the "answer" of the medium to applying an electromagnetic field, and defines the electric conductivity in terms of the induced current, $\vec{j}=\sigma \vec{E}$, where in general $\sigma$ is a tensor and depends on the frequency of the applied field. So Ohm's Law is a derived law and has its limit of validity (particularly the strength of the electromagnetic field must not be too large in order to stay in the regime of linear-response theory).

 

[sophiecentaur]

I view the definition of R as the ratio of V and I. As a definition, it can't be violated by definition (pun intended )

I wholeheartedly agree. It's a formula / definition and says nothing about whether or not Ohm's law happens to apply to what's connected to the terminals on the 'black box' we're examining. R could change, or not as V,I or T changes. If it doesn't happen to change then the component is not following Ohm's Law. But one calculation wouldn't tell you one way or the other.
This puts me in mind of the SUVAT equations with which we learned to calculate motion under constant acceleration. We don't refer to them them as 'Laws' of motion and we wouldn't dream of suggesting that a measurement of the change in velocity of an object in a given time would be the same under all conditions. But somehow, R=V/I is referred to as Ohm's Law. Teachers and lecturers can be very sloppy about these things. Aamof, I don't remember the constant acceleration thing being emphasised to me in SUVAT learning days, either. They just drew a V/t triangle and did some calculations. It left me uneasy for quite a long while. But teenagers feel 'uneasy' about a lot of things so it was actually the last of my worries.

 

[anorlunda]

Ohm's Law is derived from many-body theory. It's defining a typical transport coefficient in the sense of linear-response theory. It's the "answer" of the medium to applying an electromagnetic field, and defines the electric conductivity in terms of the induced current, $\vec{j}=\sigma \vec{E}$, where in general $\sigma$ is a tensor and depends on the frequency of the applied field. So Ohm's Law is a derived law and has its limit of validity (particularly the strength of the electromagnetic field must not be too large in order to stay in the regime of linear-response theory).

That's true for the specialized case of a linear and uniform mediums. The article addresses the general case of circuits containing any components, linear/nonlinear, active/passive. As the article says, you can always linearize about a point, define R=V/I, then use linear circuit methods to solve it.