# Talk:Ohm's law/Archive 2

## About the changes I made (moving physics section to end and renaming)

Usually, I like to give advance warning before doing a reorganization; this is particularly true for articles I normally don't edit. I probably should have done the same here, but I at least want to indicate what my purpose was after the fact.

I, similar to a number of editors above, felt that the physics section interrupted the development of the circuit theory part. It certainly has a role; physicist call J=sigma E Ohm's law as well. But even for physicists V=IR (and variants thereof) is the dominant form of ohm's law and deserves primacy of place.

Second, I don't see why temperature and strain dependence of resistance belongs in Ohm's law. I merged those sections into electrical resistance. I debated adding a short sentence to the resistor section stating something to the effect that 'real resistors have a resistance that depend on both current and temperature' then adding a main|resistor|electrical resistance to the top of that section. I think that any more description then that does not really cover Ohm's law but resistance.

Third, I added a section entitled microscopic origin of ohm's law to help give context to the equation. I disagree with the movement of that section to the top, though. I understand the tendency of some editors to want to explain things from the bottom up. Here I think that this approach hurts since knowing why Ohm's law works is both difficult and unimportant for understanding how it is used. It belongs in the physics section which belongs after circuit theory, in my opinion. Further, the section was written to come after an explanation of rho J = E. That material can be moved as well, but then we are back to the same problem the article had before. I won't move it back since it needs to be discussed first. TStein (talk) 07:17, 29 May 2009 (UTC)

For one, I think that is just what this article needed. I think you are right about the section ordering too - the vast majority of readers will be approaching this article from a cicuit analysis viewpoint. SpinningSpark 17:43, 29 May 2009 (UTC)
I think these were some good additions, but I think the "Hydraulic analogies" section should go down at the bottom of "Other versions of Ohm's law". I also agree with TStein that the section Microscopic origin of ohm's law should probably be further down, after the circuit section, for those who are interested (it is more of a physics-like topic, so should be moved down for the same reasons as that section was moved). I think either just before or just after Relation to heat conduction would be a good place for it, or just before History. Waveguide2 (talk) 01:41, 2 June 2009 (UTC)
The 'Circuit analysis' section is more of an application of Ohm's Law and I don't think it really belongs at the top. Perhaps the 'Microscopic origin of ohm's law' section can be slightly rewritten to give a better background, or a summary of the (now gone) physics section can be added. The analogy section could go at the end, but I though it would serve as a background for the less technically inclined. I do agree that the current ordering does need some adjusting -Roger (talk) 02:33, 2 June 2009 (UTC)
The physics section hasn't gone, it just got renamed. I agree with that renaming because it does not actually discuss any physics (except issues which are not really Ohm's law at the end). I think it was called "physics" only because it used notation commonly used by physicists. SpinningSpark 16:50, 2 June 2009 (UTC)
Oops, sorry I guess I didn't pay close enough attention. -Roger (talk) 22:28, 17 June 2009 (UTC)
Roger, I agree that the Circuit analysis section is more of an application of Ohm's Law, but it is the application that most people want information about, and the application upon which most other analogies are based. That is why I believe that TStein had it as the first section, with more theoretical aspects discussed further below (for those who read that far). I don't think a discussion of quantum mechanics is the first thing people coming to the article expect to find. Waveguide2 (talk) 21:30, 2 June 2009 (UTC)
The Drude model sounds a lot like the one used when I was first taught about resistance and Ohm's Law (though much more simplified). Still seems like a good introduction to me, and the physics isn't too complicated. -Roger (talk) 22:28, 17 June 2009 (UTC)

## Shouldn't it be E=IR rather than V=IR?

I learned Ohm's Law as E=IR, not V=IR. The E was for electro-motive force and measured in units of voltage. If you are to be consistent in using the units for the designation, then it would be V=AO where V is volts, A is amperes and O is ohms. Qureus1 (talk) 18:29, 17 June 2009 (UTC)

That depends on whether you are a physicist or an engineer. Physicists more typically use V for electric potential probably because P is taken for power. We also don't like E because we use it for electric field. Plus there is the tendency of physicist to hate the term electromagnetic force because it is not a force. In electrodynamics we typically deal with EMF as a script E. (There is of course no one set of symbols, but this is probably the most common.) Engineers, I believe, and old text books use E instead of V. Personally, I believe that script E might be the best compromise. On the other hand, people can get quite touchy about changing familiar equations. It is probably best to leave sleeping dogs lie. This article is not so perfect that an argument about the look of the equation is any where near the top of the list of problems. TStein (talk) 22:15, 17 June 2009 (UTC)
(ec) The criteria for inclusion in Wikipedia is not consistency, but what can be found in reliable sources. I think you will struggle to find a reliable source using O for Ohms. V is just as valid as E, perhaps more so, for instance, a current source driving into a resistance most would describe the result as a voltage, rather than an e.m.f., which in any case is a horribly misleading terminology. Voltage is most definitely not a force, it is not even a vector. SpinningSpark 22:20, 17 June 2009 (UTC)

The variable names used are less important than the conceptual framing of the law. On June 10, there was an uncommented edit (actually, this diff followed by this correction) that I missed, which changed from the traditional statement of the law to the more revisionist product form. I think the last time we discussed this, we decided to stick with the traditional form, so I put it back. Dicklyon (talk) 17:42, 24 July 2009 (UTC)

Whether emf or voltage should be used is in the eye of the beholder. Strictly speaking emf refers to the work done by an external agency in setting up a charge separation, which leads to a voltage that enters Kirchhoff's laws. However, especially in circuit theory, the distinction between the voltage and the work done by the mechanism is sloughed over, and the distinction often is lost. A puritan would use V. Brews ohare (talk) 19:36, 24 July 2009 (UTC)
Yes, it's all relative; a voltage across a load in one mesh appears to be an e.m.f generator to another mesh in the same network. As far as the rules of network analysis go, it adds nothing except confusion to try and distinguish the two. SpinningSpark 20:22, 24 July 2009 (UTC)

Perhaps this is a good place to ask why current is noted by the letter I. I've never understood that choice. Hellbus (talk) 04:04, 13 August 2010 (UTC)

Actually, a spectacularly bad place, you should have started a new thread. I is for intensity of current, a symbol chosen by Ampere himself apparently (French intensité). You can't have C, that's being used by capacitance. SpinningSpark 16:06, 13 August 2010 (UTC)

YES. Every book on electronics worth anything always puts it E=IR, where E is Electromotive Force (Voltage, measured in Volts), I=Current, measured in Amps, and R=Resistance, measured in Ohms. V=IR is as wrong as V=CR. The common representation is a circle with the top half filled with E and the bottom sectors I, and R. Now, I think it would be interesting to dig up the historical papers to see what was used in the very beginning, but note that that is historical rather than modern usage. Viva E=IR. 69.229.121.132 (talk) 07:43, 4 February 2011 (UTC)

In that case you must consider the first four electrical analysis texts that pop up in googlebooks[1][2][3][4] not to be worth anything since they all use V rather than E. Can I ask what your criterion for deciding worth in a textbook is, and can you quote a reliable source justifying that criterion? SpinningSpark 17:51, 4 February 2011 (UTC)

I don't care what's right, but I am annoyed I had to come to the talk page to find out that E=IR is a common alternative. Shouldn't the article cover that? Dprovan (talk) 06:47, 28 May 2012 (UTC)

## Possible confusion of Ohm's law with the definition of resistance

I believe that Ohm's law is not a fundamental law of nature, unlike, say, Newton's laws of motion which are always applicable. It is a law which is obeyed by certain substances, notably many metal conductors, provided other physical conditions such as temperature remain constant. Materials which obey Ohm's law we call "Ohmic" but we are happy to note the existence of non-ohmic substances (such as most semiconductors and liquids).

I learnt Ohm's law along the lines of: the ratio of voltage to current remains constant for certain materials (provided other physical conditions don't change). This ration V/I is defined as resistance, so we could alternatively state Ohm's law as: resistance is constant; it doesn't change with different voltages.

The equation R=V/I (or I=V/R for that matter) does not express Ohm's law but defines resistance. How else could we measure the resistance of non-ohmic materials for which Ohm's law doesn't apply?

I concede most people will use the equation I=V/R (or some variant) and believe this is Ohm's law. It is a lovely equation for calculating circuit values, but as far as I can see it is not actually Ohm's law. Perhaps at an elementary level some might gloss over this distinction or not even notice the problem, but R=V/I defines resistance and I don't think we can't rearrange the terms and then say it is also Ohm's law.--DDHornsby (talk) 22:41, 9 October 2009 (UTC)

Actually, the ratio V/I defines resistance only when it doesn't depend on I, that is, when Ohm's law is satisfied. Maybe we need to try to find a good source for that and clarify it in the lead. Dicklyon (talk) 00:14, 10 October 2009 (UTC)

Thanks for a rapid response. Much appreciated. I really hope we don't get into silly arguments when we probably understand the behaviour of electric circuits in the same way.

However, I read your comment about V/I defining resistance only when it doesn't depend on I with some amazement. This idea is news to me. I have never heard of this concept before. Such a statement would imply that resistance is not defined if Ohm's law is not applicable. I've searched what text books I have and cannot find any support for such a view. I re-assert my original statement that Ohm's law is about the ratio of V/I remaining constant: double the voltage and you get twice the current, etc. Expressed another way, the I/V graph is a straight line. If it is not a straight line, we have a non-ohmic material, perhaps a semiconductor diode, and Ohm's law doesn't apply, but we can still talk about its resistance at particular point on the graph (either V/I or dV/dI depending on your requirement). R=V/I is fundamentally the definition of resistance, the constant in Ohm's law and not actually the law itself. R=V/I states nothing about the behaviour of materials but simply defines resistance. Ohm tells us that some materials have constant resistance (more or less) which doesn't vary with different currents. Ohm's law doesn't define resistance.--DDHornsby (talk) 00:02, 11 October 2009 (UTC)

## Remove off-topic complexity creep

Dicklyon: I would like explanation for your deletion of sourced material beyond "complexity creep", which strikes me as vague & possibly not a good criterion.

This sourced material appears relevant to the section on complex impedance, because it says that the real and imaginary parts are not independent. Moreover, it points out that there is a connection to the very simple and basic concept of causality, a concept everyone can understand, and might be intrigued by. In addition, of course, the K-K relations are a cornerstone to understanding and calculating the complex impedance.

IMO not every part of every WP article must be understandable to a fifth grader. Also, a major strength of WP is its links between articles that help widen the scope of an inquiry beyond a narrow subject that might be landed upon in the course of inquiry, and may well not be the only or even chief interest of the reader arriving here. Brews ohare (talk) 01:35, 11 October 2009 (UTC)

Complexity creep is not so bad when it's on topic; do you have a source that connects the Kramers–Kronig relation to Ohm's law? It seems to me that the notion of complex impedance is just one step removed from the topic, but the K-K thing is another step, and it's hard to imagine why someone reading this article would want to encounter it being introduced there. There was also no explanation of the connection to the concept of causality; after checking the linked articles and the cited source, it remains unclear what you intended by the extra little teaser. The source you cite does not mention Ohm's law, but rather is about causality in dispersion relations in dielectrics.
Anybody else have an opinion on the relevance? Dicklyon (talk) 06:27, 11 October 2009 (UTC)

### Comment

I'd like to add a few words about the possible structure of this article. The introduction begins properly with the standard I = V/R version, which certainly is the most common form of Ohm's law. It then goes on to refer to generalizations, which are the most profound and important forms of this law, and are used all through solid-state physics to discuss everything from superconductivity to optical absorption. Although there is a section "Other versions of Ohm's law", the connection to the use in physics is not made.

There is also a section "Reactive circuits with time-varying signals" that brings up the frequency dependent version of Ohm's law and the complex form of the impedance, which of course, introduces frequency dependence of the impedance (aka dispersion). It is here that I attempted to add this sentence:

The real and imaginary parts of the impedance are not independent, but are coupled via the Kramers-Kronig relations, which are closely connected to the notion of causality.[1]
Source
1. ^ Herch Moysés Nussenzveig (1972). "§1.9 The Kramers-Kronig Relation". Causality and dispersion relations. Academic Press. pp. 43 ff. ISBN 0125230508.

There are, I think two issues here: (i) the present version of the article is narrow and simplistic. If editors like Dicklyon wish to constrain the size of this article by making it into a gateway (rather than a fuller explanation) to the much wider subject, that's fine. But in that case it should link to other pages where the deeper and more significant aspects are discussed. As a gateway, sufficient description of the attached link must be included to guide the reader's choice of whether to pursue the link. (ii) as a general principle (possibly not a general view) the strength of WP is its ability to link topics allowing a reader to explore a topic far beyond their initial concept of it. In appraisals of WP this aspect always ranks at the top of WP's best qualities. People believe in WP's ability to assist in scoping out a subject to a far greater extent than they think of it as accurate. In this respect, WP is most different from a print encyclopedia: it's a scoping tool more than a source of simple-minded explanation.

It is a misdirected limitation of this article to suppress the suggested sentence and its source, which provides the reader with links to one of many topics that should be in this article. "Complexity creep"? You bet. To quote Martha Stewart: "It's a good thing." Brews ohare (talk) 15:09, 11 October 2009 (UTC)

I have no desire the suppress the sentence and its source. But its connection to the topic of this article is too distant to make it appropriate here. As I mentioned, the cited source does not mention Ohm's law. Why not add this material to Impedance, which is already linked from the relevant section on Ohm's law, since there are many sources that make the connection to impedance?
As to opinions about article structure, degree of complexity, tenuous relations, and complexity in the lead, etc., that's an area where I will probably always push in the opposite direction from what you do. Isn't that also what most of the other participants in your ongoing arbitration do? Does anyone support your style of article complexification? If so, please do invite their comment here so we'll know. Dicklyon (talk) 17:28, 11 October 2009 (UTC)
Its "my owngoing arbitration", eh? You have not replied to these two points:
There are, I think two issues here:
(i) the present version of the article is narrow and simplistic. If editors like Dicklyon wish to constrain the size of this article by making it into a gateway (rather than a fuller explanation) to the much wider subject, that's fine. But in that case it should link to other pages where the deeper and more significant aspects are discussed. As a gateway, sufficient description of the attached link must be included to guide the reader's choice of whether to pursue the link.
(ii) as a general principle (possibly not a general view) the strength of WP is its ability to link topics allowing a reader to explore a topic far beyond their initial concept of it. In appraisals of WP this aspect always ranks at the top of WP's best qualities. People believe in WP's ability to assist in scoping out a subject to a far greater extent than they think of it as accurate. In this respect, WP is most different from a print encyclopedia: it's a scoping tool more than a source of simple-minded explanation. Brews ohare (talk) 03:37, 12 October 2009 (UTC)
I hope others will comment here on your ruminations; my comments are above. Dicklyon (talk) 03:40, 12 October 2009 (UTC)
My take on this is that a reader typing "Ohm's law" in the search box is highly unlikely to be looking for the Kramers–Kronig relation. There is no point sending a reader who is at the Ohm's law stage to such an article or to try and explain it to them. That's not to say that an interested reader should not be guided there. But to get anything out of such an article one first has to understand, not only Ohm's law, but also complex numbers, electrical impedance, complex frequency and finally distributed elements and a whole bunch of mathematics behind these concepts. This article quite rightly leads on to articles on complex impedance and the physics behind Ohm's law but it would be wrong to go too far and concepts like K-K should be linked from a higher level article.
I would also object that K-K only makes any sense in the context of a distributed element model (by the way an apallingly bad article which has been on my to do list for some time, and I will now make sure I mention K-K there - if someone else does not steal my idea first now that I have mentioned it here). At least, its hard to see how it could be applied to a lumped element RC circuit for instance, where almost by definition R and C are able to be independantly specified. Ohm's law (V=IR version) is patently concerned with lumped element models, not distributed models.
Like Dicklyon, I would also question whether any source links K-K to Ohm's law. The Wikipedia K-K article defines the K-K relation for complex functions that vanish as |ω|→∞. Certainly not all impedance functions do that, and certainly not the most well known distributed element circuit, the transmission line. The book "Causality and dispersion relations" linked by Brewes above limits consideration to only insulators (although it was not clear to me whether that is a limitation of K-K or just a limitation of the authors consideration), so again, no clear link to Ohm's law.
SpinningSpark 20:02, 12 October 2009 (UTC)

Um, I think Dicklyon has just moved it further down the article, not deleted it. SpinningSpark 21:05, 12 October 2009 (UTC)
Yes, as noted by my edit summary "move marginally-relevant complicating factoid out of the lead and into a section where it won't bother most readers." Dicklyon (talk) 22:30, 12 October 2009 (UTC)
I missed the relocation. Brews ohare (talk) 00:39, 13 October 2009 (UTC)

Lest it be thought that Ohm's law and Kramers-Kronig are never mentioned together, here are some examples: Rothwell, Kittel, Beaurepaire, Strange & so forth. Brews ohare (talk) 14:52, 13 October 2009 (UTC)

"For a nondispersive isotropic material,...Ohm's law...For dispersive linear isotropic materials,...Kronig-Kramers equations." SpinningSpark 19:50, 13 October 2009 (UTC)
Right, none of these discuss the KK relation in the context of Ohm's law; in most cases they're paragraphs's apart. Both topics make sense under constitutive equation, but not here. Dicklyon (talk) 20:07, 13 October 2009 (UTC)

I am arguing with you two only to this extent: the generalized j = σ E is still referred to as Ohm's law even in cases of nonlocal dispersive media. Obviously such a starting point can be specialized to I = V/R. Historically, things happened the other way around. The K-K relations apply to the generalized formulation. If you don't want anything to do with this here, that's fine. Brews ohare (talk) 20:16, 13 October 2009 (UTC)

My opinion is that if you want to make such a connection, you need a source that does it that way, more or less. I don't see that in the sources you presented. Am I missing it? On your latest point, can you show us where "the generalized j = σ E is still referred to as Ohm's law even in cases of nonlocal dispersive media"? Dicklyon (talk) 21:25, 13 October 2009 (UTC)

As I do not intend to pursue this matter, I'll leave it up to you what to do with it. I believe that the linked sources answer you questions if you want to pursue it. or try Search 1 Search 2. Brews ohare (talk) 22:28, 13 October 2009 (UTC)

OK, I lookd at those, and don't see it, so case closed. Dicklyon (talk) 23:03, 13 October 2009 (UTC)

### Complexity creep?

Reply to Dicklyon: For example Kittel: Intro to SS Physics; 7th Edition says (p. 308) "The Kramers Kronig relations enable us to find the real part of the response of a linear passive system if we know the imaginary part of the response at all frequencies and vice versa. They are central to the analysis of optical experiments on solids." Continuing for a few paragraphs on this subject he says (p. 309): "The relationships we develop also apply to the electrical conductivity σ(ω) in Ohm's law, jω = σ(ω) Eω. He then goes on to derive the KK relations and to apply them to optical reflectance data. You may be unaware that the dielectric response is connected to the conductivity in the generalized Ohm's law via (R. M. Martin "Electronic Structure", p. 494):

${\displaystyle \epsilon ({\boldsymbol {r}},\ {\boldsymbol {r'}},\ \omega )={\boldsymbol {1}}\delta ({\boldsymbol {r-r'}})+{\frac {4\pi i}{\omega }}\sigma ({\boldsymbol {r}},\ {\boldsymbol {r'}},\ \omega )\ ,}$

which is the connection of Ohm's law to much of solid-state physics. Martin goes on to say, on the same page, "Interestingly, σ(ω)[and a few other related functions] all are response functions and each satisfies the Kramers-Kronig relations". Now, the stance that Ohm's law has nothing to do with all the preceding is based upon the narrow position that Ohm's law is nothing more than I = V/R. However, I think it is established that there is a broader view of Ohm's law and it has connection to constitutive relations, linear response theory and to the K-K relations. The reason that these connections in this WP article are limited to one sentence moved out of the intro and buried where few will ever find it, is because you want it that way. It is not because the article is more useful that way, or because no reader would have any interest in these fundamental ramifications, or because it is "complexity creep". Brews ohare (talk) 13:45, 14 October 2009 (UTC)

You could also mention this in a less technical way, e.g. by simply explaining that there is a potential problem with causality if sigma(Omega) could be be just any arbitrary function (this is something every 14 year old highschooler can understand). Then you can refer to the KK relation. Count Iblis (talk) 14:37, 14 October 2009 (UTC)

## Ohm's Law is not I = V / R

Currently, the article begins by claiming the following:

In electrical circuits, Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference or voltage across the two points, and inversely proportional to the resistance between them.
The mathematical equation that describes this relationship is:
${\displaystyle I={\frac {V}{R}}}$

The two sentences quoted above are not equivalent to each other, and the second sentence is actually incorrect. As evidence of this, let me quote from page 692 of Fundamentals of Physics, 7th edition (all emphasis found in original):

Ohm's law is an assertion that the current through a device is always directly proportional to the potential difference applied to the device.

This more or less matches what the first sentence of the article says. However, proceeding on:

(This assertion is correct only in certain situations: still, for historical reasons, the term "law" is used.). . . A conducting device obeys Ohm's law when the resistance of the device is independent of the magnitude and polarity of the applied potential difference. Modern microelectronics—and therefore much of the character of our present technological civilization—depends almost totally on devices that do not obey Ohm's law. Your calculator, for example, is full of them. It is often contended that V = iR is a statement of Ohm's law. That is not true! This equation is the defining equation for resistance, and it applies to all conducting devices, whether they obey Ohm's law or not. If we measure the potential difference V across, and the current i through, any device, even a pn junction diode, we can find its resistance at that value of V as R = V/i. The essence of Ohm's law, however, is that a plot of i versus V is linear; that is, R is independent of V.

To state the problem again in other words: Ohm's law says that current and voltage are directly proportional. However, the equation I = V / R does not say that the two are directly proportional. The relationship it establishes says nothing about direct proportionality between I and V because, for example, if R decreases as V increases, then I will increase at a rate that is more than proportional to the increase in V. Therefore that equation is not equivalent to Ohm's law (despite widespread confusion on the matter). In fact, the equation I = V / R is simply a reformulation of the definition of resistance between any two points of a conductor (i.e. R = V / I).

Claiming that Ohm's law is described by I = V / R (or by the equivalent V = I * R) is a common mistake (in fact, it is what I learned from my undergraduate physics professor). Nevertheless, it is wrong.

I propose we remove the second sentence quoted above from the article in order to fix the problem. We'll also have to edit the Electrical resistance article because the same error appears in the article header there. I'll make the changes if no one has any objections.

--SirEditALot (talkcontribs) 03:44, 5 January 2010 (UTC)

My proposed change to the article is here: User:SirEditALot/Corrected_Ohm's_Law. If anyone has any objections to that, let me know. I changed the equation to make it clearer that Ohm's Law is more than just I = V / R, and I added a new source.
Does anyone think that the difference between Ohm's Law and V = IR ought to be be mentioned somewhere in the article, since it seems to be a wide-spread error (wide-spread enough that my physics book above took time to specifically point out the error)?
--SirEditALot (talkcontribs) 17:19, 9 January 2010 (UTC)

This is a big deal, I believe it needs to be fixed. (Sorry, I don't have an account, but I came across this article and was quite disappointed.) - Anonymous

I don't see what the problem is. The lead quoted above continues, "where V is the potential difference measured across the resistance in units of volts; I is the current through the resistance in units of amperes and R is the resistance of the conductor in units of ohms. More specifically, Ohm's law states that the R in this relation is constant, independent of the current." And reliable sources are cited for this classical form of Ohm's law. Dicklyon (talk) 15:21, 14 June 2010 (UTC)

## What a lot of rubbish.

POINT 1

The "provided the temperature remains the same" should be removed from the end of the first sentence.

Direct proportionality means if you double the voltage you double the current. If we divorce this from Resistance, Ohms Law has no meaning at all. You might as well put in, "provided the resistance remains the same" which implies the direct relationship between voltage and current no longer holds if you change the resistance which is all changing the temperature does.

Ohms law holds no matter what the temperature. If the temperature of a positive coefficient substance rises, the resistance increases and the current falls. OHMS LAW HOLDS, that is, if you double the voltage you double the current. For negative coefficient substances, like semiconductors, when the temperature rises the resistance falls and the current increases. OHMS LAW HOLDS which means that if you double the voltage you double the current. The only place it might fall into trouble is with superconductors but, although superconductors are usually very cold, the relationship between V, I and R has no variable for oK associated with it. This suggests a preference for V = I x R because a current can exist in a superconducting ring where resistance is 0 and voltage 0. Using I = V / R introduces division by zero.

To say such a thing you now need to quote the exact resistance and temperature where Ohms Law holds.

While you're at it, add "provided the circuit doesn't come under the influence any magnetic or electrical field changes and provided it stays still (whatever that is) and isn't moved (relativity)."

"Non ohmic substances" where Ohms Law doesn't hold. What substances? I think there is some confusion here between positive and negative coefficient substances. Ohms Law still holds for all of them.

POINT 2

Just like E=mc2 or m=E/c2, I = V / R is no different than V = I * R. Mathematically, they demonstrate exactly the same relationship. Neither can be said to be right or wrong because the law itself is quoted in text. As a literal translation from text to mathematics, I = V / R would seem more correct but we transpose adjectives and nouns translating from French to English. Perhaps the mathematical expression of the law should have both ie.

I = V / R OR V = I x R

Euc (talk) 00:38, 3 March 2010 (UTC)

## Ohm's law in a plasma

In plasma physics, the generalized Ohm's law is given by

${\displaystyle \mathbf {E} +\mathbf {V} \times \mathbf {B} ={\eta }\mathbf {J} +{\frac {\mathbf {J} \times \mathbf {B} }{ne}}-{\frac {\nabla \cdot {\mathsf {P}}_{e}}{ne}}+{\frac {m_{e}}{ne^{2}}}\left[{\frac {\partial \mathbf {J} }{\partial t}}+\nabla \cdot \left(\mathbf {JV} +\mathbf {VJ} -{\frac {\mathbf {JJ} }{ne}}\right)\right],}$

where ${\displaystyle \mathbf {V} }$ is the bulk (center of mass) velocity of the plasma, ${\displaystyle \eta }$ is the plasma resistivity, ${\displaystyle n}$ is the number density, ${\displaystyle {\mathsf {P}}_{e}}$ is the electron pressure tensor, and the quantities ${\displaystyle \mathbf {JV} }$, ${\displaystyle \mathbf {JV} }$, and ${\displaystyle \mathbf {JJ} }$ are dyadic tensors. The term ${\displaystyle \mathbf {V} \times \mathbf {B} }$ represents the convective electric field due to plasma motion. The resistive electric field is given by ${\displaystyle \eta \mathbf {J} }$. The Hall electric field, which represents decoupling between ions and electrons and acts to freeze in the magnetic field to the electron fluid, is given by ${\displaystyle {\frac {\mathbf {J} \times \mathbf {B} }{ne}}}$. The divergence of the electron pressure is given by ${\displaystyle {\frac {\nabla \cdot {\mathsf {P}}_{e}}{ne}}}$. The last term on the right hand side represents electron inertia. Magnetic topology cannot be changed by the convective electric field, the Hall electric field, or an electric field due to scalar electron pressure. However, magnetic topology can be changed by resistive effects, nongyrotropic (off-diagonal) components of the electron pressure tensor, and electron inertia. The generalized Ohm's law plays a particularly important role in magnetic reconnection.

I have removed the above section from the article because I feel it does not belong here. This expression is involving magnetic effects which go way beyond the scope of Ohm's law. While it has a place on Wikipedia, and wherever that is, it can be linked from the Ohm's law article, I don't think it should be embedded in this article. SpinningSpark 20:02, 1 April 2010 (UTC)

In a plasma, the Ohm's law does include effects related to the magnetic field since the current density and magnetic field are directly related through Ampere's law. This law is applicable to pretty much any magnetized ion-electron plasma (in particular, near-Earth space plasmas, magnetically confined laboratory plasmas, solar flares, and a wide variety of astrophysical applications). I think the section on magnetohydrodynamics may be a better place to put this, but that article is not yet sufficiently developed; magnetic reconnection is also a possibility. Perhaps a qualitative description with links would be useful here for people trying to learn about plasma physics. Spacehippy (talk) 13:52, 25 March 2011 (UTC)

## Ohm's law triangle

Is there any point in having this described in the article? Perhaps it would be of benefit if the triangle were actually to be depicted, but to describe a graphic mnemonic in text without showing it really is of no help to the reader at all, and probably just adds confusion. I propose removing it. SpinningSpark 08:23, 21 May 2010 (UTC)

Agreed. Even if there were an image, I don't see the point. It's an equation with three variables, just like F=ma and so on. Do we really need to give a visual representation of a multiplication every time such an equation arises? Oli Filth(talk|contribs) 11:26, 21 May 2010 (UTC)
It's common enough in introductory textbooks to justify its inclusion. Yes, it's fairly trivial and it would be overkill if we used triangles to illustrate every linear equation, but I think an exception is okay in this case (FYI, a Google search for "Ohm's law triangle" gives 27,000 results, and a Google Book search gives > 100). I agree that a graphic would be nice, even in place of a textual discussion. -Roger (talk) 13:49, 21 May 2010 (UTC)
Ohm's law triangle
Of course, this is a very primitive Ohm's presentation that does not add anything to the law. I can't imagine a person that can't memorize I = V/R; but it was very popular in the past and, as Roger has noted, it is a very popular presentation nowadays as well (see all these colorful images). Maybe it seems as a funny crossword for people and they love this Ohm's law interpretation or maybe, looking at the triangle, some people feel nostalgia for their college days. IMO, to give pleasure to these people, we may add an image of this exotic with a short explanation below. I have found such image in Wikimedia Commons (regretfully, it is not so attractive). Circuit dreamer (talk, contribs, email) 16:10, 21 May 2010 (UTC)
I have had some experience of teaching Ohm's law to "craft" level students and can confirm that many do find this useful - many do not have the algebraic skill to transpose equations. My objection was that describibg the method is useless without the diagram. Now the diagram is in the article, I think it can stay, but can you change the voltage symbol to match the article please? SpinningSpark 16:40, 21 May 2010 (UTC)
I can't since I'm not skilful at some svg editor. But I have asked the author to change it. Circuit dreamer (talk, contribs, email) 17:49, 21 May 2010 (UTC)
I thought it was your graphic. Never mind, I've done it myself. SpinningSpark 23:12, 21 May 2010 (UTC)
For the record, I'll repeat my objection; it is not Wikipedia's place to teach readers how to use trivial linear equations. If someone doesn't have the ability to transform V=IR into I=V/R (etc.) then they're going to be pretty screwed when faced with any non-trivial application. In that respect, I think the triangle doesn't befit an article of this nature. Oli Filth(talk|contribs) 23:49, 21 May 2010 (UTC)

## Quantum Ohm's Law

I am a bit surprized by the fact that it has not been stated that Ohm's Law extends to the quantum level. Because of the Josephson effect, quantum Hall effect. Using electric charge, Josephson constant, and the von Klitzing constant one can write Ohm's Law. —Preceding unsigned comment added by Reddwarf2956 (talkcontribs) 21:21, 1 November 2010 (UTC)

## Useless On-line Calculators?

At 19:44, on 19 November 2010 Wtshymanski deleted some links to on-line calculators, saying: "useless on-line calculators deleted; I wouldn't hire an engineer who needed an on-line calculator for this." In my humble opinion, they are not entirely useless, even for experienced engineers! A high school student might need one to find the current in a 2 ohm resistor from a 6 volt battery; a senior engineer might need one to find the current in a 220 kohm resistor from a 17 mV signal source. 193.60.61.215 (talk) 09:41, 22 November 2010 (UTC)

In each case, the calculation is simply divison. We don't need links to dedicated calculators to do that! Oli Filth(talk|contribs) 10:19, 22 November 2010 (UTC)
In those cases, the high school student should stop staring down the blouse of his lab partner, and the senior engineer should realize it's time for the old folk's home and turn in his Iron ring and professional seal. You wouldn't go to a surgeon who had to prop up his anatomy text in front of him during surgery, would you? --Wtshymanski (talk) 14:32, 22 November 2010 (UTC)

## U = I/R or V = I/R

I'm from the Netherlands, and I'm wondering why I see always the english notation as V = I/R and the Dutch notation (in symbols) as U = I/R I mean: how did the discepancy arise? at school I've allways learned that the right notation is: U = I/R. how did the use of U instead of V get common? so for example: U= 3 V, I= 6 A, R= 2 Ω —Preceding unsigned comment added by 83.81.220.80 (talk) 20:09, 29 November 2010 (UTC)

I sure hope you don't see any such formulas. I grew up on E = IR (E for electromotive force; never saw U). Dicklyon (talk) 06:06, 30 November 2010 (UTC)
I am an electronic engineer from Denmark, we always use U as symbol for voltage, I have never seen the use of V before. V is short for voltage, so it is confusing to use the same letter as the symbol, too - in my opinion. 25 Marts 2011 (UTC+1) —Preceding unsigned comment added by 80.197.111.7 (talk) 15:50, 25 March 2011 (UTC)
On the English Wikipedia, the conventions followed in the English speaking world should be used. The Danish or Dutch Wikipedias may be different, but that is not the concern of this article. SpinningSpark 18:20, 25 March 2011 (UTC)
In America, I grew up using E = IR; the E (for electromotive force, or emf, they told us) was to prevent reusing the unit symbol V I presume. But most books don't seem to do that any more. And I do hope that in Denmark they don't use U = I/R. Dicklyon (talk) 18:39, 25 March 2011 (UTC)
A quick "channel hop" through the interwiki links confirms that we are very much in the minority here. The vast majority of other languages use U. SpinningSpark 19:21, 25 March 2011 (UTC)

──────────────────────────────────────────────────────────────────────────────────────────────────── So? This is English. Those foreigners have a different word for *everything*. --Wtshymanski (talk) 19:38, 25 March 2011 (UTC)

There is no need to get tetchy, my comment was for information, I am not proposing to change anything. As I said earlier, we should follow the English language conventions. SpinningSpark 23:54, 27 March 2011 (UTC)
Web and book search show U to be much less common and E and V in this context. If we change, it should be to E. Dicklyon (talk) 20:23, 25 March 2011 (UTC)
See Ngram viewer; or this one. Dicklyon (talk) 20:26, 25 March 2011 (UTC)

## Examples

I have trouble understanding the different concepts here. I think it would help a lot if there were some examples explaining how the amount of volt could be changed without changing its ampere and vice versa. —Preceding unsigned comment added by 193.141.155.146 (talk) 11:24, 7 March 2011 (UTC)

Where exactly in the text do you think that it does imply that volts can change without changing amperes? SpinningSpark 16:21, 7 March 2011 (UTC)
It would be possible to increase or decrease voltage by varying the amount of resistance. This would be the purpose of a resistor.Sunshine Warrior04 (talk) 17:48, 26 October 2011 (UTC)
But, in full accordance with I = E/R, that will change the current too. Jeh (talk) 20:00, 26 October 2011 (UTC)
Unless it's driven by a current source, which is essentially what he asked for, silly question though it was. Dicklyon (talk) 20:02, 26 October 2011 (UTC)

## Applicability of Ohm's law to Prospect Rd, Bendigo

All

I know this is not a trouble-shooting forum but I have a question that I hope makes sense. Significant power abnormalities at an industrial estate in Prospect Road Bendigo have eluded local electrical engineers, the local safety regulator and eminent experts from Lund Uni in Sweden for quite some time. The problems have destroyed equipment and resulted in unexplained electrocutions. The issue is some form of naturally occurring DC on the AC network that cannot be tracked down. It has no signature, has multiple sources (not from the distribution company), cannot be isolated even with an isolation transformer (because of the sinewave shape) with the result that the phenomenum remains unexplained with the local geology being the main suspect (and seems to amplify low level DC that might normally be found on AC). At one stage, the experts said "Ohm's Law does not seem to apply" at the premises although it does not appear in their report which appears here.. While that seems to be a crazy statement to make, it was made by an expert in the area (at the very least, pls feel free to read his report). I'm wondering if anyone is aware of anything similar being said about Ohm's Law in the past - ever?? —Preceding unsigned comment added by 120.144.134.167 (talk) 11:40, 29 April 2011 (UTC)

Well, let's see. We can overturn a physical law that's been pretty much the base of electrical engineering for the last two hundred years, or we can assume whoever wrote the report has fogotten or missed something. Yes, let's reject Ohm's Law since there can't possibly be another explanation. The report is...unsatisifying. There's no explanation of what the "abnormalities" are, there's no single line drawing, there's no measurements. If one of my guys had asked me to proofread this before it went to a client, I'd have sent it back saying "Where's the rest of the report?". Ohm's Law was theoretically derived and confirmed under laboratory conditions - laboratory conditions means you know *everything* that affects the measurement and control all the variables. It's impossible to tell from this report what variables they even looked at, or even what the phenomenon was. --Wtshymanski (talk) 13:35, 29 April 2011 (UTC)

I can understand your cynicism but that is precisely the dilemna the experts are facing. It was said that anyone who questioned Ohm's Law would be put in a straight jacket given it is a first year uni theory - but that is what was said. There were considerable measurements taken in this instance, which were overseen by the Lund Uni experts who did visit the site. The "rest of the report" is mathematics. As you will appreciate, the report as presented was written for the broader audience, including for people like myself who are not engineers - and would not understand the 'rest of the report' underpinning what has been presented. Regrettably this is a matter of life or death as there are people who have invested their life savings into the businesses they are now having to consider walking away from. Any help would be appreciated —Preceding unsigned comment added by 120.144.134.167 (talk) 09:03, 30 April 2011 (UTC)

Ok, I think it is time to point this conversation to the Science Reference Desk. This page is for discussing improvements to the Ohm's law page and that is not what is being talked about. SpinningSpark 13:42, 30 April 2011 (UTC)
I think this is a great deal being made of an offhand remark. It's the sort of thing many people would say as a wry comment in the face of a difficult problem (along the lines of "this can't possibly be happening", when the subject phenomenon is clearly happening, but no one can figure out how). I doubt seriously that anyone there was intending to express a sincere belief that Ohm's law really didn't apply. Without a reference for the claimed utterance (with which not only the validity of the quote, but also its context and intent could be evaluated), I'd say Wikipedia should forget about it. Jeh (talk) 09:10, 21 June 2011 (UTC)
In the old (non computer) days the adequacy of an electrical power network was occasionally simulated by the use of RLC (resistance/inductance/capacitance) line segment boxes and appropriate voltage and current measurements to measure and control the ability of the system to handle power surges and functional abnormalities. The above problem is suggestive of an inductive current power supply surge demand introduced into the system by some overlarge inductive power load.WFPM (talk) 17:09, 14 October 2011 (UTC) This results in a temporary resistive overload until the motor achieves speed.WFPM (talk) 18:52, 18 November 2011 (UTC)

## Law or statistical property?

We all learn it as "Ohm's Law" but technically isn't it not a law at all as it breaks down at small small samples sizes and is routinely violated by semiconductors? Isn't it more of an emergent statistical property, much like the "ideal gas law?" Not that I'm suggesting the article be rewritten, but perhaps just mention that somewhere.--Skintigh (talk) 01:15, 22 June 2011 (UTC)

## Magnetic effects

"The continuum form of the equation is only valid in the reference frame of the conducting material."

Not only. If there is no B-field, J=${\displaystyle \sigma }$E holds also for a moving conductor.

If there is a B-field, the vxB term must be added to account for the current induced by the Lorentz force on the charge carriers. In the rest frame of the conductor this term drops out because v=0. There is no contradiction because the E-field in the rest frame differs from the E-field in the lab frame: E'=E+vxB. Rwbest (talk) 19:39, 4 September 2011 (UTC)

I rewrote this section on magnetic effects. Rwbest (talk) 10:16, 12 September 2011 (UTC)

## Two simple points to consider

1) The better expression of ohms law (or the definition of resistance, whatever you want to call it) is V=IR rather than I=V/R because V=IR is also valid for superconductors. In a superconducting loop, the resistance is zero, the voltage is zero but the current can be anything thus:- volts (0) = current (anything) x resistance (0) = 0. Using I=V/R introduces division by zero.

2) There is some confusion between negative temperature coefficient substances, ohmic substances (whatever they are) and those that obey ohms law. Even semi-conductors where resistance decreases with increasing temperature obey ohms law fine. It makes no difference whether you increase or decrease resistance with temperature. If you change resistance (in any direction) the current changes (for the same voltage) - simple. Temperature has NOTHING to do with ohms law. Euc (talk) 18:11, 23 February 2012 (UTC)euc

## History section

The position of the history section has just been moved to the top. The order of sections, including history, was discussed at length at the top of the page and a consensus reached. Should we stick with that consensus? SpinningSpark 09:40, 21 June 2012 (UTC)

## Hydraulic section consideration

On the consideration of establishing a clearer understanding of Ohm's law from the vantage of the quantum movement of electrons, note that electrons either move at the speed of light or don't, unlike the fluid in a pipe. The speed of electron flow in a wire seem, to me to be constant. Therefore I have posted this, not only to start a discussion on this subject but to have answered my own questions from any quantum expert authorities out there to fulfill my personal unknowns because knowing very precisely how electrons actually move in a wire as amperage and exactly what voltage is that powers them and how and and actually what "resistance" is, quantumly speaking, to me is a mystery and fogs my actual understanding of ohm's law and makes me uncomfortable with it, at all. In short, I need to reconcile quantum theory to Ohm's law (I don't seem to be getting that here).

It seems, to deeply and completely understand quantum concepts about voltage one would need to know what's going on inside the atom and how electrons actually begin then, thereafter continue to "flow" or "jump", if you will from atom to atom (or flow over them or both). It would seem that when the magnetic equilibrium of an atom or a group of atoms becomes disturbed when they come together to form compounds or through electromagnetic induction there becomes a magnetic pushing or pulling of electrons from one area to another which constitutes electron flow. Quantum theory seems to present that they are all jumping instead in and out of a string of atoms simultaneously. However, I would rely upon you expert quantum gurus out there to tell me exactly how they go through a wire.

Does an electron pop into a copper atom on one end of the wire and another pops out the other side of that atom and into the next and the 186 k miles per second speed of electron flow equate to the speed an electron can orbit around to the other side of all the atoms in the chain or does one pop in one side of an atom, cross the atom at 186 miles per second as the others in the chain do the same,simultaneously and an electron pops out the other end of the wire (after different electrons in that same unit of time all pop out of the exit side all in one motion in the atom chain). Is 186 miles per second the speed it takes for one electron to travel by itself in one second across a wire or is it the time it takes for all the electrons in a chain to travel across one atom respectively?

Does increased voltage cause increased numbers of individual electrons in individual streams to "jump" through the wire with each electron having its own path? What happens with the electron "flow" or "jumping" when a variable resistor is opened very slowly like a faucet would be, exactly? I wish someone could actually make an animation of electron flow within actual known ohm's law circuit lessons with wires magnified so they look like pipes when you zoom into them and they become as large as your screen and you can see how they go around tight turns in the wires like they were pipes. This whole subject fascinates me but frustrates me at getting at the factual answers. However, I feel that quantum flow of electrons, if one understands all about it would bring about a complete understanding into what electricity is, and how it works within the Ohm's law equations and would bring forth a complete "Ohm's Law" definition, not here now and certainly would be very useful and worth while because I'm not getting that full and complete definition and understanding with that left out.

Also, what needs being answered before all that is why atoms "jump" at all within an atom, one would think instead of variably changing states (in layman's words please).

Thank You. — Preceding unsigned comment added by 71.178.201.92 (talk) 02:34, 31 October 2012 (UTC)

Electrons do not move at the speed of light, even when their associated electromagnetic waves do. It's hard to explain QED in layman's language, but there are books on it. Dicklyon (talk) 03:18, 31 October 2012 (UTC)
Electrons move close to the speed of light in copper and in air pretty much at it, right? I had one expert tell me the photon is created by orbiting electrons at a certain speed changing energy levels releasing a photon at that speed in the EM spectrum. Nonetheless, they are not slowed signifigantly by anything with resistance just stopped. — Preceding unsigned comment added by 71.178.201.92 (talk) 06:22, 31 October 2012 (UTC)
As Dicklyon says, electrons do not move at the speed of light in copper wires. The average drift velocity in copper is slower than a sick snail. Typical copper cables transmit signals at around 2/3 light speed but the electrons hardly move. Please take further questions on the subject to the Science reference desk, the page here is to discuss improvements to the article, not answer people's questions. SpinningSpark 09:53, 31 October 2012 (UTC)