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)

This is a lab on thickness of the wire and how it affects resistance

Lab report on the material of wire and how it affects flow of electricity Factors affecting flow of electricity 1.Temperature 2.Lenght of wire 3.Thickness of wire 4.Material the wire is constructed from (type of wire) Factor chosen: Material the wire is constructed from or Material of wire. Purpose of lab: This lab will be on the material the wires are constructed from and how it affects the flow of electrical charge or electricity through it, it will compare the different types of materials of wire available in the physics lab by looking at the amperes, voltage, and resistance difference between the wires. This lab is on conductive materials and even though conductivity of a material( which is basically movable electric charges in the material determined by the inherent properties of the material) will need to be described in detail (as to how it takes place) I hope you can accept that I do not want to start explaining how many electrons, charges, ions e.t.c there are in the wires and how these are playing a role in the flow of electricity, I will not give exact amounts but will briefly explain it for example “wire A conducts more than B because it is made out of copper and therefore it has inherent properties which allow for more moveable electric charges than B” Research question: how does the material the wire is constructed from affect the flow of electricity? Hypothesis: I think that the electrical flow in the wire will depend on the conductivity (properties) of the material, therefore a metallic conductor like copper will have more amperes and voltage flowing through it, than compared to an alloyed metallic conductor material like brass as the materials properties will be different, therefore flow of electricity (conductivity) in a material is determined by the inherent properties of the material. My hypothesis is that the wire with metallic properties will allow the flow of elctrcity and conduct more than alloyed or non-metal material because of the metals inherent atomic structure which allows the metal to conduct electric charges. Controlled variables: length of wire, voltage and ampere supply Dependent variables: voltage across the wire Independent variables: material of wire

Equipment used: Stopwatch, Voltmeter , Ammeter , Wires , Power supply, Crocodile clips ,Brass wire(9 cm), copper wire(9 cm), iron wire(9 cm), Alluminium wire(9 cm)

Method: 1. Gather all aparratus required.

2. Set up the apparatus as shown below in a parallel circuit (note the thin line opposite of the volt meter represents the wires used for this experiment, and the squares on left and right from the wire represent the crocodile clips holding the wires) there are 4 wires make sure that they are all 9 cm in length and their thickness is the same.

3. Turn on the power supply when ready to record, record at least three readings for each type of wire and record only after 5 second intervals. There are 4 wires so get at least 12 results for amps and voltage making a total of 24 results.

4. Find the average for all the 4 wires(add all the results and then divide by 3) for amps and voltage respectively.

RESULTS: Results for the ampere observations wire Observation 1 (Amps) Observation 2 (Amps) Observation 3 (Amps) Copper 7.62 A 7.64 A 7.65 A Brass 5.96 A 5.98 A 5.97 A Iron 6.13 A 6.10 A 6.12 A Allimunium 7.61 A 7.60 A 7.57 A Note that between the recording of the observations I have enforced a five second delay. Average for ampere observations/readings Copper= 7.62 + 7.64 + 7.65=22.91 divided by 3=7.63 A(Average) Brass=5.96+5.98+5.97=17.91 divided by 3=5.97 A(Average) Iron=6.13+6.10+6.12=18.35 divided by 3=6.11 A(Average) Alluminium=7.61+7.60+7.57=22.84 divided by 3=7.59 A(Average) wire Average (Amps) Copper 7.63 Amps Brass 5.97 Amps Iron 6.11 Amps Allimunium 7.59 Amps

Results for the Voltage observations wire Observation 1 (volts) Observation 2 (volts) Observation 3 (volts) Copper 0.38 V 0.35 V 0.33 V Brass 0.28 V 0.26 V 0.28 V Iron 0.17 V 0.20 V 0.20 V Alluminium 0.15 V 0.19V 0.20 V Note that between the recording of the observations I have enforced a five second delay. Average for observation/reading of voltage of wires Copper=0.38+0.35+0.33=1.06 divided by 3=0.35 Amps(Average) Brass=0.28+0.26=0.28=0.82 divided by 3=0.27 Amps(Average) Iron=0.17+0.20+0.20=0.57 divided by 3=0.19 Amps(Average) Alluminium=0.15+0.19+0.20=0.54 divided by 3=0.18 Amps(Average) wire Average (Voltage) Copper 0.35 V Brass 0.27 V Iron 0.19 V Allimunium 0.18 V

Averages merged together wire Average (Voltage) wire Average (Amps) Copper 0.35 V Copper 7.63 Amps Brass 0.27 V Brass 5.97 Amps Iron 0.19 V Iron 6.11 Amps Allimunium 0.18 V Allimunium 7.59 Amps

Graph for Average voltage of wires

Graph average for Amps

 Observations/patterns: what I can deduct from the averages is that the materials the wire is made out of do affect the flow of electricity as all of the wires are made out of metal and the results I am getting are varied and different if the material of the wire did not affect the flow of electricity then I would get the same results for all of the wires I used. copper is the best conductor of electricity compared to the rest of the wires and this takes me back to my hypothesis where I predicted that copper being a metal will conduct more than Brass as brass is an alloy this is because of the two metals inherent properties. Therefore I can answer my research question by saying that the material the wire is made out of affects the flow of electricity because the inherent properties  of the material (like the atomic structure, number of atoms in the outer shell,  degree to which the atoms are free to move about in the outer e.t.c) determine how the material will control the flow of electricity so if a material is a conductor one would not get punished for saying that because the electrons are free to move about in the outer shell(one of the inherent properties) is the reason that it conducts electricity among other reasons as well , for example the inherent properties of the material Copper  are that it has atoms which can move freely in its outer shell this would mean that it would Conduct electricity, then if you made a diamond wire and tried to pass a current through it it will not pass as the atoms are being held together and the atomic structure will not allow it because one of the inherent properties of diamond is that its atomic structure does not allow conduction of electricity because the atructure is held together and there are no free electrons(which are vital to conduct electricity) . The above evidence proves my hypothesis that the material of the wire affects the flow of electricity because of the materials inherent properties which control the flow of electricity through the wire. The pattern would continue for copper being the best conductor as you would increase the amps and voltage.

Answering my research question: how does the material the wire is constructed from affect the flow of electricity? The material the wire is constructed from has a big effect on the flow of electricity through the wire as the materials inherent properties (like the atomic structure, number of atoms in the outer shell, degree to which the atoms are free to move about in the outer shell e.t.c) determine how the wire will control the flow of electricity, and since there are many materials a wire can be constructed from each of the different materials of the wires will have its own unique properties and this will no doubt affect the flow of electricity as in some wires the voltage and amps will be low while in other wires the voltage and amps will be higher, this is because of the inherent atomic structure of the material it has been constructed with along with other properties. It will affect the speed and amount of electricity that flows throughout the wire because of its inherent properties and its atomic structure. Reflection and evaluation What did I do to make it a fair test ?

To make it a fair test in the context of my experiment I used wires of the same length and widgth (this can affect flow of electricity), I used wires which were at room temperature(if the temperature is high the resistance of the wire will also increase and if its colder it will decrease therefore giving bad and confusing results) I recorded three results for each of the four wires to get a good average, I recorded the three readings in intervals of five seconds to give the current and voltage time to stabalise and also to get a good average.

What were the weak points and the points in the experiment that would need to be improved on? The part that I would like to improve on is the recording of results, I used a stopwatch to see when its time to record the amps and the voltage and as I was alone I was frustrated as I would look at one then the other result would have been gone so even though the results are accurate they are not recorded on the exact time interval of five seconds. I also wanted to only do one trial of a wire then change into another wire as I would have to wait for 15 seconds to get the results of one wire (amps and voltage) and during these 15 seconds the wire could heat up therefore increasing resistance and depriving me of the exact results. Another weak point of my labwork was that I only used 4 types of wire as the other wires were not the same thickness and also I could not ask for a gold or silver wire. I also think that although the thickness of the wires looked the same (and I did insist on the same thickness, I also checked it myself) I knew that all four of the wires weren’t all the same thickness. —Preceding unsigned comment added by 41.206.62.178 (talk) 09:10, 14 April 2010 (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. [[User:Spinningspark|Spinni<font style="color:#nothing except confusion to try and distinguish the two. SpinningSpark 20:22, 24 July 2009 (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.

Source

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)

Spinningspark: Your comment about distributed elements is well-taken. You didn't reply directly to the notion that "Ohm's law" in its general form (as described in Transport coefficients say), is the more profound application, and that perhaps this article should have a broader context than I = V/R. I had introduced a sentence about this with a few links, but Dicklyon removed it. What do you think about reinstating it in some form or another? Brews ohare (talk) 20:33, 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, j_ω = σ(ω) E_ω. 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):

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

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:

$I={\frac {V}{R}}$

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 (talk • contribs) 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 (talk • contribs) 17:19, 9 January 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

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

where $\mathbf {V}$ is the bulk (center of mass) velocity of the plasma, $\eta$ is the plasma resistivity, $n$ is the number density, ${\mathsf {P}}_{e}$ is the electron pressure tensor, and the quantities $\mathbf {JV}$, $\mathbf {JV}$, and $\mathbf {JJ}$ are dyadic tensors. The term $\mathbf {V} \times \mathbf {B}$ represents the convective electric field due to plasma motion. The resistive electric field is given by $\eta \mathbf {J}$. 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 ${\frac {\mathbf {J} \times \mathbf {B} }{ne}}$. The divergence of the electron pressure is given by ${\frac {\nabla \cdot {\mathsf {P}}_{e}}{ne}}$. 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)