# Talk:Electrical resistivity and conductivity

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## resistivity of Al

After searching other locations, I'm finding very different versions of resistivity for Al. Something closer to 2.6 or 2.8 rather than 2.282... --Hobit 14:19, 11 October 2005 (UTC)

–Fixed. I used the value from aluminium, which was taken at 20°C. This is equivilent to 293K, as used in this article). —deanos {ptaa*lgke} 15:18, 15 October 2005 (UTC)
what about variation of conductivity for some other temperatures (20c, 120c, 220, etc)?you may find out that its not same at 1580k.ths.user:paul — Preceding unsigned comment added by 188.25.49.46 (talk) 00:32, 24 April 2012 (UTC)

## References

The table of resistivity values looks exactly like the one in my physics textbook (Physics for Scientists and Engineers, with Modern Physics by Serway and Jewett). Is there a missing citation here or am I missing something? Mahsmanj

I've added references for most of the materials, and for those where I couldn't I've moved them from the article to here. I also redirected Table of resistivities here, because the table here was exactly the same.
Material Resistivity (ohm metres) Temperature coefficient per kelvin
Chromium 1.8 × 10-7 .0000059
Tin 1.15 × 10-5 .0042
Silver, German 3.3 × 10-5 .0004
Seawater 2.0 × 10-1 [1] ?
Pure water 2.5 × 105 ?
Human skin approximately 5.0 × 105 ?

Kevin 09:30, 4 May 2006 (UTC)

German silver is also known as nickel silver. If you look for the resistivity nickel silver instead of german silver, you will have better luck finding a source. -Rudy

## Volume?

Does anybody know how resistivity relates to the volume of an object? That is, if I had something that looked more like a sphere than a thin wire, and wanted to calculate its resistance using its resistivity, how would I do it?

Its wikipedia custom to sign your name with four tildes ~~~~, welcome to wikipedia. As for your question, I think you could calculate it with an integral if you really want to : ) . Start by approximating it as a series of circles with some thickness dx, where the thickness of circles in the series goes from 0 to the radius (of the sphere). Add all the resistivities of those circles up, and take the limit as the distance between different sized circles goes to 0.
That would probably be a difficult integral to figure out how to set up, but you could easily approximate it without taking such a limit. Simply approximate the sphere as say 5 different circles, and see what the resistivity comes out to. Fresheneesz 22:50, 27 May 2006 (UTC)

It probably involves integrals, though I don't know if the equations are straightforward. Remember that this isn't a straight volume or surface area type calculation. You're calculating the resistance of the object, but the resistance will be different for the same object depending on how the electrodes are arranged. Would you have to calculate the current flow through each differential cross section of the entire object? This gets into bulk resistance calculations that I am not familiar with (but would like to be). — Omegatron 19:00, 24 February 2007 (UTC)

The total resistance of a body is not just determined by its volume, but the area of the contacts (contact points). If you know the volume of the body, and the area of the contacts, then you can calculate the bodies "relative resistivity length" by simply dividing the volume by the area of the contacts. This will give you the value for "l". ZoftWhere 08:48, 15 March 2007 (UTC)
Performing the above-mentioned integration you can calculate the resistance for a sphere with radius r connected with opposite round contacts that penetrate a depth d (0<d≤r) into the sphere. The integration yields:
$R=\frac{\rho}{2\pi r}\ln\frac{2r-d}{d}$,
where ρ is the resistivity of the material. Note that this is the resistance of the sphere without the end caps (i.e. contacts). Mytomi 04:51, 15 November 2007 (UTC)
Do you know the formula for resistivity of coins? TY. Semiotically 05:56, 14 October 2012 (UTC)

19:59, 2 July 2007 (UTC)19:59, 2 July 2007 (UTC)155.104.37.17 19:59, 2 July 2007 (UTC) Sorry to add here, but I'm not seeing any better way to add a comment to the page.

Resistivity may also change under many conditions besides temperature. Humidity, for instance, as a material absorbs water, or even in a vacuum, where it outgasses whatever material. This is an effect we have seen before - nylon is a good example, it's resistivity goes up under a vacuum.

## combining resistivity and conductivity tables

I think it would be better if we combined the tables of resistivity and conductivity since they are so fundamentally linked. Please discuss this at Talk:Electrical conductivity. Fresheneesz 22:52, 27 May 2006 (UTC)

## Resistivity equation

somebody has just defaced the general equation: it should be rho=R multiplied by A divided by length

### The general equation is incorrect

I have changed it twice but someone keeps changing it back. It should be

${\rho={R \left. \frac{l}{A} \right.}}$

and not

${\rho={R \left. \frac{A}{l} \right.}}$

I do not make out that I understand everything that is involved with resistivity as I am only a year 11 pupil studying it for my GCSE but about this I am quite certain and I have also verified it with my teacher. Some one told me to check this up on an External sitewhich I did. There equation of

${\ {R=\left. \frac{\rho l}{A} \right.}}$ is the same as ${\ {R=\rho \left. \frac{l}{A} \right.}}$

which can be rearranged to form

${\rho={R \left. \frac{l}{A} \right.}}$

If anyone can explain why it should be the other way please try. Mrpowers999 16:16, 24 February 2007 (UTC)

If someone keeps reverting your edits, there's probably a good reason for it! Don't keep making the same edits without discussing it!
Your math is wrong. You say:

${\ {R=\rho \left. \frac{l}{A} \right.}}$ which can be rearranged to form ${\rho={R \left. \frac{l}{A} \right.}}$

but this is incorrect. Think of it this way. Divide both sides by L and multiply both sides by A:

${\ {R=\rho \left. \frac{l}{A} \right.}}$ which can be rearranged to form ${R \left. \frac{A}{l} \right. = \rho.}$

Also you should know that your equation is wrong because the units don't come out right. The correct units for resistivity are Ω·m. If you divided length by area you would get Ω/m.
Please be more careful when editing if you aren't sure of something. — Omegatron 18:32, 24 February 2007 (UTC)
I got out the old pencil and paper and realised you were right :( This will mean a few ammendments to my physics coursework 'sigh' Mrpowers999 00:50, 25 February 2007 (UTC)
If you are really eleven, don´t worry about the errors in math, but Omegatron is correct: you should be carefull because people will trust the precission of the information you post ( I did, until I cared to think twice). I would like you to forget about math and think about physics, (as an electron), while you travel bumping "against" atoms. The more length of the material means more bumps, the more surface of material means more paths to travel. So "resistance" to your travel is directly proportional to length , and inverselly proportional to surface.Resistivity comes to be a property of the material ,an indication of how difficult is to travel appart from length and surface.So your "resistance" is directly proportional also to this property called resistivity. If you want to express resistivity , all this thinking has to be expressed the other way around. Omegatron gives you a good indication, always check the units that come out of the math . They will help you to tell if your reasoning can be right.Keep your chin up, and make this page perfect.--Angel 13:22, 14 July 2007 (UTC)
The current induced by an electric field is more generally defined by J = σ E where J = I/A is the current density (amps/m²), σ is the conductivity (mhos/m) and E = V/L is the electric field (volts/m) with J and E being vectors. ρ (ohm-m) is defined as 1/σ so that (J/σ = ρ J =) ρI/A = V/L (= E) which in turn gives ρ = VA/IL = V/I A/L = R A/L.
Hence ρ = R A/L or R = ρL/A.
So the resistance R of a wire of resistivity ρ is proportional to its length L and inversely proportional to its cross-sectional area A. --Jbergquist 05:24, 14 October 2007 (UTC)
For the analagous situation of the flow of fluids through tubes subject to a pressure difference see Poiseuille's law. --Jbergquist 09:12, 14 October 2007 (UTC)
Hydraulic analogyOmegatron 16:50, 14 October 2007 (UTC)
Perhaps it would be better to define the resistivity implicitly: ρ is a coefficient chosen so that R = ρ l / A? It's a bit round-about, but it's more intuitive; we expect the resistance to increase with length and decrease with cross-section. --catslash 18:12, 14 October 2007 (UTC)

Nov 27, 2007 I corrected the units for resistivity from Ohm-meters to Ohms per meter. —Preceding unsigned comment added by 206.104.31.54 (talk) 01:24, 29 November 2007 (UTC)

Why did you do this ? Omegatron is definitely right. The only possible unit is Ohm.meter. Check the formula that is on WP at the moment (p = RA/l), check the formula given on the external site in the first comment (R = pA/l), or check the wikipedias in other languages. Jérôme (talk) 18:34, 29 November 2007 (UTC)

NB: In the UK, Year 11 is the final year of compulsary education. Mrpowers999 will be either 15 or 16, NOT 11. This is because school starts at 4 or 5 (not birth) and the first school year is called reception. Anonymous —Preceding unsigned comment added by 79.71.27.222 (talk) 18:23, 23 November 2008 (UTC)

## Is the table correct?

I think either the table is wrong, or the values in the Silver, Copper and Gold articles are wrong. Also, considering that the resistivity is given with much less precision than the coefficient, it seems misleading to add 1.47... to ~.0038... and get ~1.4738.... Κσυπ Cyp   13:06, 23 April 2007 (UTC)

Except for silver (which I reckon is just plain wrong), the values here are close to values in some electromagnetics texts I have to hand. It's likely that these values are for engineering materials, which will have trace impurities, and consequently resistivities which differ by a couple of percent from those of the pure element. I would guess that even for chemically pure metals, the resistivity would depend somewhat on the material's history (whether it had been worked, annealed or tempered).
Regarding the temperature coefficient, this could be of interest, even if smaller than the precision of the constant term: it quantifies the difference in resistance between two similar bits of metal at different temperatures (which could be used to measure a temperature difference using a Wheatstone bridge). Also it puts a bound on the variation with temperature, even if only to indicate that it's too small to worry about. I don't like the nones though. --catslash 15:16, 1 May 2007 (UTC)
Huh????? A temperature coefficient of 0.0038 is pretty damn significant if there's a delta-t of 100 K, that means the resistivity has gone up by 38%!!!- (User) WolfKeeper (Talk) 22:42, 28 June 2008 (UTC)
According to my materials text book (Materials Science and Engineering an Introduction by William D. Callister Jr.) Silver (commercially pure) at room temperature is 1.47 * 10^-8, Copper (for C11000 electrolytic tough pitch, annealed) its 1.72*10^-8, as impurities are added, it goes up. As for Commercially pure Gold its 2.35*10^-8. Hopefully this helps, feel free to PM me. ~~TheGreatCO 2:06(EST), May 7, 2007
The remark regarding the use of the coefficient is wrong, it shouldn't simply be added. The alpha value should be used as described in the "temperature coefficient" article which is also linked [AMJ] 15:14 GMT+1, May 8, 2007 —The preceding unsigned comment was added by 87.54.37.67 (talk) 13:14, 8 May 2007 (UTC).
The Al and Cu numbers, at least, disagree with those stated in my Rubber Bible. There are probably some unstated assumptions. 121a0012 21:38, 24 June 2007 (UTC)
There are a few problems here. The article still has the references for each material I added a year ago, but the values have been changed. Either the references need to be removed or the values changed back to what the references show. According to WP:V the threshold for inclusion is verifiability, not truth. For now, I'll change the values shown to what is in the reference for each material. If anyone has a different value, then the reference for that needs to be added. Kevin 03:27, 11 July 2007 (UTC)
The values are still wrong. I am not sure to what purity they are referring (perhaps this should be indicated?) but the references are definitely wrong. e.g. the reference for Copper has the value 1.59*10^-8, and this is identical to the value given in my physics textbook. So, either the references need to be changed, or the values do. And ideally the purity, etc. should be explicitely stated.124.183.118.52 (talk) 01:40, 21 March 2009 (UTC)

I get 2.45 for Al, 1.56 for Cu, 1.5 for Ag, 2.04 for Au, 4.9 for W, 8.9 for Fe, 9.8 for Pt, 19 for Pb (all 10^-8), supposedly for "commercially pure" samples between 288-298K. Revised Nuffield Advanced Science Book of Data, Addison Wesley Longman Limited. Presumably it varies greatly between samples. ⇌Elektron 02:58, 1 September 2007 (UTC)

Are the differences significant from a science/engineering point of view? (note - I am neither) Kevin 04:48, 1 September 2007 (UTC)

I don't dispute any of the values/coefficients in the table, but there is an error in the note: "*The numbers in this column increase or decrease the significand portion of the resistivity. For example, at 21°C (294.15 K), the resistivity of silver is 1.65×10^−8." Either this conductivity change was calculated for a 10°C (not 1°C) temp. change and the note should reflect such, or the coefficient used in the calculation was .038 instead of the proper value of .0038. Also, I think the simple relation Δρ = α ΔT ρ where α is the coef. is more clear than the phrase about the significand portion. Clcasto (talk) 18:19, 3 January 2008 (UTC)

Missing information?
Well I find it pretty odd that this table of resistivities is so small... Can't be right...

And why is this table not incorporated?: http://en.wikipedia.org/wiki/Electrical_resistivities_of_the_elements_(data_page) It seems to provide a full chart of all resistivities of all chemical elements... Seems pretty fundamental in any resistivity chart, don't you think? ;) —Preceding unsigned comment added by 62.131.171.23 (talk) 21:04, 18 February 2008 (UTC)

Plus very suspicious value for calcium. As far I had deal with the calcite mollusc houses, calcite containing walls, calcite stone, cement, silicate brics etc calcium much containing materials them all are roughly good isolators. I suggess may be an author had criscrossed value 3E-8 with 3E+8???? Or value is given for naturally flooded carbonites deep under soil, thus the water is that agent making so strange resistance??? —Preceding unsigned comment added by 85.254.232.1 (talk) 15:43, 30 March 2009 (UTC)

It's presumably the value for pure calcium metal, which exists but is unstable and is not found in the natural world. Calcium compounds, of course, are different. That's not at all surprising...aluminum is a very good conductor but Al2O3 is a very good insulator, etc. --Steve (talk) 16:32, 30 March 2009 (UTC)

I updated the table for conductivity by simple calculation from the already present resistivity (no other change was made) EV1Te (talk) 08:25, 28 April 2011 (UTC)

I'm sure the table is still wrong. Conductivity multiplied by resistivity is always 1. Eddietoran (talk) 20:37, 22 August 2011 (UTC)

So what is it that you think is wrong and why don't you fix it yourself? SpinningSpark 22:40, 25 August 2011 (UTC)
For many of the insulating materials the values are wrong: Conductivity multiplied by resistivity should be 1 but here we get 0.1. Judging from the article history, the conductivity data are wrong.--Ulrich67 (talk) 14:34, 23 December 2011 (UTC)

The temperature coefficient of resistivity for copper is 0.0039 everywhere but this page, where it is 0.0068. — Preceding unsigned comment added by Zxw 095 (talkcontribs) 21:35, 29 March 2013 (UTC)

## more depth ?

well, 1.56 for copper is quite good, I don't know how the guy did it, but around room temperature (18-21°C), bulk copper of high purity (99.9999% Cu) is supposed to be around 1.7-1.8 depending on the guy doing the experiment. so you'll understand that 1.56 renders me a bit suspicious of the whole book. for a scientifical / engineering point of view, 5% variation in resistivity may be very important, and 0.1% thermical variations are important as 100°C of heat during use is not unheard of, meaning that 0.1% or 0.2% per°C means either +10% or +20% resistivity, with may change all behaviours if you need precise input/output.

I had another information to add to the resistivity article, but I don't really have the time and the know-how to put it in the main article :

basically, resistivity is intrinseque to a material, depending on its atome (atomic properties such as masse, active surface...etc) then you add modifiers :

• temperature (already stated in the article) increase the active surface of phonons
• impurities (quickly mentioned in the discussion)
• microstructure of the material (indirectly stated in the discussion) : this is essentially the grain size (interaction with grain boundaries) and the cristal phases (influence the density of phonons )
• size of the sample : interaction of the electron with the surfaces of the conductor

currently the size of both grains and sample really have impact on resistivity when the dimensions approche or are under the micrometer range, but maybe the fact should be mentionned, as well as impurity effects.

here are some articles (list is non exaustive)on what I'm saying (as I work mostly in mircoelectronics, those works deal with that subject, but more general links can maybe be found, I have some thesis reports, but mostly in french):

• Y. Adda, J.M. Dupouy et J. Philibert, Eléments de métallurgie physique, volume 2 physique du métal, p. 415. INSTN - CEN Saclay. (1987)
• Blatt, F. J. (1968). Physics of Electronic Conduction in Solids. McGraw-Hill Book Compagny.
• Mayadas, A. F. et Shatzkes, M. (1970). The conductivity of thin wires in a magnetic field. Physical review B, 1(4):1382.
• Sondheimer The mean free path of electrons in metals, Advances in Physics, vol. 50, Issue 6 September 2001 , pp.499 - 537
• Steinhogl, W., Schindler, G., Steinlesberger, G., Traving, M. et Engelhardt, M. (2005). Comprehensive study of the resistivity of copper wires with lateral dimensions of 100 nm and smaller. Journal of Applied Physics, 97(2):023706.
• Thomson, On the Theory of Electric Conduction through thin Metallic Films, J. J. (1901). Proc. Camb. Phil. Soc., 11:120.

If someone wants to inclued those informations in this page, and can't find the information or want to discuss it, write in my user page, I will connect to it a bit in the near futur. Calavente (talk) 01:22, 23 January 2008 (UTC)

Hey, in spanish wikipedia...

Resistividad de algunos materiales
Material Resistividad (en 20°C-25ºC) (Ω·m)
Plata [1] 1.55 x 10-8
Cobre [2] 1.70 x 10-8
Oro [3] 2.22 x 10-8
Aluminio [4] 2.82 x 10-8
Wolframio [5] 5.65 x 10-8
Níquel [6] 6.40 x 10-8
Hierro [7] 8.90 x 10-8
Platino [8] 10.60 x 10-8
Estaño [9] 11.50 x 10-8
Acero inoxidable 301 [10] 72.00 x 10-8
Grafito [11] 60.00 x 10-8

Based on Matweb that I consider, good, for the resistivity article, we can be more accuracy in another dedicated only to the values.—Nicoguaro (talk) 14:26, 1 April 2008 (UTC)

## Table sort

Is there anyway to get the table to meaningfully sort on resistivity? The current sort doesn't seem to grok scientific notation... --Belg4mit (talk) 01:54, 11 September 2008 (UTC)

## Wire table - practical data

Resistance and Resistivity for Selected Common Metals[2]
10-ga wire Resistance
Ohms/ft      Resistivity (10-6 ohm-cm)
Silver        0.000944        1.629
Copper        0.000999        1.724
Gold           0.00114         2.44
Aluminum       0.00164         2.828
Iridium        0.00306         5.29
Brass          0.00406         7.00
Nickel        0.00452          7.8
Iron           0.00579         10.0
Platinum       0.00579         10.0
Steel          0.00684         11.8
`

This article would be more useful to the general reader if more practical data like above were added. -71.174.184.42 (talk) 00:07, 21 May 2009 (UTC)

## Reference does not match

I checked the reference for copper that is listed in the table and the two numbers do not match. We should not list a reference with a different value, or even better we should list the correct value and a reference that verifies it. —Preceding unsigned comment added by 71.33.199.247 (talk) 21:19, 26 March 2010 (UTC)

I've corrected the value. Wizard191 (talk) 23:39, 28 March 2010 (UTC)

## Sorting of tabular data

The "sort" option in tables doesn't seem to sort numbers, but instead sorts as strings - this makes it useless if using scientific notation or any number format that doesn't sort the same as strings. The "sort" function needs a stronger parser that can be told "These are numbers, not strings" and sort by magnitude of the number, not just as a string sort. --Wtshymanski (talk) 19:44, 10 February 2011 (UTC)

I suggest you re-post your message at the technical issues discussion board. :-) --Steve (talk) 20:33, 10 February 2011 (UTC)

## Recent edits by 202.81.235.24

These edits [[3]] seem to largely consist of changing the units or resistivity from Ωm to m/S and changing numerical notation from e.g. 58×106 to 58∘106. The use of m/S while technically correct is virtually unheard of (at least unheard of by Google). The dot-notation for simple arithmetic multiplication is also correct, but probably less common the than the cross. These edits are clearly made in good faith, but they are very extensive; is there anything good that in them that can be saved, or should they just be reverted completely? --catslash (talk) 11:16, 21 May 2011 (UTC)

both operations use symbols not from keyboard symbols. has he used unicode-keyboard to input? i knew you aught use [itex] — Preceding unsigned comment added by 188.25.49.46 (talk) 00:35, 24 April 2012 (UTC)

## conductivity/density product

In the table concerning conductivity and density, I feel like the product of the two parameters (what is given) is not as interesting as the quotient. A designer would be interested in conductivity per unit of mass, so you'd want resistivity/density. A high value would mean lots of conduction for a given mass. I think the given values, while correct, are not useful. — Preceding unsigned comment added by 128.196.211.58 (talk) 22:43, 5 August 2011 (UTC)

Conductivity is the reciprocal of resistivity. Therefore multiplying resistivity by density is the same as taking the ratio of density to conductivity.
If the power line has length L, cross-sectional area A, resistivity $\rho$, and density d, then the resistance is $R=L\rho/A$, and the mass is $M=dLA$. Therefore $RM=d\rho L^2$. The design spec calls for a certain maximum resistance (R is fixed) and length (L is fixed). To minimize the mass, therefore you need to minimize $d\rho$, the resistivity-density product. So that's just what the designer wants. :-) --Steve (talk) 15:25, 6 August 2011 (UTC)

## Poor formatting of numbers

some are in scientific notation (1.0x10^14), while some aren't (10x10^14). I do not know whether these were typed with the decimal forgotten, or if it's a different notation intentionally. Maybe someone could track down the poster? — Preceding unsigned comment added by 67.42.71.64 (talk) 19:49, 9 June 2014 (UTC)

The entire left side of the table lists values in a strange format, viz.

• 1.59e−8

Which I take to mean

• 1.59 × 10-8

... The whole table needs to be revised to reflect ordinary notation, as I wouldn't want anyone thinking we are using Euler's number here. I like to saw logs! (talk) 06:12, 9 August 2011 (UTC)

You are correct! Scientific notation#E notation. I do remember, a long time ago the first time I saw "e"-notation, that I was confused what it was. So we may as well change it as you suggest. :-) --Steve (talk) 13:47, 9 August 2011 (UTC)
It seems to be desirable that this table be sortable. So, I changed it to be like that because that's how the wikipedia's software works for sorting purposes. If you don't do that, then it simply doesn't sort. Unfortunately, the web server doesn't support other formats like 10-8, only 1E-8 and similar. It may be further improvable, but there's a whole bunch of bugs you have to be careful to work around.Teapeat (talk) 17:18, 15 August 2011 (UTC)
It seems to be very buggy in any case. Try repeatedly pressing the sort button and watch where the "air" entry goes for instance. It is not worth maintaining the feature if it is not going to work properly. SpinningSpark 18:41, 15 August 2011 (UTC)

## Merge with electrical resistance and conductance

Wtshymanski proposes a merge. We can discuss it here. --Steve (talk) 18:06, 9 August 2011 (UTC)

• I oppose the merge. Most of the content of the articles does not overlap and should not. The temperature-dependence section does overlap, but the solution is not to merge the whole articles, but to do something just about that section. (Not sure what...) :-) --Steve (talk) 18:06, 9 August 2011 (UTC)
Do you have any explanation of your opposition? If you look at Electrical resistance and conductance, you find headings such as " Causes of resistance / In metals /In semiconductors and insulators /In ionic liquids/electrolytes , Resistivity of various materials , Band theory simplified , Differential resistance, Temperature dependence, Strain dependence " all of which are talking about microscopic properties of materials, not the properties of a macroscopic object. If we took all those out of that article, about all it would have left in it is R= rho* L/A, which is a trivial exension of *this* article. WHy do we need two articles covering manfestly the same topic? --Wtshymanski (talk) 21:38, 9 August 2011 (UTC)
Hmm, I suppose they do have somewhat random overlap and scope right now but merging is not the answer. We can (and by and large should) take resistivity-related things out of the resistance article, while adding in other things that are pertinent to electrical resistance but not to resistivity. (Of course, it would be worth at least mentioning that the resistance of a wire is temperature-dependent etc., even if the main discussion is in the resistivity article.) (Strain should be in both...the effect of strain on resistance is a different formula than the effect of strain on resistivity, because strain obviously changes the dimensions.) Examples of things relevant to resistance but not resistivity include: Summary of what resistors do and what they're used for; differential resistance and negative differential resistance and why we care about it; how ohmmeters work; AC resistance and the skin effect; sheet resistance; the resistance of 1km of power line and other such real-world examples and why we should care about that; relation to impedance. A lot of these are already in the article and there's plenty of room to flesh them out even more. :-) --Steve (talk) 04:14, 10 August 2011 (UTC)
• I agree with Steve. Wtshymanski has a point that they are, um, mergeable, but I think that they will cover too much ground in that case (especially once they get, um, completed). It's better that we clearly delineate the scope, than to lump everything together. So yes, some cleanup and/or moving material around is required, but full-blown merge is not. We already had a similar discussion at Talk:Electrical resistance and conductance#Suggest merge. No such user (talk) 06:39, 10 August 2011 (UTC)
• I also am not in favour of this merge. Yes the subjects are connected, and in a textbook they would all be covered in the same chapter together with Ohm's law and resistors in series and parallel as well probably. But encyclopedia articles are better as smaller and more focused chunks. I thought the previous merge was a bit dubious: this is definitely too far. It really does not matter if articles have some overlap, and frankly it would be impossible to completely eliminate.SpinningSpark 17:10, 11 August 2011 (UTC)
Can anyone tell me what the "-ity" and "-ance" articles, respectively, are supposed to be about? I don't understand what the difference is supposed to be. Surely everthing in the "-ance" articles is covered in "-ity" with the exception that r = rho*l/a (or g=sigma*a/l), which is trivial. I don't understand why we need two articles to confuse the reader on the same subject. --Wtshymanski (talk) 17:51, 11 August 2011 (UTC)
Above I gave ~8 examples of topics that help someone understand resistance but are not terribly related to resistivity. To summarize: The resistivity article should be primarily about what resistivity is and why different materials have different resistivities; the resistance article should be primarily about how what resistance is and the role that resistance plays in electrical circuits. I'm not saying this is how the articles are organized at the moment, but they can be organized this way with much less effort and better result than merging. --Steve (talk) 22:39, 11 August 2011 (UTC)
• Probably a bad idea. Use your efforts to strengthen each article and focus each one to its title, with copious cross-linking or references to the other. They each need a cleanup, and certainly a combination of four words being discussed in an encyclopedia would reduce its utility. So yes, I oppose a resistance, resistivity, conductance, and conductivity article unless it merely focused on the mutual relationships and differences amongst each word. I like to saw logs! (talk) 17:59, 11 August 2011 (UTC)
I can't work on an article if I don't know what it is about. What is supposed to be the difference between the article Electrical resistivity and conductivity and the article Electrical resistance and conductance? It's the same subject matter as far as I can tell. We don't need 4 words in a title, perhaps just call it "Electrical conduction" and discuss all the others in one place. Researching anything on Wikipedia is worse than a scavenger hunt - instead of leaving fragmentary clues and see-alsos and hatnotes all over the place, let's discuss the topic in one article. (At least now we don't have 4 articles on the same topic...one more merge and we'll be done!) --Wtshymanski (talk) 18:12, 11 August 2011 (UTC)
Since no-one is going to type either of these titles in a search box, we're already relying on redirects - why not give the article a sensible short title instead? --Wtshymanski (talk) 18:18, 11 August 2011 (UTC)
Resistivity is a property of materials, resistance is a property of components. That there is a difference does not particularly strongly argue for or against a merge but I cannot believe anyone cannot truly appreciate the distinction. SpinningSpark 16:55, 15 August 2011 (UTC)
Oppose It would be like merging density and mass together. They're related but not in any major sense the same.Teapeat (talk) 21:09, 11 August 2011 (UTC)
• Unconvinced But may I suggest a clarification of the purpose of having two separate articles ? One article would be for the "Academic Scientific Theory" aspects of the subject, the other for the "Practical Technical Applications" side of the coin. I suspect these are the two approaches that would be most useful to WP users, who would probably be quite distinctly looking for one or the other. Would anyone disagree with this or suggest different basic purposes ? Is there a definite algorithm to combine them whilst maintaining this dual purposefulness ? Darkman101 (talk) 17:51, 5 September 2011 (UTC)
• I oppose the merge. Resistivity is a property of a material. Resistance is a measured effect of resistivity. Absolutely there is a lot of overlap, but the comments in the section here highlight the need to have the two separated. For example, as a geophysicist, I go and measure resistance. That measurement contains information about two things: the rock properties in the ground, AND the survey geometry/set up (sticklers will also say contact resistance between the electrodes and the ground, but I digress). If I place my electrodes in a different configuration, I will measure a completely different resistance over an area with the same resistivity. I must agree with Teapeat; if one merges these two articles, then density and mass should be combined. Andykass (talk) 16:09, 15 September 2011 (UTC)

The merge seems to have failed and I have detagged both articles.- Sheer Incompetence (talk) Now with added dubiosity! 22:45, 28 September 2011 (UTC)

## Einstein's Summation

In the Tensor Generalization, in the areas where Einstein's summation is presented, shouldn't there be a sigma there? I mean, reading it just like that would just be unclear - if you say that Ji=oijEj, one might think that for any j, J3=o3j*Ej is correct. I'm not a wiki expert, just went through the article and noticed that, and I thought why not write it here. the same thing goes right below it, with the resistivity. — Preceding unsigned comment added by 132.70.170.23 (talk) 16:05, 10 October 2011 (UTC)

The whole point of the Einstein summation convention is that the summations are implied rather than explicitly stated for simplicity of expressions. Please read the linked article. Although in this article no actual manipulations are done with tensors so the convention is not really of much benefit and could be omitted. SpinningSpark 22:23, 10 October 2011 (UTC)

## Tensor form

Here the introduction of the tensor form is mixed with introduction of inhomogeneous material. However the tensor form and inhomogeneous material are two separate steps of generalization. It would be probably easier to understand to make these two steps separate: first by allowing an inhomogeneous material by using local definition as it is already done using E and j. Its just allowing E and j to be a field instead of global values. The introduction of the tensor can then be done without reference to a position. --Ulrich67 (talk) 00:13, 20 December 2011 (UTC)

This article may not be the right place to be explaining tensors and tensor fields - so I would favour trimming this section somewhat. --catslash (talk) 02:15, 20 December 2011 (UTC)
I agree, and will reduce the length of that now.-- 19:27, 19 February 2012 (UTC)
Done. Opinions?-- 20:58, 19 February 2012 (UTC)

## Relative conductivity

These numbers are confusing. One could use the scale of copper, writing the conducitivty in percentages of copper, which is the second most doncuting pure metal and is very common. This is an accepted scale I think, called the IACS. — Preceding unsigned comment added by 31.210.186.117 (talk) 08:42, 20 April 2012 (UTC)

## Poisson's equation?

In the section Resistance versus resistivity in complicated geometries, shouldn't it be Gauss's law

$\nabla\cdot\mathbf{E}=\rho/\epsilon$

for the electric field E rather than Poisson's equation

$\nabla^2 V =-\rho/\epsilon$

for the electric potential V? It seems slightly incoherent... 18:55, 6 May 2012 (UTC)

I agree, better to say "Gauss's law". In practice you usually would solve for V not directly for E, but no need to make things more complicated. --Steve (talk) 22:19, 6 May 2012 (UTC)

## References for the origins of resistance in metals

This section is unreferenced. Pasting in what was the text there (edited now) showed that many sites are taking this unreferenced page as their reference, but revealed no good references for the claims.

Someone familiar with how electron's path through a conductor is impeded in such a way as to give rise to resistance should look at this section, and add references.

Well, there is no understanding of this displayed here at all. Maybe there is a good physicist who could spend a bit of time putting in an explanation. — Preceding unsigned comment added by 82.69.66.91 (talk) 22:59, 15 June 2012 (UTC)

## Table out of order

I noticed that the table of resistivities and conductivities seems to be sorted by increasing/decreasing resistivity, but there are several that are out of order. I'm not sure if this is just people adding stuff, or if they're trying to keep the carbons/waters together, but I think it would be most helpful if it was sorted properly. I plan to do some work on it when I get some free time. (talk) 21:23, 15 June 2012 (UTC)

## What is an ohm metre?

The article does not clearly explain what an ohm metre is. Ayrton and Mather (1911) state: "The specific resistance or resistivity of a material is usually expressed as the resistance in microhms...of a centimetre cube or of an inch cube". Using the MKS system, the equivalent would be the resistance of a metre cube. Is this correct? Biscuittin (talk) 07:26, 18 October 2012 (UTC)

Sort of ... 1 ohm meter is the resistance of a 1meter × 1meter × 1meter cube of material where two opposing faces are contacted by a perfectly-conducting sheets. This is a rather unusual and unintuitive setup, and I fear that trying to say this in the article would confuse or mislead people (unless someone made a diagram). For example if you made a 1 meter3 box out of copper (very expensive!), then mistakenly contacted it with two wires on opposite sides (instead of two perfectly-conducting sheets), then you would measure the resistance as being much higher than 1 ohm.
It seems to me that a more useful explanation is that if you have a 10cm-long wire with 1mm2 cross-section, and its resistance is exactly 100 kΩ, then the wire's resistivity is 1 ohm-meter. Or something like that... Do you think that would help?
Ohm-meter does not need a separate "definition", strictly speaking, it's just 1 ohm multiplied by 1 meter. Instead, when you say "explain", I think you're looking for some intuitive picture... --Steve (talk) 20:54, 18 October 2012 (UTC)
1 ohm multiplied by 1 meter is meaningless unless the cross-sectional area is specified. There seem to be many different definitions of resistivity. For example, my Schoolboy's Science Pocket Book gives it in "ohms per circular mil per foot", which is closer to your suggested definition. Biscuittin (talk) 08:10, 19 October 2012 (UTC)
The article states "The SI unit of electrical resistivity is the ohm⋅metre", but I can't find a reference to support this, so I have added a "fact" tag. Biscuittin (talk) 15:27, 19 October 2012 (UTC)
Ωm is just a simplification of Ωm2/m, the units of (resistance ×cross-sectional-area per unit length). You can think of it as the number of ohms per unit length you get for a given cross-section, or as the size of cross-section you can have for a specified ohms per unit length. The units follow directly from the formulae in the Definition section, so it doesn't really need a reference to support it. --catslash (talk) 16:41, 19 October 2012 (UTC)
(That would have to be ohm circular mils per foot not ohms per circular mil per foot, since the latter has dimensions of resistance per volume which is not what's required. --catslash (talk) 21:02, 19 October 2012 (UTC))

## Factual accuracy

If ohm metre is an abbreviation for ohm metres per square metre then why doesn't it say so in the lead section? The lead section is completely unreferenced and I also question the statement "Electrical resistivity (also known as resistivity, specific electrical resistance...). Surely specific electrical resistance is simply a ratio (based on Silver = 1) and has no units? Because of these questions, I have added an "accuracy" tag. Biscuittin (talk) 18:04, 19 October 2012 (UTC)

It's not an abbreviation; ohm square-metres per metre is the same thing as ohm metres, just as 6/3 is the same thing as 2.
The article only claims that specific electrical resistance is the same quantity as resistivity. It does not say what units are commonly used with specific electrical resistance. The term specific electrical resistance is not familiar to me - it may be archaic, and therefore it's possible that it is/was commonly reported as a multiple of the resistivity of Ag rather than in SI units. I can find no evidence of this however. What is your source for this silver-based scale? --catslash (talk) 18:53, 19 October 2012 (UTC)
My mistake. I was assuming that specific electrical resistance was the same as relative resistance but it seems this is not the case. My source for the silver-based scale is Practical Electricity by Ayrton and Mather, published 1911 by Cassell & Co. Here is an extract from the table on page 229:
Name of metal Centimetre cube † Inch cube † Relative resistance
Silver 1.48 0.583 1
Copper 1.55 0.610 1.04
Aluminium 2.43 0.96 1.64
Iron 9.7 3.82 6.56

† Resistance in international microhms at 0°C

What is your source for the statement "ohm square-metres per metre is the same thing as ohm metres"? Biscuittin (talk) 22:07, 19 October 2012 (UTC)

Yes, it makes sense to use silver as a basis for comparison as it has the lowest resistivity. It seems though that this is an ad-hoc scale devised for the purpose of the article in that book, since (1) the column header relative resistance is not defined when the terms specific resistance and resistivity are defined on the previous page and (2) relative resistance is used for a different quantity in a different table on the next page. --catslash (talk) 22:51, 19 October 2012 (UTC)
No, I can't find a source for: area / length = length, but it is commonly accepted as true. --catslash (talk) 23:31, 19 October 2012 (UTC)
Agreed. Table VI is relative resistance for the same length and sectional area, while Table VII is relative resistance for the same length and weight. "Commonly accepted as true" is not good enough for Wikipedia. We must have a reference. Biscuittin (talk) 09:01, 20 October 2012 (UTC)
I have found a reference which supports Catslash's view and I have added it to the article. Biscuittin (talk) 20:32, 20 October 2012 (UTC)
Biscuittin, I wonder whether you are familiar with the factor-label method, dimensional analysis, etc. It is completely appropriate to cancel "meters" from the numerator and denominator!
Relatedly, you don't seem to appreciate the difference between "a unit for resistivity" and "a formula for resistivity". If you're not sure how something is defined, it is a very bad idea to look at the unit and guess. It is not possible to do that in most areas of physics, and it is unreasonable for anyone to expect that.
For example, you are obviously familiar with the formula $\rho = RA/L$. An equally valid - actually more general - formula is $\rho = J / E$ where J is current density and E is electric field. So you could say the unit of resistivity is "(amps per meter) per (volt per meter)". It turns out that a material which is "11 (amps per meter) per (volt per meter)" also happens to be exactly 11 ohms meter^2 / meter! (In the sense that a meter cube with opposite faces contacted has a resistance of 11 ohms). Is that an amazing coincidence?? No, it is the factor-label method in action! If you cancel the units in "11 (amps per meter) per (volt per meter)" you get "11 ohm meter", the same as "11 ohm meter^2 / meter". I happen to know that 100 ohm-cm equals 1 ohm meter. I did not have to think about how the resistance of a 1 cm^3 cube compares to the resistance of a 1 m^3 cube ... I just used the factor-label method.
Therefore your edit was misleading in saying that the resistance across opposite faces of a cubic meter just happens to be referred to as an ohm-meter. It is quite literally the result of multiplying an ohm by a meter, a pure abstract mathematical operation. It would be incorrect to call the unit anything else.
I rewrote it and added mention about the cube later in the article. --Steve (talk) 21:02, 21 October 2012 (UTC)
(that's $\rho = E / J$ in "(volts per metre) per (amps per square-metre)" of course --catslash (talk) 01:09, 22 October 2012 (UTC))
Steve - I'm sure you are technically correct but that's not the whole story. Wikipedia is supposed to be comprehensible to the layperson and I still maintain that ohm metre is meaningless without an explanation. I also note that nobody has provided a reference to any official SI publication. I've searched and I can't find one. Biscuittin (talk) 15:38, 22 October 2012 (UTC)
That the defining formula requires the SI units to be Ωm will not be obvious to all laypersons. However, the use of units is a general question not specific to resistivity, and perhaps the units of measurement page is the right place for a detailed exposition of this subject. The number of SI derived units is unbounded; official SI publication will list derived units with special names, like newton = kg m s-2, and very likely some commonly used combinations (such as newton metre), but to specify all possible combinations is neither possible nor useful. --catslash (talk) 23:44, 22 October 2012 (UTC)

## SI units

Metre is an SI base unit and ohm and siemens are SI derived units. Ohm metre and siemens per metre appear to be derived derived units so I question whether they are SI units at all. See [4] [5] Biscuittin (talk) 18:39, 22 October 2012 (UTC)

Derived2 = Derived. In the second of these links you will see (for example) both Force newton: N = m kg/s2 [derived from base units] and Moment of force: metre newton: N m = m2 kg/s2 [derived from a derived unit] listed as SI Derived Units. --catslash (talk) 22:40, 22 October 2012 (UTC)
OK, but why do ohm metre and siemens per metre not appear on any lists of SI derived units? Biscuittin (talk) 23:20, 22 October 2012 (UTC)
Very probably for the same reason that m10 does not. --catslash (talk) 23:47, 22 October 2012 (UTC)

## Question

What is the objection to having an explanation (for non-technical readers) of the term ohm metre in the lead section of the article? Biscuittin (talk) 18:35, 23 October 2012 (UTC)

Does it need explanation in the lead? The rest of the article is the explanation. Unless you want to give an application like "A material with a resistivity of one ohm-metre has a resistance of one ohm between two opposite faces of a cube, one metre on a side." but we get to this later on in the article. --Wtshymanski (talk) 19:47, 23 October 2012 (UTC)
Why not have it in the lead? Why have to search through the article for it? We are not all experts. Biscuittin (talk) 19:59, 23 October 2012 (UTC)
The "explanation" of the term an ohm meter in relation to the resistance of a 1m×1m×1m cube is not terribly useful, by itself, unless the reader needed to calculate the resistance of a 1m×1m×1m cube!! The formula for resistivity is far more useful. So we should say the formula first. That's what the article does: The formula ρ=RA/l is in Section 1.1. Readers who want to use the formula but don't understand the factor-label method will come across the "cube" example (which will hopefully point them in the right direction) very quickly, within Section 1.1. This seems appropriate to me. I don't think the cube example should be in the intro. --Steve (talk) 23:35, 23 October 2012 (UTC)
I am not a physicist and I simply want to know how an ohm metre is defined. I probably wouldn't read the rest of the article because it is too technical. That is why I want the definition in the lead. Biscuittin (talk) 08:18, 24 October 2012 (UTC)
It's not like the kilogram, where you can point to a lump of platinum and say "Here's the definition of a kilogram" - an ohm-metre is a terribly abstract thing and you have to spend more than 8 seconds reading the intro if you want to understand it. I'm not sure why one would care about the definition of the ohm-metre outside of the context given by the article. If I wanted to know what an erlang was, I'd expect to read up a bit on telecomms to understand it. --Wtshymanski (talk) 15:04, 24 October 2012 (UTC)
I think it is quite easy to define - it is the resistance across opposite faces of a 1 metre cube of the material. Why object to having this in the lead? Biscuittin (talk) 18:24, 24 October 2012 (UTC)
That's brilliant, but it's only been suggested twice in the last week or so. Better let it get suggested a few more times onteh talk page so we can achieve holy consensus. --Wtshymanski (talk) 19:26, 24 October 2012 (UTC)
Yes, I suggested it because it is a clear explanation which can be understood by non-technical people. I have put it, with a reference, in the article. If you remove it, please explain why you are removing it. Biscuittin (talk) 20:18, 24 October 2012 (UTC)
Why have I have reworded? For one thing, this is an article on the topic "electrical resistivity and conductivity", not the topic "ohm meters". Second, the definition of an ohm-meter is "what you get when you multiply an ohm by a meter". It is not defined by a particular object in a particular geometry. Third, the quote from Ayrton and Mather will certainly confuse readers. You are hoping for it to define "ohm meter" and "ohm cm" but it doesn't even mention that unit, let alone define it, but it does talk about temperature (which is entirely irrelevant to defining resistivity), etc. etc. I hope my reworded version is acceptable to you. I have grudgingly kept the cube example in the introduction. --Steve (talk) 12:24, 26 October 2012 (UTC)

## Teflon

The resistivity listed in the table for Teflon seems too high (therefore, too small of a conductivity). From other sources, it appears that the bulk DC conductivity of Teflon should be somewhere between 10^-15 and 10^-18 [S/m]. — Preceding unsigned comment added by 129.7.16.24 (talk) 01:10, 22 November 2012 (UTC)

## name

Wikipedia:Naming conventions#Titles containing "and" — Preceding unsigned comment added by 24.131.80.19 (talk) 00:03, 20 November 2012 (UTC)

## Corrections needed for table in Resistivity of Various Materials section

The table listing resistivity and conductivity of various material needs correction. Since resistivity and conductivity should be reciprocals, the table cannot be correct. Two examples: 1. Assuming the resistivity for GaAs is correct at 5 x 10^-7 to 10 x 10^-3 (that should actually read 1 x 10^-2)... the conductivity for GaAs should be 1 x 10^2 to 2 x 10^6 . 2. Assuming the resistivity of Carbon (diamond) is correct at 1 x 10^-12 .... The conductivity for Carbon (diamond) should be 1 x 10^12. . There should be no wiggle room for variations as the units are simply reciprocals... nothing novel is introduced so there should be no variation. 1/2 dozen is always 6 never ~7 — Preceding unsigned comment added by 70.171.44.124 (talk) 16:08, 16 October 2013 (UTC)

## Nernst-Einstein

Hello!

My friend was disappointed that he could not find here the Nernst-Einstein law (and used it to tell me that Wiki is not that great). This law is described on the French article, at the very end. Would it make sense to add this here?

Thank you for any insight on this!

Meumeumarj (talk) 16:25, 1 March 2014 (UTC) // Talk on my French page

That law, as written in the french article, says "If you happen to know the diffusion coefficient of an electron in a material, here is the conductivity." But that is a pretty unusual situation. I, for one, don't know the diffusion coefficient of an electron in any material (although I know how to calculate it). They are not tabulated the way mobilities and conductivities are.
(I guess it would come up more often when discussing the conductivity of an electrolyte...)
Hmm, I think this article should at least say that conductivity equals concentration times mobility, which is generally true and useful (and it's surprising that it's not already in the article). Then the mobility article in turn has the Einstein relation between mobility and diffusion coefficient.
I'm slightly opposed to putting in a direct relation between conductivity and diffusion coefficient, but only slightly. :-D --Steve (talk) 18:54, 1 March 2014 (UTC)

## Causes of conductivity | In metals: do electrons really move from one end of the conductor to the other?

I was reading in a forum

"Remember that it isn't a matter of electrons moving from one end of the wire to another;
instead, the electromagnetic field moves through the wire, making electrons jump from one
atom to the next, and then another electron from that atom to the next, in a wave."

This seems more in line with the Band theory simplified given in the previous paragraph. — Preceding unsigned comment added by 95.237.142.70 (talk) 09:03, 20 August 2014 (UTC)

Thanks for pointing it out. I fixed the paragraph and hopefully made the mechanism much clearer. I admit that the Newton's cradle analogy is a bit of original contribution of my own (although I presume someone has made it before), but nonetheless I hope it helps understanding the phenomena. I'm far from an expert in physics, but I hope the explanation is sufficiently accurate for a layman. No such user (talk) 10:16, 20 August 2014 (UTC)