Convert resistivity units to conductivity units

A. Hi Anwar. Please start by understanding that, as explained on this page, a Siemen or a mho are the same thing, and they are the inverse of an ohm. So if the volume conductivity is 292 micro Siemens/cm, the volume resistivity is 1 / .000298 mho/cm, which equals 1/.000298 ohm-cm.

Luck & Regards,

A. Hi, Merlyn. One is simply the inverse of the other. If the resistivity is 18.4 million ohm-cm, then the conductivity is 1/(18.4 million ohm-cm) = 1/(18.4 million) S/cm = 1/18.4 microS/cm.

Regards,

A. I don't think the previous answer is restricted to surface resistivity vs. surface conductivity, Brendan. These terms are intended to be the inverse of each other regardless of the units or dimensions. But I feel your pain about obfuscatory terms like "volume resistivity" which seem to defeat the application of our everyday intuition :-)

I think the easiest way to keep it from going hopelessly abstract on us is to start with Ohm's Law, i.e., that current equals voltage divided by resistance. We know intuitively that if one wire is twice as long as another, it's resistance will be twice as great, which is to say that its conductance is half as great. If the diameter of one wire is twice the diameter of another, it's area is four times as great, so it's like having four wires in parallel, and the conductance is quadrupled, which is to say the resistance is quartered. If two wires are the same length and diameter, but one is made of a metal that carries electricity only half as well as the other, its resistivity is twice that of the other material, which is to say that its conductivity is half as great.

So, if we express resistivity in Ohm-inches, and length is expressed in inches, and area is expressed in square inches, then resistance is expressed in Ohms. Checking the logic of this by checking the units: to get the resistance in Ohms, we multiply the resistivity of the conductor in Ohm-inches by the length of the conductor in inches and divide by its area in inches², and all the units cancel out except the Ohms.

A. Again, conductivity is simply the inverse of resistivity, Paula. That is: Conductivity = 1 / Resistivity. Or Resistivity = 1/ Conductivity. In fact the term 'mho' is not the name of any scientist, but was invented just to be the mirror image or 'inverse' of Ohm. These days people tend to use Siemen rather than mho though.

But you can't get sloppy with 'the units' or you'll stay hopelessly confused forever... mhos is not a valid unit for conductivity and megOhms is not a valid unit for resistivity! Please start at the top of the page and study slowly. Also be careful with expressions like 'mmhos' because a leading m is usually an abbreviation for milli or 1/1000 when working in the metric system, whereas I think you are treating it as an abbreviation for micro or 1/1,000,000. Since we certainly don't like our answers to be wrong by 3 orders of magnitude, I don't think you should take the chance of using that abbreviation :-)

Good luck.

A. Ted Mooney,
All of your answers are correct. The reason that resistivity or conductivity are volumetric is that the number represents a value given a medium of area unit and length unit, therefore volume.
Soil in a box 1 meter wide, 1 meter deep, and 1 meter long will measure OHM*meter. The value can then be converted to OHM*cm, or OHM*mm or OHM*inch. Resistivity of a sample of one cubic cm, or cubic mm, or cubic inch.

A. Hi, Chris. Conductivity is the opposite (or, more properly, the reciprocal) of Resistivity.
Years ago a Siemen/cm was called a "mho/cm"; something nice about that terminology was that it implied that a mho/cm is the reciprocal of an ohm-cm (which it is).

So, if you have

18,400,000 ohm-cm, then the reciprocal is

1 / (18,400,000 ohm-cm) or

1 Siemen / (18,400,000 cm)

.00000005.4 Siemen/cm or .054 microS/cm.

Regards,

A. If Conductivity = 0.054 µS
= 0.054 x 10-6 S
= 0.54 x 10-5 S
= 0.54 x 10-5 mho

Now Resistivity = 1 / Conductivity
= 1/ 0.54 x 10-5 mho
= 1.84 x 10-5 mho
= 18.4 Mmho

A. Hi Amol,

Please explain your situation that prompts you to ask. While resistivity is a meaningful physical quality, "SR" and "VR" are more in the nature of mathematical constructions than meaningful physical qualities, and the relationship between the two is a simple mathematical manipulation rather devoid of original physical insights, similar to converting length from meters to inches. Picture:

Take a short slice of a piece of wire; it's a cylinder. You can measure the electrical resistance of this cylinder in Ohms, or you calculate the resistance by dividing the voltage across it by the current that flows through it. If you look at the cylinder end-on, you see a circle, and that circle has some specific area or surface area or cross sectional area. If you multiply that surface area x the length of the slice of wire (or you could call it its thickness) you have the volume of the cylinder.

Resistivity, is a property of the wire and if you multiply the resistivity by the length and divide by the area you get the resistance.

If a coating on a substrate is more conductive than the substrate, it has lower resistivity than the substrate, and mathematical manipulations, like whether or not you include thickness in your units, doesn't change the fact.

A. Hi Jag. This is not something you calculate so much as something you must take the time to implicitly comprehend. A microohm is a millionth of an ohm and a cm is 1/100 of a meter. So you take the value you were given and insert the conversion factors (1,000,000 microOhms)/ohm and (100 cm)/m.

Because these conversion factors are "equalities", always equal to 1, it doesn't matter whether you invert them. So you put them into your equation either as I have written them or 'upside down' as ohm/(1,000,000 microOhms) and m/(100 cm) depending on which way will let you cross out the microOhms term and cm terms you started with and leave you with the Ohms and m terms you want to end up with. You must learn to always "watch the units", and such conversions will come easily and always work right.

Example, with 5000 microOhms per cm

Try 5000 microOhms/cm x (1,000,000 microOhms)/ohm x (100 cm)/m ...

We have cm in the denominator of the first term and the numerator of the third term, so they can be crossed out, leaving ...

5000 microOhms x (1,000,000 microOhms)/ohm x 100/m, but this leaves us with microOhms in the numerators of the first and second terms. They can't be crossed out; but it is valid to invert the second term since it's an 'equality'...

5000 microOhms x ohm/(1,000,000 microOhms) x 100/m; now we can cross out microOhms since its in the numerator (of the first term) and denominator (of the second term), leaving ...
5000 x ohm/1,000,000 x 100/m = 0.5 Ohms/m.

Regards,

A. Hi Azhar. Although the question is a bit abstract for me to follow, I'd say you can determine the conductance because it is the reciprocal of the resistance, but not the conductivity because you can't make the units match without additional terms like thickness.

Regards,

Hi Ted Mooney
Thanks for your answer!

A. Hi Azhar. Your question went unanswered a long time; perhaps other people had difficulty understanding it as well. Now that I very slowly re-read it, I see that you are asking how you can determine the resistance from a graph of current vs. voltage. Ohm's Law says V=IR, which can also be expressed as R=V/I. So you simply take any point on the line you graphed, and the resistance in Ohms is simply whatever the voltage (in Volts) is at that point divided by the current (in Amps) at that point.

Regards,

A. Hi Ajay. You'll make best continuing progress on this if you carefully think it through, and then be very careful of your words and their precise meanings. The suffixes "-ance" and "-ivity" are very different and must not be confused. So your question cannot be answered because it is improperly asked; although a length of wire might exhibit a resistance of 0.04328 Ohms for each meter of its length, please carefully study the thread and figure out what is wrong with your question, and I think the answer will come to you. Thanks and good luck.

Regards,

Thanks for your feedback. Understanding that Volume resistivity is Resistance/(Cross Sectional Area*Bond Line Thickness) the computation I made is at best, ambiguous. I don't have any of the original material for conducting a Volume Resistivity test. However, I do have a sample of the new material and the original manufacturer's test procedure used for "Bond Joint Resistance". Therefore, I will determine a "Bond Joint Resistance" for the new material and be able to compare it's electrical property. This seems to be the only way that I can get an answer that I can depend on. Also, the NSN for the original new material are the same, indicating that the Federal Government recognizes them to be suitable substitutions. I appreciate your comments and will post the conclusion when available.

A. Hi Adam. I'm not sure I understand, but this approach doesn't sound right from the get-go. It seems that you are trying to use a Fluke V-O-M as some sort of signal generator instead of using it as a meter; it wasn't designed to generate signals, and I don't know that it will generate a reliable and reproducible one. Although it generates a small voltage when in Resistance mode, there is no reason to even assume that the voltage is consistent for different scales.

I think what you need to do to calibrate a conductivity module is to connect it to a series of resistances or a resistor whose resistance can be varied, and make sure the module is reading the right resistance/conductance.

Regards,

Thank you Ted. That makes sense. I can simulate the mV signal and temperature signal just fine from the Fluke Documenting Processor, but it doesn't seem to work well with resistance. I can get a signal on the conductivity module, but it doesn't move no matter what I enter in the Fluke meter. I will try to locate a modifiable resistor to perform this task successfully. Thank you!

A. Hi Bernard. Good question, thanks. But a mho or Siemen is just the reciprocal/inverse of an Ohm.
1 Ohm is 1 Siemen, 2 Ohms is 1/2 Siemen, 1 million Ohms is 1/1,000,000 Siemen.
1 Siemen is 1 Ohm, 2 Siemens is 1/2 Ohm, 1 million Siemens is 1/1,000,000 Ohms.

Graphs of the reciprocal function (y=1/x) are easy enough to make for a mathematics lesson, but not useful for this because if you make a graph that goes to a million Ohms you won't even be able to see 1000 Ohms on it, let alone 100 Ohms or 2 Ohms. I think it's just easier to say that Ohms = 1/Siemens and Siemens = 1/Ohms.

Regards,

Q. I had thought that if one axis is falling as the other rises, that the resultant would be a straight line, infinity conductance and zero Ohms sharing the "zero" point on both axes.

A. Hi again. I suppose you could label the origin of the axis "infinite conductance" instead of "zero" is you wish, but it wouldn't be a straight line: "y= -x" would be a straight line, but that's not the relationship; it's "y= 1/x". It's a reciprocal function and asymptotic rather a straight line, so the graph won't be readable except over a very narrow and non-useful range. Thanks again.

Regards,

Ted, you could make a log-log plot, slope = -1, as many orders of magnitude as you like.

Good point, Dan, thanks for reminding me! Unfortunately, I did a google image search for "graph resistivity vs. conductivity" and scanned a hundred graphs without finding one, but if a patient reader finds such a graph, or makes one, we'll be happy to link to it.
To me the reciprocal function, which is exact, is so easy that a graph seems a bit silly ... but different people think differently; and I suppose that if no one had invented electronic calculators capable of instantly dividing 1 by another number I'd feel differently :-)

Regards,

A. Hi Diana. Your head will continue to spin, and there is nothing anyone else can do to help you, until you slow down and take it one small bite at a time and think about each bite.

Do you know what a "Siemens (S)" is? We told you above that is 1/Ohms; that is,
S = 1/Ω or Ω = 1/S. So 10 Ωs is 0.1 S, 2 Ωs is 0.5 S, 1 Ω is 1 S, 1/2 Ω is 2 S, and 1/10 Ω is 10 S. Start by learning and understanding that.

After you're sure of that, do you know what dS means? It means deciSiemens. A dS is one tenth of a Siemen, just as a decimeter is one tenth of a meter. So, building on what you learned above, 10 Ωs is 1 dS. 2 Ωs is 5 S, 1 Ω is 10 S, etc. You could say dS = 10/Ω or Ω = 10/dS.

Hopefully you now see how you can convert dS to Ωs and Ωs to dS ... but that you're not going to be able to convert Ohms to dS/m because, while dS is a measure of conductance (which is the inverse of resistance), but dS/m (dS per meter) has that extra unit of length in it. Your report which mentions Ohms, must also mention a unit of length (Ωs per inch, or Ωs per cm, or Ωs per meter, or something like that. Get back to us with that and it will be possible to carry on. Good luck.

Regards,

 Thank you so much Ted for your generous and very clear explanation. The report gives no mention of length at all but I now understand what I need.

Best wishes

Diana

A. Hi Syed. I have never done such measurements and never seen a Solinst TLC, but the instructions seem to indicate that "999.9M" means the conductivity is beyond what the instrument can measure.

Regards,

A. Hi Samuel. You may know more about this than I do, but my understanding is that standard liquid level controls cannot be used to reliably measure/control foam. Googling 'foam level control' seems to explain that simple conductivity measurements will not work because dried foam fouls the electrode immediately.

Regards,