Convert resistivity units to conductivity units

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.

Ted Mooney, P.E. RET finishing.com Brick, New Jersey

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 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.

Ted Mooney, P.E. RET finishing.com Brick, New Jersey

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,

Ted Mooney, P.E. RET finishing.com Brick, New Jersey

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.

Ted Mooney, P.E. RET finishing.com Brick, New Jersey

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,

Ted Mooney, P.E. RET finishing.com Brick, New Jersey

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,

Ted Mooney, P.E. RET finishing.com Brick, New Jersey

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,

Ted Mooney, P.E. RET finishing.com Brick, New Jersey

A. Hi Ajay. You'll only make progress on this when you take the time to carefully think it through, and then take the time to be very careful of your words and their precise meanings. Your question cannot be answered because it is improperly asked; and you will learn best from carefully studying and figuring out for yourself what is wrong with your question.

Regards,

Ted Mooney, P.E. RET finishing.com Brick, New Jersey