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Converting resistivity units to ohm-meter from microhms/cm^3

 

I am try to calculate the temperature increase in a wire, but I don't understand the units for resistivity given in a table, ohms/cmf or microhms/cm^3. How do I convert this to Ohms-meter? Resistivity = (Resistance)*(cross sectional Area)/(length of wire) I am trying to plot the boiling curve of a wire using a pool boiling experiment.

Javier Rosado
UIC - Chicago, Illinois, USA

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Javier,

You have written down the formula for resistivity. Now it is a matter of using correct dimensions. Make it all cm or meters. Convert cm to meters (i.e. 1 cm = 10E-2 meters) and ohm to microhms (microhm = 10E-6 x ohms).

Resistivity = ohm-cm = ohm x (.01 meter) and so on.

Also, resistance/length = resistivity/area from your formula. So, ohm/cm = 10E-6 ohm-cm/cm. sq.

I wonder if there is a mistake in that cm cube.

Mandar Sunthankar
- Fort Collins, Colorado
 

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Explaining the terms and relationships of resistivity of wire such as rho and CMF.

Unfortunately the reference data books and manufacturers data sheets often use different terms, which makes conversion necessary. If you don›t use this data frequently it is easy to get lost in the conversion details and lose the fundamental relationships you desire to manipulate. You can find yourself using cm (for centimeter) and cm (for circular mil) in the same calculations.

Example 1: My CRC Handbook of Chemistry & Physics [adv: on Amazon & AbeBooks & eBay] gives a rho (p) value of 33 X 10 ^6 ohm-cm for German Silver wire. Think about what this defines. If you had a block of this material 1-cm (centimeter) on each side, it would measure 33 µohms. The cube units of ohm-cm is unique. It is derived from the resistance of the area of one end surface (1 cm ^2) measured along a length of 1 cm. This could be written as ohm cm^2/cm. One cm cancels top and bottom leaving ohm-cm.

Example 2: What is the ohms/cm for a 20-awg wire? Note that this is different from the previous paragraph. We want a practical application of how many ohms we get for a certain length of a certain wire. Ohms per cm for a long wire, not ohm-cm for a reference cube of material.
First determine the wire diameter in mils. Always express wire diameters in mils. It will simplify unit confusion in calculations. If your data book says 0.0319, you write down 31.9 mils.
Second, determine the cross sectional area in square mils. Area of a circle = pi*r^2. Note, do not get confused here with circular mils which is d^2. I will not discuss the difference here, but since our reference cube is dimensioned in square units we need to find our wire area in square units. So for this example of 20 awg wire, pi * r^2 = 804 sq. mils.
Third, ask yourself how many of these square unit wires would fit in our reference cube? Since a cm is approximately 393 mils of an inch long, wide and high, the cm^2 end area of the cube is 154449 sq. mils. Dividing this by the end of our wire in sq. mils we get 15449/804 or 192.
Fourth, finally we get to a useful number. We know that our wire cross section is 1/192 of the cross section of the reference cube so the resistance of our wire will be 192 times the p value of 33 µohms for one centimeter. 192 * 33 µohm-cm = .006336 ohms/cm Notice that we multiply not divide. Resistance decreases with cross section area, and increases with length.
Fifth, what if we want the ohm/foot? There are 12 inches * 2.54 cm or 30.48 cm in a foot, therefore 30.48 * .006336 ohms/cm = .193 ohms/ ft.

Example 3: Before I continue with the next example we need to understand the conversion from sq. mils to circ. Mils. Note I avoid using cm for circular mils, because of the obvious confusion. Since sq. mils = pi (d/2)^2 and circ. Mils = d^2 therefore Sq. mils = pi/4 circ. Mils. Circ. Mils = sq. mils * 4/pi

Example 4: What is the ohm/CMF of the previous wire listed as p = 33 µohm-cm? We need to know how to convert this as many of the wire manufacturers express their data this way. Probably they like to give ohm/CMF for the different materials because they can do it one time and not have to work out the ohms/foot for each wire gauge. That problem is left to the user and is probably why you are here reading this. Some brands give you a calculator to convert each wire, but it is better if you know how to do it yourself.
First, you know the p = 33 µohm-cm for this example.
Second, you must know the area of the end of our reference cube. We already know from the previous example 393 *393 = 15449 sq. mils.
Third: convert the reference cube end area to circ mils. Using the conversion from the previous example 15449 * pi/4 = 196768 circ. Mils.
Fourth: What exactly is this CMF the suppliers specify? It stands for circular mil foot. Visualize a wire 1 mil in diameter exactly 1 foot long.
Fifth, find how many CMF end areas would fit in the end of our reference cube. We already calculated the end area as 196768 circ. Mils so the answer is 196768.
Sixth, determine the resistance for one foot of this wire. The resistance is 33 µohm * 196768 * 30.48 = 197 ohm/CMF.

Bill Herzog
- Rogue River, Oregon, USA

the minimum resitvity is 1000000 ohm square meter, what should be the range of instrument to check the same

Shrikant Ajgaonkar
- Mumbai, India
June 4, 2009