Resistivity And Resistance In Electrical Conductors

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Resistivity And Resistance In Electrical Conductors

By Thomas Keyes
Nov. 25, 2005

Recently I received correspondence about resistance in electrical conductors. In household wiring, the length of a conductor is a negligible consideration, but in lost-distance transmission of electrical power, resistance becomes a considerable factor. In my article “Pylons and Line Geometry”, where incidentally I made the small mistake of calling copper the best conductor, when actually silver is slightly better, I didn’t get into a material property called ‘resistivity’.

Each metal has an inherent degree of resistivity, which varies somewhat depending on temperature too. Silver’s resistivity at 20 C (68 F) is 1.59^-8 Ohm-meters. Copper’s is 1.68^-8 Ohm-meters. Aluminum, the metal used in high-voltage lines, has a resistivity of 2.65^-8 Ohm-meters. In ordinary notation these numbers are read .0000000159, .0000000168 and .0000000265, the decimal moving 8 places leftward with zeroes added as needed. The phrase ‘Ohm-meters’ denotes a product of Ohms and meters. Resistivity usually is denoted by Greek ‘r’ (rho), which I probably cannot e-mail, so I’ll just say ‘rho’. Here is the URL of a resistivity table:

http://hyperphysics.phy-astr.gsu.edu/hbase/Tables/rstiv.html

The historic treatment of resistivity is somewhat annoying. This is like the treatment of gauge-thickness sheets of metal, which makes 16 gauge sheet thinner, not thicker, than 12 gauge sheet. A better way to approach conduction would be to use conductivity, which increases with the diameter of the conductor, instead of decreasing, as resistivity does. The reciprocal of an Ohm is a Siemens, also called a Mho. But I’ll just stick to the more traditional units.

Anyway, to calculate the resistance in a conductor, one may use the following formula:

R = rho x L / A. (Resistance = Resistivity x Length / Área)

Here ‘Length’ refers to the length of the conductor and ‘Area’ to the cross-sectional area, which must be expressed in meters and square meters. So, if we have a length of 200 kilometers (124 miles), this is converted to 200,000 meters, and if we have an area of 40 square centimeters (a circle with a diameter slightly under 3 inches), this is converted to .004 square meters. If the conductor is aluminum, we calculate the resistance thus:

R = .0000000265 Ohm-meters x 200,000 meters / .004 square meters = 1.325 Ohms

Obviously, if our conductor were 20 kilometers long, our resistance would be .1325 Ohms. So there’s a tenfold difference, which could be significant is the matter of selection and configuration of parallel conductors from the generating power plant.

For the household case, assume we have copper conductors with an area of 5 square millimeters, which converts to .000005 square meters. The first conductor is 10 meters long and the second is 20 meters long. Then we have:

Resistance #1 = .0000000168 Ohm-meters x 10 meters / .000005 square meters = .03 Ohms

Resistance #2 = .0000000168 Ohm-meters x 20 meters / .000005 square meters = .06 Ohms

A light bulb has a resistance of about 100 Ohms and a toaster about 15 Ohms, so the conductor connecting such an appliance, if it has a resistance of .03 or .06 Ohms, makes no significant contribution to the total resistance in the circuit.

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About the author Thomas Keyes: I have written two books: A SOJOURN IN ASIA (non-fiction) and A TALE OF UNG (fiction), neither published so far.

I have studied languages for years and traveled extensively on five continents.

Email: udikeyes@yahoo.com

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