Let’s say you have some material. It has a resistivity ρ (Greek rho) and the actual resistance of whatever you have is going to be ρ multiplied by the length l and divided by the cross sectional area A. You derive the ohms/cubic inch by assuming a unit cube (1 inch by 1 inch by 1 inch) of the material and calculate ρ.
I agree with you that it is a bit of a bogus unit, but it shows up all the time in things like soil samples where you are trying to get an idea of how conductive the soil in a particular area is for purposes of electrical grounding. Since it is basically related to ρ you can use it to calculate the impedance you’ll get for driving a copper ground rod into the earth to a particular depth.
Ahh, so the unit assumes a cube of a certain dimension. :rolleyes: So a “resistivity” of 5 Ω/cm[sup]3[/sup] means a cube of the material with dimensions 1 cm X 1 cm X 1 cm has a face-to-opposite-face resistance of 5 Ω. Yep, *very *nonstandard. Weird and non-scalable. Why don’t they just use Ω•m, which is a standard SI unit for volume resistivity?
Beats me. I always assumed that it came from how they actually determined the resistivity, i.e. they actually took a cube of the material cut to size and measured it.
If the resistivity ρ of the material is given in Ω•m, then you can calculate the resistance of simple-shaped resistors based on their geometry. The resistance in ohms will be proportional to the length of the resistor, and inversely proportional to the cross-sectional area (which determines current density):
Meh. Not any worse than something measured in dB, where you have to specify dB relative to something. For example, antenna gain is typically given in dB, which might be relative to an isotropic radiator (dBi) or a half-wave dipole (dBd). Sound is one I often see just listed in dB.
How exactly is this different from using cubic meters? Like using cubic centimeters or cubic meters to measure volume. As an example of how this can be applied to real life, a 0.01 cm2 (0.1x0.1 cm), 100 centimeter long rod of the material with the resistance you cite would have a resistance of 50,000 ohms (100 times longer and 1/100 of the cross-sectional area). This works the same way with Machine Elf’s equation, just using cm instead of m; only the units have to stay the same:
(5Ω•cm) * (100cm/0.01cm2) = 50,000Ω
Incidentally, to convert between ohm-centimeters to ohm-meters, divide by 100 (10,000 times the area, 100 times the length) and vice-versa, which is actually convenient since you know that 1 meter = 100 cm. 5 ohm-centimeters is 0.05 ohm-meters:
(0.05Ω•m) * (1m/0.000001m2) = 50,000Ω
This will also work with millimeters and so on (which is probably better for really small things, so you don’t have numbers like the 0.000001 in the above equation):
(50Ω•cm) * (1000mm/1mm2) = 50,000Ω
Note again that all you have to do to go from cm to mm is to multiply resistivity by 10, or 1,000 to go from m to mm (I imagine that they use units like ohm-micrometers and such for things like chip fabrication, and indeed, such a unit appears to be in use; 1 ohm-meter = 1,000,000 ohm-micrometers; given the resistance of pure silicon as 640 ohm-meters, you can make a 1 cubic micron resistor with up to 640 megohms of resistance, although it will normally be much lower due to doping the material).
What are you talking about? Ω/square is an inherent characteristic of a surface resistivity, in that measurement of any size square will give the same value. It’s used it all the time, and I’m not sure what you’d replace it with that would be easier to use.
