I'm trying to calculate the resistance of a copper bar in a DC current, but I'm not sure how to do it. The only things I've seen online calculate the resistance of a wire and ask for its gauge, but a bar is not a wire and it doesn't have a gauge. It's a rectangular prism shape and its dimensions are 1.3cm x 2.5cm x 30cm. You don't have to do the math for me I just would like a formula for getting the resistance.
Electronic – How to calculate the resistance of a copper bar
copperresistance
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If you work it backwards, then the amplifier can be dissipating 800 watts with only 100 volts available at its end of the long cable.
That's 8 amperes the amplifier will need, and if there's 120 volts at the socket and 100 volts at the amplifier's end of the cable, the maximum allowable cable resistance will be
R = (120V - 100V)/8 ohms = 2.5 ohms.
Since the cable will be 200 feet long, that'll be 2-1/2 ohms for the 400 foot round trip, which is 6.25 ohms per 1000 feet.
16 AWG has a resistance of 4.016 ohms per 1000 feet, so it would work.
But, since the cable itself will be dissipating about 20V * 8A = 160 watts, it'll heat up a little, increasing its resistance, and if it's lying in the sun it'll get even hotter, increasing its resistance even more.
So, just for insurance I'd bump the cable up to 14 AWG or even monster 12 AWG if there was a chance I'd need it later, and I'd do the math just for fun. Just not now... ;)
26 AWG is 40 ohms / 1000 foot as per this table: -
A 50 foot length of this wire (2 ohms) with 8A will dissipate 128 watts i.e. it doesn't sound a sensible choice. The volt drop at 8A will be 16 volts.
As for your formula I can't tell whether it agrees or disagrees with whatever reference you have.
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Best Answer
While you can look up the resistivity of copper on wikipedia or Kaye & Laby, you'll find that the answer is given in units of 10^-8/m. I don't know about you, but I always miscount powers of 10 when using that sort of unit. Instead I commit the following to memory
1 metre of \$1mm^2\$ copper wire has a resistance of 17 \$m\Omega\$ (roughly)
If you can't remember that resistance is proportional to length, and inversely proportional to area, then just think series resistors, or parallel resistors.
10m of wire would have 10x the resistance, it's like ten 1m lengths in series.
If the wire is 4mm2, it will have 1/4 the resistance, because it's like four 1m lengths in parallel.
Copper, like all pure metals, has a fairly strong temperature coefficient of resistance, which is why I've only given the resistivity to 2 significant figures. The tempco is 0.4% per degree C, or a whopping 10% change for 25 degree change in temperature. It can be useful to remember that when you want to estimate the temperature rise of (say) transformer windings, just measure their resistance cold, and again when hot.