Where I
2R comes from:
(DC) Watts = E * I
E = IR
Substituting, Watts = IR * I = I
2R
Also:
Watts = E * I
I = E/R
Substituting, Watts = E * E/R = E
2/R
Lancie1 said:
Careful here, Alaric. We know what you mean, but that last part "same internal heating" might be slightly misleading.
For example,assuming 24 VDC and 1000 VDC, and if a long wire has a resistance (the factor that causes voltage drop) of 1 Ohm, then the current due to the resistance would be I = E/R = 24/1 = 24 Amps, and the VA would be 24 x 24 = 576 VA, but for 1000 volts it is I = 1000/1 = 1000 Amps, and VA would be 1000 A x 1000 V = 1 million VA. I think 1 million VA would produce more internal heating than 576 VA.
Power Consumed is dependent on both volts and amps.
Thank you Lancie for bringing up a needed clarification.
If you will notice, I said
"A wire carrying 10 amps connected to 24 volts or connected to 1000V has the same internal voltage drop per inch." I added the constraint of 10 amps (making the assumption that there is an appropriate circuit load) because we are talking about only the heating that occurs in the wire itself, therefore the voltage of concern in the VOLTAG DROP in the wire itself, not the voltage drop across the entire circuit. Thus if we constrain the current at 10 amps, in Lancie's wire with a resistance of one ohm there is a voltage drop of 10 volts, whether the circuit input voltage is 24V or 1000V (again, assuming an appropriate soruce/load at the ends of the wire for a complete 10A circuit) and a power dissipation in the wire of 100 watts. We must hope that Lancie's hypothetical wire is quite long or its going to glow.
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FWIW, I made a Q&D calculation on the OPs 22 guage wire - a 1 meter lenght will burn about 15 watts at 10 amps of current flow. It doesn't sound like much, but its more than enough to warm up that wire to an undesirable temperature, depending on how long its on and environmental conditions it could definitely cook the insulation.
Stationmaster said:
...in practical use the ampacity tables I have seen only concern themselves with: wire material, wire gauge, and length of run. I have never actually seen them take into account VOLTS other than as it relates to the insulation.
That's because the interal voltage drop of the wire itself is accounted for when the tables are drawn up. The heating is caused by this voltage drop at a specific current and the tables are adjusted accordingly based on the ability of the wire to dissipate the heat. When you pack the wires in a conduit, you interfere with this heat dissipation, so the wires are derated. On the flip side, I use water cooled kickless cables on vacuum furnaces that are 400MCM yet are rated to carry 10,000 amps - its all about the heat removal and whatever voltage drop you are content to tolerate.