Heat buildup in wiring

It is correct as to heat developed, (generated), by the higher current. If you want the temperature produced, it does depend on how the heat is dissipated from the conductor, which includes the factors you mention as well as others.

It may seem simplistic, but that's the answer.

Now what isn't so simple is just how hot the conductor gets when carrying 30A vs 20A. Maybe that's what you're thinking of?

With 2.25 times the heat generated, it should take 2.25 times the temperature difference between ambient if all other factors are the same. So if you had a 20C rise in conductor temperature over ambient at

But it actually is a bit worse than that because at 30A, with a higher temperature in the conductor, the resistance of the conductor is somewhat higher. So the power dissipated is slightly more than 2.25 that at 20A.

If the temperature rise at 20A is more because of insulation, conduit, embedded in a wall, etc..., than the rise for 30A will still be 2.25 times as much, but that can be too much. For example if the temperature rise with 20A was 40C, than carrying 30A would make the rise 90C. And that's probably too high for the equipment and insulation.

And of course if the ambient temperature is abnormally high, adding on the same rise (either 45C in the first case or 90C in the second case), it can still push the resulting temperature over some limits. That's why cabling is de-rated for high ambient temperature installations.

daestrom

Simplistic or not, this description is quite accurate. The biggest error will arise if R is not constant.The largest variation in R is likely to come from a change in temperature of the conductor.

Simple doees not mean wrong.

Bill

Same effect with heating at contact and connection resistances too. That's why really good connections are essential with high current circuits. When heating does start, this often results in the quality of the connection changing for the worse, and the resistance rising. This generates more heat, and the two effects fuel each other, and you get a runaway, resulting in the connection grossley overheating and failing.

and also (in UK at least, and probably most places) derating for cable grouping - running multiple conductors togther where mutual heating effects result in a higher temperature rise.

The assumption is that the same conductor is used at 30A as at 20A . You could do it, but in most jurisdictions, the codes take into account the changes in heating and dictate appropriate wire sizes.

Take a look at:

Descriptions of reality are simplistic--starting before Ohm's law. As you increase current through a conductor, the conductor's resistance USUALLY increases, Eventually, the conductor melts. Ask any fuse about what happens to Ohm's law when it blows?

Bill