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Yes that's about the size of it, and Carl boiled it down nicely to the desire to keep the voltage drop equal in both cases, the first where we have a given current and the second where we have double the current. Keeping the voltage drop equal has advantages.
However, what i find is that for a regular normal round cross sectional wire (which this rule is usually accepted for) using this rule the cross sectional area of the wire increases as the current increases, but the surface area of the wire only increases as the square root of the current, yet the power dissipated inside the wire goes up as the ratio of the new current to the old current (ie I2/I1).
What this means is that the temperature of the newly selected wire (for our example of 2x the current) would go up and it may go up a lot. So the temperature of the second wire would go up by some factor KT where KT is positive and greater than 1.
Let me make it clear that when i say "as the current increases" i dont mean the current increases in the SAME wire, i mean it increases in the second wire selected which in our example is the wire with twice the cross sectional area, and for the example the current 'increased' to two times the original current in the first wire which also had 1/2 the cross sectional area.
If the cross sectional area increased more then the temperature would remain the same, but as this area is increased the resistance goes down so the surface area does not have to increase by 2 times because with a little less resistance we get a little less power and that means we dont need the entire 2x surface area. What would work out is somewhere between the original and two times the surface area, but not either of those exactly. This of course would reduce the voltage drop too from the original 2x area selection because the cross sectional area would be more than 2x now.
This is pretty interesting i think and i wonder what you guys' take on this is.
i think the original intent is to keep the % voltage drop the same as the current is proportionally increased.
the second effect is heat transfer from the surface area and the ambient temperature. In AC distribution one does take into account the number of wires in the raceway. What is to say, if you changed the insulation to Teflon from PVC or reduced the temperature to 0K. Temperature has a dramatic effect and the ability to transfer heat to the surroundings will be impaired if a conduit is filled to capacity. It all matters. "Rules of thumb" are not meant to be used as the "law of the land", but rather used between narrow bounds (% voltage drop, same temperature).
For power circuits the wire gauge is typically selected so that the voltage drop is small and the power dissipated per unit wire length is also small. Thus the temperature increase for a single wire if the gauge is increased to keep the voltage drop constant for a higher current would also be small. It would likely only be of concern in a raceway with many other wires, as KISS noted.
Well something still doesnt look right. Yes, maybe going from one wire gauge to another for 2x the current would not be too much of a problem because the temperature rise might not be too much anyway. But sooner or later something has to give if we keep assuming this, and although i dont and maybe you dont but many wire tables seem to go by this rule, and it's very strange, or at least it seems that way.
For example, wire gauge 20 might be quoted at 3 amps, and then 17 gauge would be quoted at 6 amps, and gauge 14 at 12 amps, then 11 gauge at 24 amps, etc. Lighter gauge wires would go the other way, for 23 gauge wire it would be 1.5 amps, etc.
So taking it up one step (from N gauge to N+3 gauge wire) might be ok, but the wire tables seem to take the rule completely the way it is stated, and dont make any adjustments.
The power goes up fast too, for example, for a wire A that dissipates 1 watt over a given length, a wire B of twice the area used for 2 times the current dissipates 2 watts, yet the surface area does not increase by that same factor of 2. The diameter goes up by sqrt(2) which is about 1.4142 so the surface area only goes up by the square root of 2. Now again, this might work for one step from wire A to wire B, and maybe even another step to wire C (4 times the area of A and 4 times the current) but surely it can not work over the entire range of wire sizes from 36 gauge to OOO gauge. This tells me that the temperature rise was never thought about when making some of these tables, they just take it for granted that the rule works all the time.
There is also a quote sometimes for wire size based on current where we would use say 600 circular mils per amp, and that boils down to the same rule because they imply that the area should be proportional to the current.
We see constraints like this in other areas too like bone size in animals, where the diameter has to increase as the size of the animal increases, and because of certain factors like the bone itself starts to add to the weight, there is a limit on the possible size of an animal that can live on the Earth because of the amount of gravity near the surface. There though they dont pretend they can increase the size of the bone to no end and therefore create a creature as big as Godzilla because they know if the creature gets too big the total weight is too high for the muscles to allow much locomotion, and adding muscle tissue has its constraint too in that it adds to the weight also and therefore the bone size has to increase and therefore the muscle has to increase again, etc.
"The power goes up fast too, for example, for a wire A that dissipates 1 watt over a given length, a wire B of twice the area used for 2 times the current dissipates 2 watts, "
should be wire B of twice the area used for 2 times the current also dissipates 1 watt, - because it has half the resistance.
Well i am sorry to say but, the power does not stay the same when we half the resistance and double the current.
The power in any resistance is:
P=I^2*R
so we see right away that the power goes up as the square of the current while it goes up only proportional to R.
Ok, lets see what we get when we take that simple equation and double the current and halve the resistance...
P=(2*I)^2*(R/2)
expanding a little:
P=4*I^2*R/2
simplifying:
P=(4/2)*I^2*R
or:
P=2*I^2*R
and enclosing I^2*R in parens so we can see what happened to the power we have:
P=2*(I^2*R)
So the original power was I^2*R and the resulting power after the changes was 2 times that, so the power definitely went up by a factor of 2, which is twice the power as before the changes were made.
If we quarter the resistance then we get the same power: I^2*R, but then the surface area increases more than we need so we dont actually have to quarter the resistance, but it would be good to go down a little more than half anyway.
I went through the calculations for this over several wire sizes and the temperature should go up as we keep applying this rule, but it may not be as bad as it seems at first as it might be ok if the originial size did not get too hot in the first place. If the original size got too hot to begin with, then the final wire size will probably get too hot for comfort.
As others have pointed out, it's probably more important to know how many wires are in close proximity to each other. A transformer winding is a good example where they are often packed close and there's a lot of them.
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