[RE-wrenches] Parallel Wire combining

Larry larry at starlightsolar.com
Wed Dec 3 17:29:09 PST 2014


You ask a simple question to this group and stunning brilliance floods 
my inbox. RE-Wrenches, You are truly amazing. Thanks to all that 
discussed this for the knowledge I have gained.

Larry


On 12/2/14 3:47 PM, Daniel Young wrote:

> It all boils down to how ampacity is determined in the NEC.
>
> Ampacity is really related to temperature as far as the NEC is 
> concerned. The ampacity of a 1/0 wire at 90c is the constant current 
> it can carry in free air (30 C air) and not achieve an internal 
> temperature of more than 90 C. the 75 c ampacity is the same, the 
> amperage it can carry while not going over 75 C.
>
> Now, if you double the diameter of a circle, the circumference also 
> doubles, but the cross sectional Area actually goes up much more (4x 
> more in fact) because cross sectional area is based on the square of 
> the diameter and circumference is simply based on the diameter ^1 power.
>
> Wire dissipates heat from its surface only, so the dimension critical 
> for the amount of heat a wire can dissipate is circumference, not 
> cross sectional area. So even though the wire is larger and has a much 
> lower resistance, the heat dissipating area does not increase by as 
> much, so in the end the larger wire has a lower current carrying 
> capacity per unit cross sectional area, than a smaller wire.
>
> Here is an example that lets me keep the math simple: (the #’s are all 
> round #’s and not based on real ampacities/resistances, just to keep 
> the math simple.)
>
> Wire 1:
>
> A diameter of 10 units and can carry 100A through it and stay at 90C. 
> It has a resistance of 1 ohm/1000ft.
>
> Wire 2:
>
> A diameter of 20 units. It has 4times the cross sectional area, and 
> double the circumference (which means 2x the outer surface area) to 
> dissipate heat. It has a resistance of .25 ohm/1000ft (1/4 that of 
> wire 1 since it has 4x the amount of copper to carry current).
>
> For wire 1 to stay at 90 C, it has to dissipate (P=I^2*R), 
> P=(100amps^2)*1 omh=10,000 watts per unit of outer surface area.
>
> So if Wire 2 has double the surface area to dissipate heat, it can 
> dissipate about 2x the energy, or 20,000watts. So if we work it 
> backwards (P=I^2*R is the same as I=sqrt[P/R]) 
> I=sqrt[20,000/.25]=sqrt[80000]=282amps
>
> So wire 2 can handle (282amps/100amps)=2.8 times the amperage, even 
> though it has 4times the cross sectional area, all because it only has 
> 2 times the surface are to get rid of heat. There are other factors 
> with heat transfer that make the larger wire have even lower ampacity, 
> but this demonstrates the main contributing factor.
>
> [In the NEC table 310.15(B) we see that a 250kcmill copper wire 
> handles 255A @75C, and a 100kcmill (4x the area) can only take 545A, 
> or 2.2 times the current, so not too far from my example].
>
> I hope the above helps more than it hurts.
>
> With Regards,
>
> Daniel Young,
>
> NABCEP Certified PV Installation Professional^TM : Cert #031508-90
>
> NABCEP Certified Solar Heating Installer^TM : Cert #SH031409-13
>
>

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