I forget who originally posted this--but thank you--
That formula is used to find the "withstand rating" of a conductor. You will not find this in the NEC.
Here's an example of how it is used:
Copper can withstand 1-ampere for 5-seconds for every 42.25-circular mils.
So take a #8 AWG conductor. #8 = 16,510 cm / 42.25 = 391-amperes.
Using the formula, amps squared x time=A. 391 x 391 x 5 = 764,405
(^2 means squareroot of)
To find the withstand rating, consider a 1/4 cycle overcurrent device protecting a #8 AWG conductor.
A 1/4 cycle = .0042 seconds. So, using this information and the answer from above:
The Square Root of (764,405 / .0042) = 13,491 amperes for 1/4 cycle.
What does this mean? If the circuit has an available fault current exceeding 13,491 amperes and the overcurrent device does not open faster
than 1/4 cycle, the #8 conductor will fail.
Using the above formulae 16AWG can handle 2107 amps for 1/4 cycle--or 1489 for a half cycle--
And 14 AWG is 3356A for 1/4 cycle and 2373 for a half cycle
just saying....