DIYbanter - View Single Post - Adiabatic short-circuit compliance on very short short-circuits

In article ,
(Andrew Gabriel) writes:

Being a physicist rather than an electronic engineer, I'll

Oops, s/electronic/electrical/

Thus a fault current of 1.846kA for 0.01 sec will result in a temperature
rise of about 35.5 Centigrade in the copper conductors. If cable was
previously within its correct operating temperature range (i.e. = 70 C),
it will survive this without damage (i.e. not exceed 160 C for PVC).

So an interesting follow-on question is how short can your 2.5mm
cable be before it does pass enough current to damage itself in
this scenario?

Working backwards, max temperature rise allowed is 90C.
Mass of copper per metre is 448g.
Resistance per metre is 0.18 ohms.
Max energy per metre is 90 * 448 * 0.385 = 15523 Joules.
Max power per metre for 0.01 sec = 1552300 Watts.
Max current = sqrt(P/R) = sqrt(1552300 / 0.18) = 2.923kA
Circuit resistance for 2.923kA is 240 / 2923 = 0.0817 ohms.
Subtract supply impedance of 0.04 ohms, leaving cable impedance of 0.0417.
Length of cable with impedance of 0.0417 is 0.0417 / 0.18 = 23cm.

So you will be in trouble if your 2.5mm^2 T&E cable is less than
23cm long and was operating at max temperature at the time of
the short circuit (if I didn't make a mistake in the calculations;-).

Actually, I didn't take into account change in resistance at
higher temperatures, which will make a small difference.

--
Andrew Gabriel