Calc Formula [patched] - Cable

: [ S_min = \frac25,000 \cdot \sqrt0.2143 \approx \frac25,000 \cdot 0.447143 \approx 78 , mm^2 ] 185 mm² >> 78 mm² — thermal withstand OK.

…but that’s only the beginning. The steady-state ampacity of a cable is derived from the heat balance equation:

The core relationship is:

Simplified (common form):

[ S = \fracI_sc \cdot \sqrtt\sqrt\epsilon \cdot \frac1k ] In non-linear loads, harmonic currents cause extra (I^2R) losses. The effective RMS current is: cable calc formula

For AC circuits:

[ I_sc^2 \cdot t = \kappa^2 \cdot S^2 \cdot \ln\left(\frac\theta_f + \beta\theta_i + \beta\right) ] : [ S_min = \frac25,000 \cdot \sqrt0

(IEC 60364-5-52): Base cable 120 mm² Cu XLPE → 380 A in free air. Derate: (k_amb = 0.87), (k_group = 0.8) → (380 \times 0.87 \times 0.8 = 264 A) → too low. Try 185 mm² → base 500 A → derated = (500 \times 0.696 = 348 A) — acceptable.