Cable Sizing

Three checks:

1. Ampacity — the cable's rated current, after applying derating factors for ambient temperature, grouping and installation method, must exceed the design current, and the protective device rating must sit between them: $I_b \le I_n \le I_z$.
2. Voltage drop — single-phase: $\Delta V = 2 I L (R\cos\phi + X\sin\phi)$; three-phase: $\Delta V = \sqrt{3} I L (R\cos\phi + X\sin\phi)$. A common limit is about 3–5 % of nominal voltage.
3. Short-circuit withstand — $S \ge \dfrac{I\sqrt{t}}{k}$ (adiabatic equation; $k$ ≈ 115 for PVC-insulated copper, 143 for XLPE copper).

Copper vs aluminium: aluminium is lighter and cheaper but needs about 1.6× the cross-section for the same resistance, and proper lugs to avoid loose, hot joints.