VOLTAGE DROP

  ΔU  =  2  × I × L × (R'·cos φ + X'·sin φ)     (DC / AC single-phase)
  ΔU  =  √3 × I × L × (R'·cos φ + X'·sin φ)     (AC three-phase)

  Variables :
    R'     per-metre conductor resistance = ρ / S  (Ω/m)
    X'     per-metre cable reactance ≈ 0.08 mΩ/m   (Ω/m)
    ρ      conductor resistivity (Ω·mm²/m)
    L      cable length (m)
    S      conductor cross-section (mm²)
    I      current (A)
    cos φ  power factor   ·   sin φ = √(1 − cos²φ)
    2      outward + return conductor (neutral or PE)
    √3     line-to-line / phase-to-neutral ratio in three-phase

  Rationale : ΔU is the difference between the voltage at the head of the
  cable and at the load end. The reactance term X'·sin φ becomes significant
  on inductive loads (motors, low cos φ) and large cross-sections — it is
  ignored by purely resistive calculators. In DC it does not exist.


RELATIVE DROP · VOLTAGE AT LOAD

  ΔU%   =  (ΔU / U) × 100
  U_load  =  U − ΔU

  Rationale : IEC 60364 limits — ≤ 3 % for lighting, ≤ 5 % for other
  circuits (4 % is the common cap between origin and load). Beyond this:
  equipment malfunction, heating, nuisance tripping, disturbed motor
  starting. The voltage actually available at the load is U − ΔU.


MAXIMUM ADMISSIBLE LENGTH

  L_max  =  (ΔU%_lim / 100) × U / [ factor × I × (R'·cos φ + X'·sin φ) ]

  Rationale : for a fixed current, cross-section and limit, this is the
  length beyond which the drop exceeds the threshold. The real field
  question: "how far can I run this cable?".


CONDUCTOR RESISTIVITY

  ρ_Cu  =  0.0175  Ω·mm²/m  (at 20°C)
  ρ_Al  =  0.0290  Ω·mm²/m  (at 20°C)

  Rationale : copper is the reference. Aluminium has about 65 % of its
  conductivity but costs ~50 % less for the same current — hence its use
  on large cross-sections (≥ 25 mm²) and overhead lines.