Voltage Drop vs. Power Loss — Linear vs. Squared, on the Same Wire

Double the current in a conductor, and voltage drop only doubles. Power loss — the heat that same current generates — quadruples. Same wire, same length, two constraints that grow at completely different rates.

Voltage drop across a conductor is V = I × R — a straight-line, linear relationship with current. Power loss in that same conductor is P = I² × R — current squared. Those two facts, sitting on top of the exact same resistance and the exact same current, are why voltage-drop-based wire sizing and heating/ampacity-based wire sizing are genuinely different constraints — not two ways of checking the same thing — and why a conductor sized to satisfy one can still fail the other.