power-loss

Deliver power down a wire. Watch where the joules go. Higher voltage means lower current for the same power, so I²R drops fast.

load [W] 1000 voltage [V] 48 distance [m] 10 wire AWG 14

current—

wire R (round-trip)—

voltage drop—

wire loss (I²R)—

efficiency—

delivered lost in wire

Power lost in a wire is P_loss = I²R. Resistance scales with length and inversely with cross-section (AWG number — bigger means thinner wire). Hold the load fixed and double the voltage: the current halves, so the wire loss drops by 4×. That's the entire reason long-distance power transmission runs at hundreds of kilovolts.

Wire R model: copper round-trip on stranded AWG R[Ω/m] = 0.001 · 2 · 10^((g-10)/-10) / 0.5067 (approx). Reactance, skin effect, and temperature coefficient are ignored. DC, steady-state.