Every metre of wire has a little resistance, so some voltage is lost before it reaches the load. Set the system, source voltage, current, run length, conductor metal and AWG gauge, and see the drop as Vdrop = k·I·ρ·L/A: how many volts and what percentage are lost, the voltage left at the load, and the power burned as heat in the cable. Watch the drop climb along the run and read straight off the drop-versus-length curve — a longer run or a thinner wire costs you more. It all runs on your device.
You are in the Physics lab.
What the shaded wire, the readouts and the drop-versus-length curve are telling you.
The schematic shades each conductor from green at the source toward the load: blue while the drop stays under 3%, amber past 3%, and red past 5%. The badge in the corner reads the drop in volts and percent, and the label at the load shows the voltage that actually arrives. Nudge the current or length up and the whole run reddens — a direct picture of energy leaking away along the cable.
The lower graph plots percentage drop against one-way run length. Because resistance is proportional to length, that plot is a straight line through the origin: double the run and you double the drop. The dashed 3% and 5% guides mark the usual limits, and the operating dot slides up the line as you drag the length slider — the moment it crosses a guide, the readout changes colour.
Step the AWG gauge down (to a thicker wire) and the line tilts flatter, pulling the operating point back under the limits — because resistance falls as area rises. Switching from copper to aluminium does the opposite: aluminium's higher resistivity lifts every point by about 64%. The power lost in wiring readout is the same story in watts — that is the heat the cable has to shed.
A resistance per metre, a run length, a phase factor, and the source voltage that turns volts into a percentage.
A conductor of resistivity ρ and cross-sectional area A has a resistance ρ/A per metre. Over a one-way run of length L carrying current I, the voltage lost is k·I·(ρ/A)·L. The factor k = 2 for DC and single-phase circuits, because the current travels out and back through two conductors; for a balanced three-phase line-to-line drop, k = √3. Copper's ρ is 1.724×10⁻⁸ Ω·m and aluminium's 2.82×10⁻⁸ Ω·m at 20 °C.
Wire gauge is just a code for cross-sectional area. The AWG definition gives a diameter d = 0.127·92^((36−n)/39) mm for gauge number n, and the area is A = π·d²/4 (gauges 1/0 to 4/0 continue the scale with n = 0 to −3). Every three AWG steps roughly doubles the area and so halves the resistance — which is why upsizing a wire or two is the standard fix for a long run.
The drop in volts does not depend on the supply voltage — but the percentage does: %drop = Vdrop / Vsource × 100. The voltage that reaches the load is simply Vsource − Vdrop. Because the same volts are a larger slice of a smaller supply, a run that is fine at 230 V can be unusable at 12 V, which is why low-voltage DC systems demand such heavy cable.
Whatever voltage the cable drops while carrying current I is power turned into heat: P = I²·R over all the current-carrying conductors (two for DC and single-phase, three for three-phase). That heat is wasted energy and it warms the insulation, which is the safety reason gauges are limited by current. This is a resistive model — it uses conductor resistance only and ignores AC reactance, which is negligible for DC and for typical branch-circuit lengths.
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