Power Systems — Distribution

Feeder voltage drop

continues from lesson 3 — values defined earlier in the course stay live here

ELI5: copper isn't free and distance isn't either — a long feeder loses voltage along the way as current pushes through the wire's own resistance. Electrical codes cap the drop (~3% for branch circuits), which sets the minimum wire gauge.

\rho _{cu} := 1.72e-8 ohm * 1 m

= 1.72e-8 ohm m copper resistivity

L_{run} := 60 m

= 60 m one-way length

A_{w} := 21.2 mm^2

= 21.2 mm^2 4 AWG cross-section

I_{feed} := 50 A

= 50 A

V_{drop} = \frac{2 \cdot \rho_{cu} \cdot L_{run} \cdot I_{feed}}{A_{w}}

= 0.0000048679 (ohm m m A) / mm^2 round-trip drop

✓ pass

V_{drop} < 0.03 * 240 V

inside the 3% budget (try 13.3 mm² — 6 AWG — and watch it fail)

Real-world hook: voltage drop is why a far-away outlet makes lights dim when the AC kicks on, and why long runs (to a barn, a pump, an EV charger) need fatter wire than the load alone would suggest.