Circuits & Electrical Power · Feeders and voltage drop
The cable takes its cut
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The cable takes its cut

Every conductor has resistance, so every conductor keeps some of the voltage for itself. Vd=2ρLIAV_{d} = \dfrac{2 \rho L I}{A}, read aloud V-d equals two rho L I over A. VdV_{d} is the voltage drop in volts; ρ\rho — rho — is the conductor's resistivity, 0.0172 Ω·mm²/m for copper; LL is the one-way run length in metres, panel to load; II is the load current in amperes; and AA is the cross-section of one conductor in mm².

That leading 2 is the named trap of this lesson, and it is not a fudge factor: the current goes out along one conductor and comes back along another, and both of them drop volts. Measure the run one way, let the 2 do the return trip, and never do both.

A balanced three-phase run has no return conductor at all — the three currents return through each other — so the 2 becomes 3\sqrt{3}: Vd=3ρLIAV_{d} = \dfrac{\sqrt{3} \, \rho L I}{A}, with II the line current and VdV_{d} the line-to-line drop. Same cable, same load, about 13% less lost. That is one of the quiet reasons industry runs three-phase.

Codes are written in percent, not volts: %Vd=100VdVs\%V_{d} = \dfrac{100 \, V_{d}}{V_{s}}, where VsV_{s} is the nominal supply voltage. The familiar allowances are 3% for a branch circuit and 5% for the whole path from the service to the load. Three volts is nothing on 400 V and ruinous on 24 V — which is exactly why the rule is a ratio.