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TOPIC-03 · Engineering guide

DC Voltage Drop on a Two-Wire Cable

DC drop on a two-wire run is 2 × I × L × r. At 20 A, 50 m and 0.003 Ω/m the drop is 6 V, the end voltage is 224 V, and 100 × 6 / 230 is 2.609% when rounded to three decimals.

Formula, variables and conditions

DC: ΔV = 2 × I × L × r
Single-phase AC: ΔV = 2 × I × L × (r × pf ± x × sinφ)
Balanced three-phase: ΔV = sqrt(3) × I × L × (r × pf ± x × sinφ)
The reactance sign follows the declared lagging or leading direction. L is one-way length in metres and r is ohms per metre after the temperature correction you enter.

Variables and units

  • I: current in A.
  • L: one-way route length in m. The DC and single-phase formulas already include the return path by the factor 2.
  • r: conductor resistance in Ω/m at the stated temperature, divided by the parallel count.
  • x: reactance in Ω/m. It is zero for DC and when reactance is explicitly ignored.
  • Allowed drop percent: a user threshold, not an approval.

Conditions

  • The English worked example sets temperature so the entered resistance is used as given, with one parallel path.
  • Loss is 2 × I² × L × r for DC and single-phase, and 3 × I² × L × r for balanced three-phase. This example quotes drop, not the cost case.
  • Chinese cable cases recompute GB/T 3956 resistances at 220 V. They are a different fixture, not a translation of these 230 V numbers.

Worked example

English teaching fixture CASE-001. Resistances are illustrative inputs, not a copied cable table.

Circuit
230 V DC, 20 A
One-way length
50 m
Candidate A
0.003 Ω/m
Candidate A drop
6 V, 2.609% of 230 V, end 224 V
Candidate B
0.002 Ω/m
Candidate B drop
4 V, 1.739% of 230 V, end 226 V

Both candidates are under the user-entered 3% threshold in this fixture. That comparison does not rate the conductor.

Boundaries and common mistakes

Boundaries

  • No manufacturer table is reproduced.
  • Ampacity, grouping, ambient correction, protection and installation rules are not evaluated unless you turn on the separate user-entered ampacity screen, which only compares numbers you type.
  • The AC formulas are the model’s equations. This numeric example does not invent an AC fixture.

Common mistakes

  • Using one-way resistance without the return path on a DC or single-phase circuit.
  • Applying the √3 formula to a DC loop.
  • Copying the English 230 V, 0.003 Ω/m example into a Chinese GB/T 3956 case. Those cases use 1.83 Ω/km and 1.15 Ω/km at 220 V.

Sources