Single-Phase Conductor Voltage Drop
Single-Phase Conductor Voltage Drop
Every conductor has resistance, so current flowing through it dissipates some voltage along the way — the longer or thinner the run, the larger that drop. In a single-phase circuit the current makes a round trip (out and back), so the voltage drop depends on twice the one-way conductor length.Excessive voltage drop causes dim lighting, motors that run hot and underpowered, and equipment that fails to meet its rated performance, which is why electrical codes cap allowable voltage drop (commonly around 3–5%) and conductor sizing calculations like this one are a standard part of circuit design.
The voltage drop is Vd = 2·I·L·R, twice the current times the length times the conductor resistance per unit length. where I is the circuit current, L is the one-way conductor length, and R is the conductor resistance per unit length.
Inputs
I_c := 40 A=40 A
L_c := 50 m=50 m
R_km := 1.15 Ohm/km=1.15e-03 kg·m/A^2/s^3
The factor of two accounts for both the outgoing and return conductors carrying the same current over the same length, so the resistive drop is doubled.
Vd := 2·I_c·L_c·R_km=4.6 V
Results
A drop of about 4.6 V on a 230 V circuit is roughly 2%, well within the typical 3–5% code limit, so this conductor size is adequate for the run. If the run were significantly longer or the current higher, Vd would climb linearly with both, and the usual fix is to upsize the conductor (lowering R) rather than simply accepting a larger voltage drop.
Assumptions & limitations
- DC or low-frequency AC resistance only; skin and proximity effects at higher frequencies ignored.
- Single-phase, two-conductor circuit (out and back).
- Conductor temperature assumed constant at its rated resistance value.