Voltage Drop

In plain English

A cable is not a perfect conductor. When current flows, a little voltage is used up pushing it through the wire, so the equipment at the far end gets less than the supply voltage. That loss is the voltage drop. Long cables, thin cables and high currents all make it bigger.

Technical definition

Voltage drop is the difference between the voltage at the origin of a circuit and the voltage at the load, caused by the current flowing through the impedance of the conductors. In DC and resistive circuits it follows Ohm’s law (ΔV = I × R); in AC circuits the conductor reactance and the load power factor also contribute.

How it works and where it is used

Conductor resistance depends on the material (copper or aluminium), the cross-section and the temperature — a conductor at its full operating temperature has noticeably higher resistance than a cold one. In a two-wire circuit the current flows out and back, so the drop involves twice the route length. Wiring rules commonly limit voltage drop to a few percent of the supply voltage so that motors start and equipment works properly.

Formula

DC and single-phase: ΔV = 2 × I × L × (R cos φ + X sin φ)

Three-phase (line-to-line): ΔV = √3 × I × L × (R cos φ + X sin φ)

I = current, L = one-way route length, R and X = resistance and reactance of one conductor per unit length, cos φ = power factor (1 for DC). Percentage drop = ΔV ÷ supply voltage × 100%.

Worked example

A single-phase 230 V circuit, 30 m long, carries 16 A in 2.5 mm² copper cable. IEC 60228 gives a maximum of 7.41 Ω/km at 20 °C; at 70 °C the resistance is about 7.41 × (1 + 0.00393 × 50) = 8.87 Ω/km.

ΔV = 2 × 16 × 30 × 0.00887 = 8.5 V, which is 8.5 ÷ 230 = 3.7% of the supply.

In the workshop and in practice

Voltage drop decides cable sizes for long runs: workshop supplies to outbuildings, pumps, lighting circuits and solar or battery systems with low DC voltages, where even small drops are a large percentage. It is checked together with current-carrying capacity and fault protection, which are separate requirements.

Common mistakes and misconceptions

• Using one-way length only in a two-wire circuit (the drop is on both conductors).
• Using cold resistance for a cable that runs hot.
• Treating voltage drop as the only cable check. A cable with acceptable drop can still overheat or fail to trip protection.
• Ignoring motor starting current, which can be several times running current and causes much larger temporary drops.

Related calculators

• Voltage Drop Calculator — Estimated voltage drop, % drop and cable losses for DC, single-phase and three-phase circuits.
• Ohm’s Law Calculator — Enter any two of voltage, current, resistance and power to find the others.
• Single & Three-Phase AC Power Calculator — kW, kVA, kVAR and current for single-phase and three-phase loads.

Related topics

• Power Factor — How much of the apparent power drawn from the supply does useful work.

References

• IEC 60364-5-52: Low-voltage electrical installations — Selection and erection of electrical equipment — Wiring systems (Annex G: voltage drop)
• IEC 60228: Conductors of insulated cables (maximum conductor resistance)
• IEC 60287-1-1: Electric cables — Calculation of the current rating (resistivity and temperature coefficients)