Wire Resistance

Formula

Description

Wire resistance depends on the material's resistivity, the wire length, and its cross-sectional area. Copper is the most common conductor with ρ = 1.724 × 10⁻⁸ Ω·m at 20°C. Aluminum has ρ = 2.65 × 10⁻⁸ Ω·m (about 60% of copper's conductivity). Longer wires and thinner wires have higher resistance. This resistance causes voltage drops and power losses (I²R heating) that must be accounted for in power distribution, speaker wiring, motor cables, and any application where current flows over significant distances.

Variables

• R — Wire resistance (Ω)
• ρ — Resistivity of the conductor material (Ω·m)
• L — Wire length (m)
• A — Cross-sectional area (m²)

Practical Notes

Resistivity increases with temperature. Copper has a temperature coefficient of +0.00393/°C, meaning resistance increases about 0.4% per degree C. For a 10m run of 16 AWG copper wire (A = 1.31 mm²), R ≈ 0.132Ω. At 5A, this drops 0.66V and dissipates 3.3W per conductor. Remember to account for both supply and return conductors.