Why wire resistance matters
Every wire turns a little electrical energy into heat. In a short lamp cord the loss is negligible, but in a long run to a shed, a low-voltage lighting circuit or a 12-volt solar system, wire resistance causes voltage drop, dim lights, slow chargers and warm cables. Knowing the resistance helps you pick the right gauge and spot a problem before it becomes a hazard.
The formula
R = ρ × L ÷ A
- ρ (rho) is the resistivity of the metal, in ohm-meters.
- L is the length of the conductor.
- A is the cross-sectional area.
Resistance also changes with temperature: R_T = R₂₀ × (1 + α × (T − 20 °C)), where α is the temperature coefficient.
Resistivity of common conductors at 20 °C
| Metal | ρ (Ω·m) | α (per °C) |
|---|---|---|
| Silver | 1.59 × 10⁻⁸ | 0.0038 |
| Copper (annealed) | 1.724 × 10⁻⁸ | 0.0039 |
| Gold | 2.44 × 10⁻⁸ | 0.0034 |
| Aluminum | 2.83 × 10⁻⁸ | 0.0040 |
| Tungsten | 5.6 × 10⁻⁸ | 0.0045 |
| Nichrome | 1.10 × 10⁻⁶ | 0.0004 |
AWG sizes
The American Wire Gauge diameter is d = 0.127 mm × 92^((36 − AWG) ÷ 39). Every 3 gauges halve or double the area, and every 6 gauges halve or double the diameter. 12 AWG copper is 2.05 mm across (3.31 mm²) and has about 1.59 Ω per 1,000 ft.
Example
A 100-foot run of 12 AWG copper at 68 °F carrying 15 A:
- One-way resistance: 0.159 Ω
- Round trip (hot and neutral): 0.318 Ω
- Voltage drop: 0.318 × 15 = 4.8 V, about 4% of 120 V
- Heat in the cable: 0.318 × 15² ≈ 72 W
The National Electrical Code recommends keeping voltage drop under about 3% for a branch circuit. Here, upsizing to 10 AWG would bring the drop down to about 3.0 V.
Practical notes
- Stranded wire has slightly more resistance than solid wire of the same gauge.
- Wire at its rated operating temperature, such as 167 °F (75 °C), has about 22% more resistance than at room temperature.
- Connections, terminals and breakers add resistance too; a loose connection can heat up far more than the wire itself.
- Nichrome is used in heaters and toasters precisely because its high resistivity turns current into heat in a short length.