Resistivity
Resistance grows with length and falls with cross section: R = ρl/A. A nichrome wire 2 m long with 0.5 mm² cross section has R = 100 × 10⁻⁸ × 2 / (0.5 × 10⁻⁶) = 4 Ω.
Resistivity
R = ρl/A. Resistivity ρ belongs to the material, at 20 °C; the bars use a log scale so copper and nichrome both show. Tap a material to use it.
Nichrome wire4 Ωρ = 100 × 10⁻⁸ Ω m
- Silver1.60 × 10⁻⁸0.064 Ω
- Copper1.62 × 10⁻⁸0.0648 Ω
- Aluminium2.63 × 10⁻⁸0.11 Ω
- Tungsten5.20 × 10⁻⁸0.208 Ω
- Iron10.0 × 10⁻⁸0.4 Ω
- Nichrome100 × 10⁻⁸4 Ω
- Nichrome: ρ = 100 × 10⁻⁸ Ω m
- A = 0.5 mm² = 5 × 10⁻⁷ m², since 1 mm² = 10⁻⁶ m²
- R = ρl / A = 100 × 10⁻⁸ × 2 / (5 × 10⁻⁷) = 4 Ω
Why it works
- Doubling the length of a wire doubles its resistance: R ∝ l.
- Doubling its area of cross section halves its resistance: R ∝ 1/A.
- Together R ∝ l/A, and the constant is the resistivity ρ: R = ρl/A.
- ρ depends on the material and its temperature, not on the shape. Its SI unit is Ω m.
- Metals have ρ near 10⁻⁸ Ω m. Alloys such as nichrome are about a hundred times higher, which suits heaters.
Resistivity: quick answers
What is the SI unit of resistivity?
The ohm metre, Ω m, from ρ = RA/l: ohms times square metres over metres.
Why are heating elements made of alloys like nichrome?
An alloy has a much higher resistivity than a pure metal and does not oxidise readily when hot. The same wire in copper would have only 0.0648 Ω.
Does stretching a wire change its resistivity?
No. Resistivity belongs to the material. Stretching makes the wire longer and thinner, so its resistance R rises, but ρ stays the same.