The formula
R = ρ × L / A
- R
- resistance of the piece (ohms)
- ρ
- resistivity of the material (ohm·metres)
- L
- length along the current path (metres)
- A
- cross-sectional area (square metres)
Worked example
10 m of copper wire with a 1 mm² cross-section (ρ = 1.68 × 10⁻⁸ Ω·m).
- Convert the area: 1 mm² = 1 × 10⁻⁶ m²
- R = (1.68 × 10⁻⁸ × 10) / (1 × 10⁻⁶)
- R = 1.68 × 10⁻⁷ / 1 × 10⁻⁶
R = 0.168 Ω — small, but at 16 A that is already 2.7 V lost in the cable.
Where you'll use it
Cable sizing, shunt design, and the standard exam question about doubling a wire's length or halving its diameter. Also explains why resistors drift with temperature, since ρ itself is temperature-dependent.