Wirax

Meet Wirax, a copper wire whose resistance grows the longer and thinner she gets.

Resistance depends on what a wire is made of and on its shape. Resistivity, ρ, measures how strongly a material resists current. A longer wire gives electrons more distance to struggle through, and a wider wire gives them more room, so R = ρL / A.

Copper has a resistivity of about 1.7 × 10⁻⁸ Ω·m at 20 °C. A 10 m wire with a cross-section of 1.0 mm² (1.0 × 10⁻⁶ m²) has R ≈ 1.7 × 10⁻⁸ × 10 / (1.0 × 10⁻⁶) ≈ 0.17 Ω. Double the length and the resistance doubles; double the area and it halves.

Copper's low resistivity is why house wiring and power cords use it. Nichrome, with a resistivity about 60 times higher, is used in toasters and heaters, where the aim is to turn electrical energy into heat.

For metals, resistivity rises with temperature, because the vibrating atoms scatter electrons more. Some materials, cooled enough, become superconductors with zero resistance.