# Problem: Consider two wires, one aluminum with resistivity 2.65 × 10–8 Ω•m and one copper with  1.72 × 10–8 Ω•m. Find the ratio of the diameter of aluminum to copper wire, if they have the same resistance per unit length (as they might in household wiring).

###### FREE Expert Solution

Resistance per unit length:

$\overline{){\mathbf{R}}{\mathbf{=}}\frac{\mathbf{\rho }\mathbf{l}}{\mathbf{\pi }{\mathbf{r}}^{\mathbf{2}}}}$

For alluminium:

Ra = ρal/π(da/2)2

For copper:

Rc = ρcl/π(dc/2)2

###### Problem Details

Consider two wires, one aluminum with resistivity 2.65 × 10–8 Ω•m and one copper with  1.72 × 10–8 Ω•m. Find the ratio of the diameter of aluminum to copper wire, if they have the same resistance per unit length (as they might in household wiring).