Resistance per unit length:

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

For alluminium:

R_{a} = ρ_{a}l/π(d_{a}/2)^{2}

For copper:

R_{c} = ρ_{c}l/π(d_{c}/2)^{2}

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).

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