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:

R=ρlπr2

For alluminium:

Ra = ρal/π(da/2)2

For copper:

Rc = ρcl/π(dc/2)2 

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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).

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