A silver wire and an aluminum wire of the same length have the same resistance. What is the ratio of the diameter of the silver wire to that of the aluminum wire.

The ratio of the diameter of the silver wire to that of the aluminum wire is 0.751

Explanation:

The resistivity of silver wire is 1.59*10^-8 ohm-meter. Let its diameter be Ds. Area = πDs^2/4

The resistivity of aluminum wire is 2.82*10^-8 ohm-meter. Let its diameter be Da. Area = πDa^2/4

Resistance and length of both wires are the same

Resistance/length = resistivity/area

1.59*10^-8/πDs^2/4 = 2.82*10^-8/πDd^2/4

(Ds/dD) ^2 = 0.564

(Ds/Dd) = √0.564 = 0.751