Question

Two wires are identical, except that one is aluminum and one is copper. The aluminum wire has a resistance of 0.835. What is the resistance of the copper wire? Take the resistivity of copper to be 1.72 x 10-8 Ω·m, and that of aluminum to be 2.82 x 10-8 Ω·m.

Answer 1

The ratio of the resistances will be the same as the ratio of the resistivities, if lengths and diameters are the same.

R(Cu)/R(Al) = 1.72 x 10-8/2.82 x 10-8
= 0.61

R(Al) = 0.509 Ù

Answer 2

Well, for resistance of wire we have formula as,
R = (resistivity * length of wire ) / crosssectional area. As both wires are identical, there length and crossectional area are same. So, as resistance is directly praportional to resistivity,
R(Cu) / R(Al) = resistivity of copper / resistivity of Aluminum.
So, R(Cu) = R(Al ) * 1.7241* 10-8 / 2.82 x 10-8.
R(Cu) = 0.835 * 1.7241/ 2.82 = 0.51047518 ohm