Two wires have the same resistance and radius. If the wires are made of copper and platinum with resistivities respectively of 1.70 ✕ 10−8 Ω · m and 11.0 ✕ 10−8 Ω · m, determine the ratio of their lengths.

L1/L2 = 6.47

Explanation:

In order to calculate the ratio of the lengths of the wires you use the following formula for the resistivity of a wire:

       (1)

r: radius of the cross-sectional area of the wire

R: resistance of the wire

L: length of the wire

Then, you have for each wire:

The resistance and radius of the wires are the same, that is, R1 = R2 = R and r1 = r2 = r. By taking into account this last and dive the equation for the wire 2 into the wire 1, you obtain:

The ratio of the lengthd of the wires is L1/L2 = 6.47

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