Question

An electrician wishes to cut a copper wire (ρ=1.724×10−8Ωm) that has no more than 10Ω of resistance. The wire has a radius of 0.725mm. Approximately what length of wire has a resistance equal to the maximum 10 Ω?

Answer 1

The resistance of wire

$$R=\rho\frac{l}{A}.$$

Hence, the length of wire

$$l=RA/\rho=R\pi r^2/\rho$$

$$=\frac{10\times 3.14\times (725\times 10^{-6})^2}{1.724\times 10^{-8}}=957\:\rm m.$$