Question

A 200 m long aluminum wire has the same resistance and cross-sectional area as a carbon wire.What is the length of the carbon wire?

Answer 1

$$R_{Al}=R_{C}$$

$$\rho_{Al}\frac{l_{Al}}{A}=\rho_{C}\frac{l_C}{A}$$

So

$$l_C=l_{Al}\frac{\rho_{Al}}{\rho_{C}}\\ =200*\frac{2.65*10^{-8}}{3.50*10^{-5}}=0.15\:\rm m=15\: cm$$