Question

A conductor has a diameter of 3.0 mm. How many meters of this

material is needed to have a resistance of 1ohm? The resistivity of the

conductor is 1.68 x10−8 Ω. m

Answer 1

$$R=\frac{\rho\ l}{A}=\frac{\rho l}{\pi d^2/4}=\frac{4\rho l}{\pi d^2}$$

$$l=\frac{\pi d^2R}{4\rho} =\frac{3.14*(3.0*10^{-3})^2*1.0}{4*1.68*10^{-8}}=420\:\rm m$$