Calculate the resistance of a copper wire of length $\displaystyle 1000$ m and area of cross-section $\displaystyle 2 \mathrm{~mm}^{2}$. Resistivity of copper is $\displaystyle 1 \cdot 6 \times 10^{-8} \Omega \mathrm{~m}$.

\[\begin{aligned} & \mathrm{R}=\rho \frac{l}{\mathrm{~A}} \\ & \rho=1.6 \times 10^{-8} \Omega \mathrm{~m} \\ & \mathrm{~A}=2 \times\left(10^{-3} \mathrm{~m}\right)^{2} \\ & l=1000 \mathrm{~m} \\ & \therefore \mathrm{R}=\left(1.6 \times 10^{-8} \Omega \mathrm{~m}\right) \times \frac{1000 \mathrm{~m}}{2 \times\left(10^{-3} \mathrm{~m}\right)^{2}} \\ & \quad=8.0 \Omega \end{aligned} \]