If a neglegibly small current is passed through a wire of length $$15\,m$$  and of resistance $$5\,\Omega $$  having uniform cross-section of $$6 \times {10^{ - 7}}{m^2},$$    then coefficient of resistivity of material, is

Solution :
Resistance of a given conducting wire is given by
$$R = \rho \cdot \frac{l}{A}$$
where, $$\rho $$ is the specific resistance of the material of the conductor.
Here, $$l = 15\,m$$
$$\eqalign{ & A = 6 \times {10^{ - 7}}{m^2} \cr & R = 5\,\Omega ,\rho = ? \cr & \therefore \rho = \frac{{RA}}{l} \cr & = \frac{{5 \times 6 \times {{10}^{ - 7}}}}{{15}} \cr & = 2 \times {10^{ - 7}}\Omega - m \cr} $$