A wire $50\mathrm{cm}$ long  $1{\mathrm{mm}}^2$ in cross–section carries a current of 4A when connected to a 2V battery. The resistivity of the wire is

Solution:

Length$l=50\mathrm{cm}$  Cross-sectional area  $A=1{\mathrm{mm}}^2=1\times {10}^{-6}\mathrm{m}$
Current $\mathrm{i}=4\mathrm{A}$ Potential difference $\mathrm{V}=2\mathrm{V}$
Resistance  $\mathrm{R}=\frac{\mathrm{V}}{\mathrm{I}}=\frac{2}{4}=0.5\mathrm{\Omega }\Rightarrow \mathrm{\rho }=\frac{\mathrm{RA}}{\mathrm{\ell }}=\frac{0.5\times {10}^{-6}}{50\times {10}^{-2}}\therefore \mathrm{\rho }={10}^{-6}\mathrm{\Omega m}$