Obtain a relation between the current flowing in a conductor and drift velocity of electrons in it. Hence, obtain Ohm's law.

Volume of the wire \(\displaystyle =A l\) No. of \(\displaystyle \mathrm{e}^{-}\)in this volume \(\displaystyle =n A l\) Charge on the conductor \(\displaystyle =(n A l)_{\mathrm{e}}\) The amount of charge crossing the area A in time \(\displaystyle \Delta \mathrm{t}\) is \(\displaystyle \mathrm{I} \Delta \mathrm{t}\); where I is the magnitude of the current. Hence, \[\mathrm{I} \Delta \mathrm{t}=+n \mathrm{e} A\left|\mathrm{v}_{d}\right| \Delta \mathrm{t} \] \(\displaystyle \Rightarrow \mathrm{I}=\) neAv \(\displaystyle _{d}\) Since \(\displaystyle \left|\mathrm{v}_{d}\right|=\frac{\mathrm{e} E}{m} \tau\) \(\displaystyle \mathrm{I}=n \mathrm{e} A\left(\frac{\mathrm{e} \tau}{m}\right) \frac{V}{l}=\left(\frac{n \mathrm{e}^{2} \tau}{m}\right) A\left(\frac{V}{l}\right)\) \(\displaystyle \Rightarrow \frac{V}{\mathrm{I}}=\left(\frac{m}{n \mathrm{e}^{2} \tau}\right) \frac{l}{A}\) Hence \(\displaystyle \frac{V}{\mathrm{I}}\) is constant for a given conductor at constant temperature. \(\displaystyle \Rightarrow V \alpha \mathrm{I}\)