Physics - Current Electricity Question with Solution | TestHub

Relation between current and drift velocity : Consider a conductor of length $l$ and area of cross – section $A$ having $n$ electrons per unit length, as shown in the figure.The volume of the conductor = $Al$ $\therefore$  Total number of electrons in the conductor= Volume  $\times$  electron density = $Aln$If $e$ is the charge of an electron, thentotal charge contained in the conductor, $Q=enAl$ Let a potential difference V is applied across the conductor. The resulting electric field in the conductor is given by $E=\frac{V}{l}$ Under the influence of this field E, free electrons begin to drift in a direction opposite to that of the field. Time taken by electrons to cross – over the conductor is $t=\frac{l}{v_d}$ where,  $v_d$  is the drift velocity of electrons.Therefore, the current through the conductor is given by $I=\frac{Q}{t}=\frac{enAl}{I/v_d}$ or  $I=neA{v}_d$  $\Rightarrow I\alpha v_d$                                                        $[\because n,e,A$  are all constant]Hence, Current density is proportional to drift velocity.