\(A\). The drift velocity of electrons decreases with the increase in the temperature of conductor. \(B\). The drift velocity is inversely proportional to the area of cross-section of given conductor. \(C\). The drift velocity does not depend on the applied potential difference to the conductor. \(D\). The drift velocity of electron is inversely proportional to the length of the conductor. \(E\). The drift velocity increases with the increase in the temperature of conductor. Choose the correct answer from the options given below:

\(v _{ d }=\left(\frac{ e \tau}{ m }\right)\left(\frac{\Delta V }{\ell}\right)\)

\(\Delta V=\) Potential difference applied across the wire

As temperature increases, relaxation time decreases, hence \(V _{ d }\) decreases.

As per formula, \(V _{ d } \propto \frac{1}{\ell}\)

\(v _{ d }=\frac{ I }{\text { neA }}\), as it is not mentioned that current is at steady state neither it is mentioned that \(n\) is constant for given conductor. So it can't be said that \(v _{ d }\) is inversely proportional to \(A\).

\(I=n e A v_{d}=\frac{V}{R}=\frac{V}{\rho \ell} A\)

\(v _{ d }=\frac{ V }{\rho \ell \text { ne }} \quad\left( E =\frac{ V }{\ell}\right)\)

\(v _{ d }=\frac{ eE \tau}{ m }\)

\(\tau\) decrease with temperature increase.

First and fourth statements are correct.