$A$ battery is connected to a uniform resistance wire $AB$ and $B$ is earthed. Which one of the graphs below shows how the current density $J$ varies along $AB$?

The relaxation time $\tau$ is nearly independent of the applied $E$ field,whereas it changes significantly with temperature $T$. The first fact is (in part) responsible for Ohm's law,whereas the second fact leads to the variation of resistivity $\rho$ with temperature. Elaborate why?

An electron takes $40 \times 10^3 \ s$ to drift from one end of a metal wire of length $2 \ m$ to its other end. The area of cross-section of the wire is $4 \ mm^2$ and it is carrying a current of $1.6 \ A$. The number density of free electrons in the metal wire is

The electric intensity $E$,current density $j$,and specific resistance $\rho$ (often denoted as $k$ in some texts) are related to each other by the relation:

Drift speed $(v_d)$ varies with the intensity of the electric field $(E)$ as per the relation:

The drift velocity of electrons in a conducting wire is of the order of $1 \, mm/s$. However,when the switch is turned on,the bulb glows almost instantaneously. This is because: