Question

Though the electron drift velocity is small and electron charge is very small, a conductor can carry an appreciably large current because
(A) relaxation time is small
(B) electron number density depends on temperature
(C) drift velocity of electron is very large
(D) electron number density is very large

Answer 1

The electrons that do not attach to the nuclear force and are free under the electric and the magnetic field are said as free electrons. The conduction of the current is mainly done by the free electrons in the material. If the substance has many free electrons, they are said to be conductors.
Formula used:
The formula of the current is given by
$I = Ane{v_d}$
Where $I$ is the current, $A$ is the cross sectional area of the conductor, $n$ is the number density of the free electrons in the conductor, $e$ is the charge of the electron and ${v_d}$ is the drift velocity of the free electrons in the conductor.

Complete answer:
Let us consider the formula of the current.
$I = Ane{v_d}$
The above formula shows that the current directly depends on the area, electronic charge, drift velocity of electrons and the number of free electrons density. If the drift velocity and the charge is less, the current value increases if it possesses greater number density of the free electrons. While considering the other options, the relaxation time is the time between the electronic collision and this decreases the conduction of the current. The electron number density is independent of temperature.

Thus the option (D) is correct.

Note:
The conductors possess nearly ${10^{28}}\,c{m^{ - 3}}$ of the free electrons in it. If there are no free electrons, the materials do not conduct electricity and they are said to be insulators. The example of the conductors are most of the metals. The examples of the insulators are wood, rubber etc.