Question

The electron drift speed is small and the charge of the electron is also small but still, we obtain large current in a conductor. This is due to
(A) The conducting property of the conductor
(B) The resistance of the conductor is small
(C) The electron number density of the conductor is small
(D) The electron number density of the conductor is enormous.

Answer 1

Besides the electron drift speed and the charge of the electron, the current flowing through a conductor is also directly related to the electron number density of the conductor. The electron number density is the number of free electrons in a unit volume of the conductor.

Formula used: In this solution we will be using the following formula;
$\Rightarrow I = nevA$ where $I$ is the current flowing through the conductor, $n$ is the electron number density of the conductor, $e$ is the charge of the electron, $v$ is the drift speed of the electron when in the conductor and $A$ is the cross sectional area of the conductor.

Complete step by step solution:
In a conductor, the movement of electrons is what constitutes current. The speed $v$ of the electron is directly related to the current. Besides the speed of the electrons, the current is also directly related to the electron number density $n$ and the charge $e$ .
Mathematically, the current is given as
$\Rightarrow I = nevA$; where $A$ is the cross sectional area. Thus, even though the electron charge and drift speed are low, we can still obtain a high current if the electron number density is extremely high. Hence, we can conclude that this must be the reason why we can obtain a large current in a conductor.
Thus, the correct answer is D, the electron number density of the conductor is enormous.

Note:
Alternatively, investigating the definition of the electron number density, which is defined as the number of free electrons (i.e. electrons available to move) per unit volume of the conductor. It can be given as $n = \dfrac{{\rho N}}{A}$ for an atom which as one free electron per atom, where $N$ is the Avogadro’s number, $\rho$ is the density of the element, and $A$ is the atomic number. The Avogadro’s number is of the order of ${10^{23}}$ atoms. Hence the electron number density must be high not low. Hence, we can conclude that the electron number density is enormous and must be the reason for large current as it is a fundamental part of the conductor’s structure.