Question

A steady current flows in a metallic conductor of non-uniform cross-section. Which of the following quantities is constant along the conductor?
A. Drift speed.
B. Current.
C. Current density.
D. None of these.

Answer 1

Hint: To solve this question, we have to know the relationship between the current and the cross-section and other quantities. Then we will find the factors that will not get affected by the non-uniform cross section.
Formula used: $I = nA{V_d}e$, $j = \dfrac{I}{A}$.

Complete Step-by-Step solution:
We know that, the current flowing through the conductor due to the drift electrons is given by,
$ \Rightarrow I = nA{V_d}e$ ……..(i)
Where A is the area of cross section ${V_d}$is the drift velocity of electrons and e is the charge on electrons and n is the number of electrons per unit volume in the conductor.
So now, from equation (i), we get
${V_d} = \dfrac{I}{{neA}}$, this states that
$\therefore $ ${V_d} \propto \dfrac{1}{A}$
Here, the cross-section, A is non uniform.
Hence, if A changes then ${V_d}$ also gets changed.
Now, we know that the current density, j is given by,
$ \Rightarrow j = \dfrac{I}{A}$, this states that
$\therefore $ $j \propto \dfrac{1}{A}$
Hence, if A changes, then current density, j also gets changed.
According to the question, the current is steadily flowing through the conductor, which means current is constant.
Hence, we can say that only current flowing through the conductor is constant and drift speed and current density gets changed when the area of cross-section changes.
Therefore, the correct answer is option (B).

Note: Whenever we ask such types of questions, first we have to find out the relationships between all the given quantities. Then we have to find out the proportionality between them that which quantity is affecting the other. Then by using the statements given in the questions, we can identify which quantity gets changed and which remains constant. Through this we will get the answer.