Question

When the current $i$ is flowing through a conductor, the drift velocity is v. If current 2i is flowed through the same metal but having double the area of cross-section, then the drift velocity will be
A. $\dfrac{v}{4}$
B. $\dfrac{v}{2}$
C. $v$
D. $4v$

Answer 1

Hint: Here in this question, a current I is flowing out of the conductor, indicating that a coulomb with per unit time cross section area is going through the cross section area of the conductor, from which we deduce that the conductor's charge density will be constant in every situation.

Formula Used:
The expression of drift velocity is,
${v_d} = \dfrac{J}{{ne}}$
The formula of Current Density is,
$J = \dfrac{i}{A}$
Here, $J$ is the current density, $n$ is the charge density, $e$ is the charge on the electron and $A$ is the area of the cross section.

Complete step by step solution:
As in the above formulas we get that, the drift velocity is depending upon the current density too. By which we can also say that the drift velocity is directly proportional to current density as when we increase the value of drift velocity the value of current density also increases from which we stated that,
${v_d} \propto J$
Since, from above data we can say that,
${J_1} = \dfrac{i}{A}$

As according to question the charge density will also be same for the second case,
${J_2} = \dfrac{{2i}}{{2A}} \\ $
By comparison of both the current density we get that, as from the law used as for proportionality,
${({v_d})_1} = {({v_d})_2}$
Out from this we can say that,
${({v_d})_1} = {({v_d})_2} = v$
Therefore, the correct answer is $v$ .

Hence, the correct option is C.

Note: The molecular structure of the wire, and thus the conductor's material, is another factor that affects the drift velocity. It is well known that the drift velocity is mostly reliant on the applied voltage. Additionally, a slight temperature dependence is seen.