Q. A current $I$ is passing through a wire having two sections $P$ and $Q$ of uniform diameters $d$ and $d/2$ respectively. If the mean drift velocity of electrons in sections $P$ and $Q$ is denoted by $v_{P}$ and $v_{Q}$ respectively, then
A) $v_{P} = v_{Q}$
B) $v_{P} = \frac{1}{2}v_{Q}$
C) $v_{P} = \frac{1}{4}v_{Q}$
D) $v_{P} = 2v_{Q}$
Explanation
(c) Drift velocity $v_{d} = \frac{i}{neA} \Rightarrow v_{d} \propto \frac{1}{A}$ or $v_{d} \propto \frac{1}{d^{2}}$
$\Rightarrow \frac{v_{P}}{v_{Q}} = \left( \frac{d_{Q}}{d_{P}} \right)^{2} = \left( \frac{d/2}{d} \right)^{2} = \frac{1}{4} \Rightarrow v_{P} = \frac{1}{4}v_{Q}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.