First slide

Drift velocity

Question

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 $ν_{P}$ and $ν_{Q}$ respectively, then

Easy

A

$ν_{P} = ν_{Q}$
B

$ν_{P} = \frac{1}{2} ν_{Q}$
C

$ν_{P} = \frac{1}{4} ν_{Q}$
D

$ν_{P} = 2 ν_{Q}$

Solution

$\begin{array}{l} D r i f t v e l o c i t y ν_{d} = \frac{i}{n e A} \Rightarrow ν_{d} \propto \frac{1}{A} o r ν_{d} \propto \frac{1}{d^{2}} \\ \Rightarrow \frac{ν_{P}}{ν_{Q}} = {(\frac{d_{Q}}{d_{P}})}^{2} = {(\frac{d / 2}{d})}^{2} = \frac{1}{4} \Rightarrow ν_{P} = \frac{1}{4} ν_{Q} \end{array}$

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