A current I is passing through a wire having two sections P and Q… - Vidyadip

MCQ

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
$v_P = \frac{1}{2}v_Q$
✓
$v_P = \frac{1}{4}v_Q$
D
$v_P = 2 v_Q$

✓

Answer

Correct option: C.

$v_P = \frac{1}{4}v_Q$

c
(c) Drift velocity ${v_d} = \frac{i}{{neA}} \Rightarrow {v_d} \propto \frac{1}{A}{\rm{ or}}\,{v_d} \propto \frac{1}{{{d^2}}}$

$ \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}$.

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