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3. current electricity — Physics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 SciencePhysics3. current electricity1 Mark
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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