A current I flows through a uniform wire of diameter d when the m… - Vidyadip

MCQ

$A$ current $I$ flows through a uniform wire of diameter $d$ when the mean electron drift velocity is $V$. The same current will flow through a wire of diameter $d/2$ made of the same material if the mean drift velocity of the electron is :

A
$v/4$
B
$v/2$
C
$2v$
✓
$4v$

✓

Answer

Correct option: D.

$4v$

d
$j=\frac{I}{A}=n e v_{d}$

$\frac{4 I}{\pi d^{2}}=n e v$

$\frac{161}{\pi d^{2}}=n e v^{\prime}$

From equaiton $( I )$ and $( II )$

$\frac{4 I}{16 I}=\frac{v^{\prime}}{v^{\prime}} \Rightarrow v^{\prime}=4 v$

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