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  4. 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

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Q. 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

Current Electricity

Solution:

$j=\frac{I}{A}=n e v_{d}$
$\frac{4 I}{\pi d^{2}}=n e v ..... (i) $
$\frac{16 I}{\pi d^{2}}=n e v' .......(ii) $
From equations (i) and (ii) $\frac{4 I}{16 I}=\frac{v}{v'}$
$ \Rightarrow v'=4 v$