A current $I$ flows through a uniform wire of diameter $d,$ when the mean drift velocity is $v_d.$ The same current will flow through a wire of diameter $d/2$ made of the same material, if the mean drift velocity of the electrons is
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$I\, = \,neA{v_d}{\kern 1pt} \,\,A{\kern 1pt} \, = \,\pi {r^2}\, = \,\pi \,{\left( {\frac{d}{2}} \right)^2}$
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