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(C) The relationship between current $I$ and drift velocity $v_d$ is given by $I = neAv_d$,where $n$ is the electron density,$e$ is the charge of an e

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$4v_d$

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(C) The relationship between current $I$ and drift velocity $v_d$ is given by $I = neAv_d$,where $n$ is the electron density,$e$ is the charge of an electron,and $A$ is the cross-sectional area.Since the material is the same,$n$ and $e$ remain constant. Thus,$I \propto A v_d$.The cross-sectional area $A$ is given by $A = \pi (d/2)^2 = \pi d^2 / 4$,so $A \propto d^2$.Therefore,$I \propto d^2 v_d$.Since the current $I$ is the same in both cases,we have $d_1^2 v_{d1} = d_2^2 v_{d2}$.Given $d_1 = d$,$v_{d1} = v_d$,and $d_2 = d/2$,we substitute these values:$d^2 v_d = (d/2)^2 v_{d2}$$d^2 v_d = (d^2 / 4) v_{d2}$$v_{d2} = 4v_d$.

$A$ 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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