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(C) The current $I$ in a wire is given by the formula $I = neAv_d$,where $n$ is the number density of free electrons,$e$ is the charge of an electron,

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$I/2$

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(C) The current $I$ in a wire is given by the formula $I = neAv_d$,where $n$ is the number density of free electrons,$e$ is the charge of an electron,$A$ is the cross-sectional area,and $v_d$ is the drift velocity.Since the material is the same,$n$ and $e$ remain constant.The cross-sectional area $A$ is given by $A = \pi r^2$.For the first wire: $I_1 = ne(\pi r^2)v$.For the second wire: $r_2 = r/2$ and $v_{d2} = 2v$.$I_2 = ne(\pi (r/2)^2)(2v) = ne(\pi r^2 / 4)(2v) = (1/2) ne \pi r^2 v$.Comparing the two,$I_2 = I_1 / 2 = I/2$.

In a wire of cross-section radius $r$,free electrons travel with drift velocity $v$ when a current $I$ flows through the wire. What is the current in another wire of half the radius and of the same material when the drift velocity is $2v$?

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