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

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$I/2$

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(C) The current $I$ in a wire is given by the formula $I = n e A v_d$, 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.For the first wire: $I_1 = n e (\pi r^2) v$.For the second wire: $r_2 = r/2$ and $v_{d2} = 2v$. The area $A_2 = \pi (r/2)^2 = \pi r^2 / 4 = A_1 / 4$.Thus, $I_2 = n e A_2 v_{d2} = n e (A_1 / 4) (2v) = (1/2) n e A_1 v$.Substituting $I_1 = n e A_1 v$, we get $I_2 = I_1 / 2 = I/2$.

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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