Wire A and Wire B are each carrying the same current.If the diameter of Wire A is twice that of Wire B,how does the drift velocity v_dA in Wire A compare to that in in Wire B? A)v_dA = v_dB B)v_dA = 2 v_dB C)v_dA = v_dB /2 D)v_dA = v_dB /4

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Quizplus · Accepted Answer

The drift velocity $v_d$ in a conductor is inversely proportional to the cross-sectional area $A$ of the conductor when the current $I$ is held constant, as given by the equation $I = nAev_d$, where $n$ is the charge carrier density, $e$ is the charge of an electron, and $v_d$ is the drift velocity. If the diameter of Wire A is twice that of Wire B, the cross-sectional area of Wire A is four times that of Wire B (since area $A = \pi r^2$, and doubling the diameter doubles the radius, resulting in an area four times larger). Therefore, for the same current, the drift velocity in Wire A is one-fourth that in Wire B.

Wire a and Wire B Are Each Carrying the Same