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In the figure provided a wire consists of two segments made from the same material but with different cross sectional areas such that A2𝐴2 = 2 A1𝐴1. Which of the following is true about the strength of the electron drift velocities in the two segments? (vd)1(𝑣𝑑)1 = 2 (vd)2(𝑣𝑑)2 (vd)1(𝑣𝑑)1 = (vd)2(𝑣𝑑)2 (vd)1(𝑣𝑑)1 = 4 (vd)2(𝑣𝑑)2 (vd)1(𝑣𝑑)1 = 0.5 (vd)2

Question

In the figure provided a wire consists of two segments made from the same material but with different cross sectional areas such that A2𝐴2 = 2 A1𝐴1. Which of the following is true about the strength of the electron drift velocities in the two segments? (vd)1(𝑣𝑑)1 = 2 (vd)2(𝑣𝑑)2 (vd)1(𝑣𝑑)1 = (vd)2(𝑣𝑑)2 (vd)1(𝑣𝑑)1 = 4 (vd)2(𝑣𝑑)2 (vd)1(𝑣𝑑)1 = 0.5 (vd)2

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Solution

The drift velocity (vd) of electrons in a conductor is given by the equation:

vd = I / (nAe)

where: I is the current, n is the number density of free electrons, A is the cross-sectional area of the conductor, and e is the charge of an electron.

Given that the wire is made of the same material and carries the same current in both segments, the number density of free electrons (n) and the current (I) are the same in both segments. Therefore, the drift velocity is inversely proportional to the cross-sectional area of the conductor.

Given that A2 = 2A1, the drift velocity in the second segment (vd2) is half of the drift velocity in the first segment (vd1). Therefore, the correct answer is (vd)1 = 2 (vd)2.

This problem has been solved

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