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Question

Consider a wire of length 4 m and cross-sectional area 1 mm2 carrying a current of 2 A. If each cubic metre of the material contains 1029 free electrons, find the average time taken by an electron to cross the length of the wire.

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Solution

Given:
Current through the wire, i = 2 A
Length of the wire, l = 4 m
Area of cross section, A = 1 mm2 = 1 × 10–6 m2
Number of electrons per unit volume, n = 1029
We know:
i=nAVdeVd=inAe=21029×10-6×1.6×10-19Vd=18000 m/s,
where Vd is the drift speed.
Let t be the time taken by an electron to cross the length of the wire.
t=Length of the wireDrift speed=lVd t=418000=32×103 s

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