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20 December, 21:59

2.0 3 102 - km - long high - voltage transmission line 2.0 cm in diameter carries a steady current of 1.0 3 103 A. If the conductor is copper with a free charge density of 8.5 3 1028 electrons/m3, how many years does it take one electron to travel the full length of the cable?

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  1. 21 December, 00:28
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    21.2 years

    Explanation:

    Length, L = 2.03 x 10^2 km = 2.03 x 10^5 m

    Diameter, d = 2 cm

    radius, r = 1 cm = 0.01 m

    Current, i = 1.03 x 10^3 A

    charge density, n = 8.53 x 10^28 electrons/m^3

    Let the time taken by the electrons be t.

    By the use of the formula for the drift velocity

    i = n e A vd

    where, e be the electronic charge, A be the area of crossecion and vd be the drift velocity

    1.03 x 10^3 = 8.53 x 10^28 x 1.6 x 10^-19 x 3.14 x 0.01 x 0.01 x vd

    vd = 3.033 x 10^-4 m/s

    time taken, t = length / drift velocity

    t = 2.03 x 10^5 / (3.033 x 10^-4)

    t = 6.69 x 10^5 seconds

    t = 21.2 years

    Thus, the time taken is 21.2 years.
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