a 340-km-long high-voltage transmission line 2.00 cm in diameter carries a steady current of 1,060 a. if the conductor is copper with a free charge density of 8.50 1028 electrons per cubic meter, how many years does it take one electron to travel the full length of the cable? (use 3.156 107 for the number of seconds in a year.)



Answer :

13.70 years it take one electron to travel the full length of the cable.

Why is high transmission voltage necessary?

Electricity is transported across great distances using high voltage transmission lines. To minimize the quantity of energy lost over the distance, a high voltage is required. Electricity cannot be stored when it is not in use, unlike other energy sources like natural gas. A blackout happens when demand outpaces supply.

I = 1,060 A

L = 340 km = 340, 000 m

diameter = 2 cm

radius, r = 1 cm = 0.01 m

Area, A = 3.14 x 0.01 x 0.01 = 3.14 x 10^-4 m^2

n = 8.5 x 10^28 per cubic metre

Use the relation

I = n e A vd

vd = I / n e A

vd = 1,060 / (8.5 x 10^28 x 1.6 x 10^-19 x 3.14 x 10^-4)

vd = 2.48 x 10^-4 m/s

Let time taken is t.

Distance = velocity x time

t = distance / velocity = L / vd

t = 340000 / (2.48 x 10^-4) = 8.91 x 10^8 second

t =13.70 years

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