Question

A 280-km-long high-voltage transmission line 2.00 cm in diameter carries a steady current of 1,250 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 1

Solution: Given:- Length of line=280km, Diametr of wire, D=2cm, Current,I=1250A, Charge density of copper,q= 8.50x10²⁸electrons per m^3, No. of seconds in a year= 3.156x10⁷.

The drift speed of electrons in a high voltage line is given by:

,

Here, =drift speed of electron, I=Current, q=charge on each electron, A=Area, n=charge density.

m/s.

Time taken by the electron to travel 280km is given by:

seconds.

But 1 year = 3.156x10⁷

So, Time in year,

year

years. Ans.