Question

A 310-km-long high-voltage transmission line 2.00 cm in diameter carries a steady current of 1,190 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

Answer 1

Answer:

t = 141.55 years

Explanation:

As we know that the radius of the wire is

r = 2.00 cm

so crossectional area of the wire is given as

$A = \pi r^2$

$A = \pi(0.02)^2$

$A = 1.26 \times 10^{-3} m^2$

now we know the free charge density of wire as

$n = 8.50 \times 10^{28}$

so drift speed of the charge in wire is given as

$v_d = \frac{i}{neA}$

$v_d = \frac{1190}{(8.50 \times 10^{28})(1.6 \times 10^{-19})(1.26\times 10^{-3})}$

$v_d = 6.96 \times 10^{-5} m/s$

now the time taken to cover whole length of wire is given as

$t = \frac{L}{v_d}$

$t = \frac{310 \times 10^3}{6.96 \times 10^{-5}}$

$t = 4.46 \times 10^9 s$

$t = 141.55 years$