Question

The aluminum wire in a high-voltage transmission line is 2.7 cm in diameter. It is designed to carry a current of 1100 A. What is the voltage drop across a 32-km-long segment of this power line?

Answer 1

1660 V

Step-by-step explanation:

Resistance should be determined and then voltage drop across the power line can be determined.

R = ρ L /A

Here ρ = Resistivity of aluminum =
`2.7* 10^(-8)\Omega m`

L = length = 32 km = 32,000 m

Area of cross section = A = π r² = π (0.027/2)² = 0.00057255 m²

Resistance = R =

(
`2.7* 10^(-8)\Omega m` (32,000)/(0.00057255) = 1.5090 Ohms.

Voltage drop = V = I R = (1100)(1.5090) = 1659.9 V.

(If resistivity value is different, then the resistance will be different and hence final answer for voltage will also vary ).