A high-voltage transmission line carries 1 000 A at 700 kV for a distance of 100 miles. If the resistance per length in the wire is 0.5 Ω/mile, what is the power loss due to resistive losses?

50 MW

Explanation:

We are given;

Current = 1000A

Voltage = 700 KV

Resistance per length = 0.5 Ω/mile

Length = 100 miles

The total resistance would be;

R=0.5 Ω/mile x 100 miles = 50Ω.

Now, the current is the same throughout the wire, but the voltage is only at the beginning of the line, and thus the current for the power equation is;

P = I²R

So;

P = (1000A) ² x 50Ω. = 50,000,000W = 50MW