A high-voltage transmission line carries 756 A at 488 kV for a distance of 169 km. If the resistance in the wire is 0.248 Ω/km, how much power is dissipated due to resistive losses? Answer in units of W.

23954216.83 W

Explanation:

The formula of power dissipated due to resistive losses is

Pr = I²R ... Equation 1

Where Pr = Power dissipated due to resistive losses, I = current, V = Voltage.

But,

R = βL ... Equation 2

Where β = resistance per length of the wire, L = Length of the wire.

Substitute equation 2 into equation 1

Pr = I²βL ... Equation 3

Given: β = 0.248 Ω/km, I = 756 A, L = 169 km.

Substitute into equation 3

Pr = 756² (0.248) (169)

Pr = 23954216.83 W

23954216.8 W

Explanation:

Power loss = I²R where I current = 765 A

R = 0.248 Ω/km * 169 km

R = 41.912 Ω

Power loss due to resistive losses = 765 ² * 41.912 Ω = 23954216.8 W