A high-voltage powerline operates at 500,000 V rms and carries an rms current of 500 A. If the resistance of the cable is 0.050 Ω/km, what is the resistive power loss in 200 km of the powerline?
A)250 kW
B)500 kW
C)1 megawatt
D)2.5 megawatts
E)250 megawatts

Question

Quizplus · Accepted Answer

The resistive power loss in a powerline can be calculated using the formula:

Power loss = I^2 * R * L

where I is the rms current, R is the resistance per unit length, and L is the total length of the powerline.

In this case, we know that:

I = 500 A
R = 0.050 Ω/km
L = 200 km

To use the formula, we need to convert the resistance per unit length to total resistance by multiplying it by the total length:

total resistance = R * L = 0.050 Ω/km * 200 km = 10 Ω

Now we can plug in the values and calculate the power loss:

Power loss = (500 A)^2 * 10 Ω = 2,500,000 W = 2.5 MW

Therefore, the answer is D) 2.5 megawatts.

A High-Voltage Powerline Operates at 500,000 V Rms and Carries