Question

What current is needed to transmit 100 MW of power at a voltage of 25.0 kV?

a) 4000 A
b) 2500 A
c) 5000 A
d) 2000 A
Find the power loss in a 1.00-Ω transmission line.

a) 100 MW
b) 1.00 MW
c) 10 MW
d) 0.01 MW

Answer 1

The current needed to transmit 100 MW of power at a voltage of 25.0 kV is 4000 A, and the power loss in a 1.00-Ω transmission line would be 16 MW, representing a 16% power loss.

Step-by-step explanation:

Calculating Current and Power Loss

To calculate the current needed to transmit 100 MW of power at a voltage of 25.0 kV, you can use the power formula: P = IV, where P is power, I is current, and V is voltage. Rearranging this formula to solve for current gives us I = P/V. Therefore, the current I = 100 MW / 25.0 kV = 100,000 kW / 25.0 kV = 4000 A. So, the correct answer is (a) 4000 A.

Next, to find the power loss in a 1.00-Ω transmission line, we use the formula for power loss: P_loss = I^2 * R, where I is the current and R is the resistance. Using the current we found above, P_loss = (4000 A)^2 * 1.00 Ω = 16,000,000 W or 16 MW. Thus, the correct answer is (c) 16 MW, which represents a substantial 16% loss of power in the transmission line.