The question is incomplete! The complete question along with answer and explanation is provided below.
Question:
Suppose 79 kW is to arrive at a town over two 0.115 Ω lines. Estimate how much power is saved if the voltage is stepped up from 150 V to 1500 V and then down again, rather than simply transmitting at 150 V. Assume the transformers are each 99%% efficient. Express your ans up to two decimal points.
Answer:
Power saved = 30772.58 W or 30.77 kW
Explanation:
Since the power loss depends upon current, we need to find the current at each voltage level.
Current at 150 V:
I = P/V = 79,000/150 = 526.67 A
Current at 1500 V:
Considering transformer efficiency of 99%
79,000/0.99 = 79797.97 W
I = P/V = 79,797.97/1500 = 53.19 A
Power loss at 150 V:
P = I²R = (526.67)²*0.115 = 31898.84 W
Power loss at 1500 V:
Here we have to consider both of the losses, due to the transmission line and due to transformer itself
P = I²R = (53.19)²*0.115 = 325.35 W
So the total power at the sending end would be
Receiving end power + losses
79,000 + 325.35 = 79,325 W
Power at the input of the transformer is
79,325/0.99 = 80126.26
Power lost in the transformer is
80,126.26 - 79,000 = 1126.26 W
So the power that can be saved by stepping up the voltage from 150 to 1500 V is
Power saved = 31898.84 - 1126.26
Power saved = 30772.58 W
Power saved = 30.77 kW
