Transmission Lines Question

Question

a)Rwires is the resistance found in the transmission lines. We want the wires to remain as cool as possible since heat is considered a waste of energy (a loss). Discuss why it is better for a Power Plant to transmit 100 MW of power at a high voltage and low current (recall: P = VI) as opposed to a high current, low voltage.

I got this one, Higher voltage decreases current so power loss will be less. 


B) If the Power Plant is delivering 5 x 107 W of power to the lines using 2.5 x 105 V, how much current is travelling through the lines?

I also figured out the answer tot his one which is I=5000000/250000=200 I=200A 

c) The resistance of the lines themselves is 2 ohms. How much power is dissipated (used up) by the lines? This is considered to be the “Power Lost”.

And this one, ^P=I2R =200² x 2  P=80,000 W


d) Therefore, how much of the original power ends up at the city? You’ll recall that efficiency is a ratio of output/input using either energy or power. What is the efficiency of the lines?

 

I can't figure this one out, my textbook says the answer should be n=99.8% 

 

Please help 

Answer 1

Take total power minus power lost to get the power delivered to the city.  For efficiency, divide this by total power and multiply by 100.

Answer 2

In part (b) you are supplying P₁ = 5 x 10⁷ W at the source.  In part (c) you calculated that you lose ΔP = 80,000 W along the transmission line.  Therefore, the power P₂ delivered at the end of the line is the power at the source minus the power lost along the line:

 

P₂ = P₁ - ΔP = (5 x 10⁷ W) - (80,000 W) = 49,920,000 W

 

Efficiency is power delivered at the end divided by power supplied at source:

 

η = P₂ / P₁ = (49,920,000 W) / (5 x 10⁷ W) = 0.9984

 

In terms of percentage, the efficiency is 100η = 99.84%, which agrees with the answer provided in the problem statement.