Electric Power
Electric Power?
A power plant produces 1000MW to supply a city 40km away. Current flows from the power plant on a single wire of resistance .050 ohms/km, through the city, and returns via the ground, assumed to have negligible resistance. At the power plant, the voltage between the wire and ground is 115 kV. (a) What is the current in the wire? (b) What fraction of the power is lost in transmissions?
Someone please help me with this question.
I have tried, and I am getting results that don’t look right:
(a)
I = V/R
I = 115,000 / (.050 x 40)
I = 5.75 x 10^4
(b)
P = (I^2)R
P = [(5.75 x 10^4)^2](.050×40)
P = 6.61 x 10^9
But the latter result is greater than the original 1000MW = 1 x 10^9 W. What am I doing wrong here? Which formulas should I use to solve this problem?
Thank you,
Anthony
I’m not going to do it all, but I’ll tell you the mistake you are making.
The R you are using is not the only R in the system. It is only the transmission R. The calculation you are doing is if there were a short circuit at the far end of the transmission line.
To figure the current start with the gigawatt and divide by the transmission voltage.
Then you can do I squared R to get the power LOST in the transmission line. You figured the transmission R correctly….
That should be enough to let you solve it.
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