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AstroJMT42
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Homework Statement
Power station produces AC power at 2.5Mw, I = 100A.
Transferred along 100km line with a resistance of 50 ohms to a factory. Calculate power lost and % efficiency
Homework Equations
P=VI
P = I2R
The Attempt at a Solution
Initial power at the station is 2.5x106 . Using I2R you get new power at the factory of 1002x50 = 5x105W
This means a total loss of 2x105 and a percentage of 8%.
I'm pretty confident this is correct but a fellow student is adamant that I2R is power loss not total power out. His conclusion is that the line is actually 80% efficient, which sounds way to efficient to be correct, especially seeing as there are no transformers. Can anyone please confirm which of us is correct?
second part then takes the same original power and introduces a 1:5 step up transformer and 5:1 step down and asks to calculate the new power loss and new efficiency.
I worked initial V = 25,000 and after step up V = 125,000
New power after this using I2R is 2,480,000W which I calculated to be an efficiency of 99.2%
Again could you please check my logic is sound? There were no answers given.
Apologies it is actually 2 questions being asked but the second one leads directly from the first so thought it was best to keep it in one post.
Thanks!