This came from a set of problems to review for a midterm coming up later in Physics II this week. A group of us have looked at this problem and we’ve come up with various ways of doing it, but none are correct (the problems offer “tries” on the internet to see if you’ve done it correctly).

  1. Consider a transmission line that delivers 1 MW of power and has a resistance of 7 ohms. Calculate the dollars lost annually due to the transmission line if the power is delivered at (a) 500000 V and (b) 440 V, if the cost of electric power is 12 cents/kWH.

I’m not asking for anyone to provide an answer, just a point from which we can probably figure out what we’ve done wrong and what we’re not considering.

We’ve only tried part a so far, and we’ve come up with things like $4,288, $428, $42,880… things like that.

Again, just looking for a hint or suggestions on which way to go.


P = VI
P[sub]loss[/sub] = I[sup]2[/sup]R

From that, you should be able to calculate the instantaneous power loss.

Next, work out the energy loss by converting to annual kWh, i.e., convert to kW and multiply by the number of hours in a year.

Them work out the cost.


P[sub]loss[/sub] = 500000[sup]2[/sup] / 7 ?

/ 1000 = 35714285.714285714285714285714286 kW * 8765.81277 hours = 313064741785.71428571428571428571 kWH?

  • .12 = $37567769014.29?

I think I messed up. sigh

Yes, you did.

Try again.

P = 1000000
V = 500000
I = ?

R = 7

P[sub]loss[/sub] = I[sup]2[/sup] x 7 = ?

Cost = P[sub]loss[/sub] x 8760 / 1000 x $0.12 = ?

Wow, I’m an idiot.

Thanks for your help.