Finding the Power Loss Through a Transmission Line

[Larfleeze]

Homework Statement

A factory receives 120kW of power from a power station 20km away via transmission lines. If the resistance in the power lines is 0.5Ω/km, what is the power loss in the lines if the electricity is transmitted at 100kV (Approximate to a simple DC circuit).

Homework Equations

V = IR
P = VI = I²R = V²/R

The Attempt at a Solution

Now first I simply found the total resistance in the wires by

R_w = 20km * 0.5Ω/km = 10Ω

The DC circuit I then approximated consisted of 2 resistors, one representing the total resistance from the wires and the other being the load of the factory. Since the question states the voltage is transmitted at 100kV I used that as the EMF and set up my imaginary circuit thusly:
http://img15.imagevenue.com/img.php?image=951360451_Circuit_122_536lo.jpg

However, it appears at this point I don't have enough information to answer the question, since I don't have the current or the Voltage over either resistor. Am I missing something or is there an easy solution I'm just not seeing?

(I'm not very knowledgeable in this area of Physics, only did it in my first year of my undergrad, but I am mathematically inclined so I don't think I'll be frightened by the solutions... hopefully)

 

[voko]

What does "transmitted at 100 kV" mean? Is that the voltage at the source, or voltage supplied to the factory?

 

[lendav_rott]

I suspect 100 kV is the voltage at the source.

One quick thing to mention - you will make your life a lot easier if you think in SI-units. Yes, I can see that when you calculate the wire-resistance there is a kilo- in the numerator and the denominator, but still.

You are given all the necessary data to solve this problem. There is a voltage drop across the line and you are given the power the destination receives. In a series, the current stays the same throughout.

 

[Larfleeze]

The 100kV being the source was the conclusion I came to as well.

Thanks, lendav_rott, I think I may be getting where I'm going. I think I can find the current by reducing to a quadratic equation by saying that:

V = I(R_w + R_f)

=> V = I(R_w + P_f/I²)

=> R_wI² - VI + P_f = 0

And just solving for I. From there I can figure out all of the other data, I think.

Personally, I don't tend to worry about number crunching until I get there.

 

[voko]

You should also compute the loss assuming that the voltage given is the voltage at the factory. If the results differ significantly, you should warn the instructor that the problem is formulated ambiguously.