Solving Power Transmission Homework for Small Town | 1.00MW @ 35km

[Jenn123]

Homework Statement

A small town requires 1.00MW of electricity.
The town is located 35 km away from power source.
Electricity delivered at 120 Volts.

(1) What current is required by the town?
(2) Assume answer to part (1) is the current flowing along the transmission lines. Waste heat during transport equal 10% of energy delivered to town (waste heat = 0.10MW, total power = 1.10MW). What must the generator voltage be to supply power to town at 120V?
(3) What diameter of copper wire is required to deliver electricity based on above conditions? (Resistivity of copper = 1.72*10^-8)
(4) Introduce transformers. Assume copper wires are 0.100 m diameter and waste heat is 10% of power, again. Assume generator voltage is the same as part (2). Calculate transmission voltage and transmission current. Calculate turns ratio of step-up transformer at power plant.

Homework Equations

P=IV
P=I^2(R)

The Attempt at a Solution

I tried the first part of the problem (hopefully I'm right).
I=P/V
I=10^6 W / 120 V = 8333A

I'm stumped on the second part of the question and hence, I can't move on to the next parts...
Any help is appreciated, thanks!

 

[NascentOxygen]

Hi jenn123. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

You've worked out the current, so now work out what voltage is required for it to be 1.1MW

 

[Jenn123]

Hi there,

Thank you for replying. I've tried and came up with an answer of 132V which I was quite uncertain of because it didn't seem like the generator voltage should be that low...

 

[haruspex]

Hi there,

Thank you for replying. I've tried and came up with an answer of 132V which I was quite uncertain of because it didn't seem like the generator voltage should be that low...

Yes, it's unrealistic, but follows directly from:

Assume answer to part (1) is the current flowing along the transmission lines

 

[Jenn123]

Alright! I should be able to solve the rest myself. Thank you so much for all the help and for confirming my doubts with the problem!

 

[davenn]

Hi there,

Thank you for replying. I've tried and came up with an answer of 132V which I was quite uncertain of because it didn't seem like the generator voltage should be that low...

What you haven't considered is that the voltage supplied by the power station isn't 120 ( or something close to that) Volts
the main national grids are usually up around 220 kV. it gets stepped down to several 1000 V at the town for distribution around the town
then stepped down again to 120V on a street by street ( or block by block) basis

The generators at the power station may be running in 100's of volts. It gets stepped up at the power station to that 220kV for transmission over any distance

As haruspex say ... your stated problem is an unrealistic situation, not found in real life
but doesn't stop you finding an answer ( for the stated situation) with the information you were given

Dave

 

[haruspex]

What you haven't considered is that the voltage supplied by the power station isn't 120 ( or something close to that) Volts
the main national grids are usually up around 220 kV.

Not sure what point you are making. It seems to me Jenn123 did indeed consider that, and was consequently surprised by the numerical answer to the question.