Power, Resistance of cables?

Question

Copper and Aluminum are being considered for the cables in a high-voltage transmission line where each must carry a current of 50A. The resistance of each cable is to be .15ohms per kilometer.

A. If the line carries power from Niagra Falls to New York (500Km), mow much power is lost along the way in the cable?


Compute for each choice of cable material
B. the necessary cable diameter

C. mass per meter of cable

Please correct if you see anything that may be off
Solving for part a:
Power = I deltaV, since deltaV was not given IR=deltaV
so
Power = (I^2)R = 50^2 x 75 = 187.5 kW <-- answer
R= 75 since R= .15 ohms/ km x 500km

B) resistivity of copper = 1.7 x 10^-8 ohm m
resistivity of al = 2.82 x 10^-8 ohm m
R = (resistivity x length)/Area
what do i use for R? is it the 0.15 ohm/km or 75 ohm?

using the 75 ohm as R, I get that the radius of the copper wire is 0.0000361 m and the diameter is then 0.0000722.
Am i on the right track?

Answer 1

a) Power = (Current) (Voltage) = (Current)^2 / (Resistance)
You got it good job

b) I would rearrange your equation a bit to minimize computation.

R = (resistivity x length) / Area
Therefore
(R / l) = (rho) / A
They give you (R/I) = 0.15 ohms/km and they give you rho.
Just solve for A. Your way of doing the calculation in bits (finding R and then finding A) is good, too, though. I didn't actually check your numbers. The only pitfall would be forgetting to convert km to m.

Answer 2

As the resistivity of copper and aluminum are different,to have the the same resistance,the sections are different.
The losses per cable are Ri^2 = 0.15*500*50^2
( just for the sake of completness,the power transmission lines have three cables)
If you take lenght 1km you have to use0.15
ohm,which is the same as using 500km and R =75 ohm
Be careful to use the same units of lenght in resistivity and distance.
You are on the right track

Answer 3

I think you went wrong with the length. If R= (resistivity x length)/Area, make sure you are using length as 500,000m as the units should be in meters, not km. R is going to be 75 ohms because you are considering the entire length. Then solve for area and radius.

Answer 4

a three middle 1100 volt cable will choose an insulation resistance of two to three meg-ohms making use of a 1000volt megger tester. the rule of thumb is the cable must have a minimum of one million meg-ohm in preserving with kv score.