- #1
rdjohns12
- 2
- 2
- Homework Statement
- A small city requires about 15 MW of power. Suppose that
instead of using high-voltage lines to supply the power, the
power is delivered at 120 V. Assuming a two-wire line of
0.50-cm-diameter copper wire, estimate the cost of the
energy lost to heat per hour per meter. Assume the cost of
electricity is about 9.0 cents per kWh.
- Relevant Equations
- [tex] P=IV [/tex]
[tex] P=I^2R [/tex]
[tex] R=\rho\ell/A [/tex]
This problem is trivial, but I cannot make sense of my answer (I am not even going to bother with the cost calculation.
First, I used [tex] P=IV [/tex] with P=15 MW and V=120 V to find I=125 kA
So far so good. Then I calculated the resistance per meter as [tex] R=\rho\ell/A=(1.68\times 10^8\Omega\cdot m)(2m)/(\pi(0.005m/2)^2) =1.68m\Omega[/tex]
Now, I calculate the power per meter dissipated in the transmission line as [tex] P=I^2R=(125 kA)^2(1.68m\Omega)=27 MW [/tex] I have checked the solutions manual and so I am certain this value is correct.
This does not make sense to me. In my understanding, we started with the assumption that the transmission line losses were going to be small enough that we could use [tex] P=IV [/tex] where P was both the power from the plant and the approximate power delivered to the city, but now we are finding line losses that are nearly double that power.
I could, obviously, go ahead and calculate the voltage drop across 1 m with [tex] V=IR=(125kA)(1.68m\Omega)=200V[/tex] which is larger than 120V.
Is this problem poorly thought out, or do I fundamentally not understand something?
First, I used [tex] P=IV [/tex] with P=15 MW and V=120 V to find I=125 kA
So far so good. Then I calculated the resistance per meter as [tex] R=\rho\ell/A=(1.68\times 10^8\Omega\cdot m)(2m)/(\pi(0.005m/2)^2) =1.68m\Omega[/tex]
Now, I calculate the power per meter dissipated in the transmission line as [tex] P=I^2R=(125 kA)^2(1.68m\Omega)=27 MW [/tex] I have checked the solutions manual and so I am certain this value is correct.
This does not make sense to me. In my understanding, we started with the assumption that the transmission line losses were going to be small enough that we could use [tex] P=IV [/tex] where P was both the power from the plant and the approximate power delivered to the city, but now we are finding line losses that are nearly double that power.
I could, obviously, go ahead and calculate the voltage drop across 1 m with [tex] V=IR=(125kA)(1.68m\Omega)=200V[/tex] which is larger than 120V.
Is this problem poorly thought out, or do I fundamentally not understand something?