Electric Current Power Plant problem

[xaer04]

[SOLVED] Electric Current

Homework Statement

"A power plant produces 1000 MW to supply a city 40km away. Current flows from the power plant on a single wire of resistance .050[itex]\Omega/km[/tex], through the city, and returns via the ground, assumed to have negligible resistance. At the power plant the voltage between the wire and ground is 115kV. a.) What is the current in the wire? b.) What fraction of the power is lost in transmission?"

Initial Power [itex]= P_0 = 1.0x10^9[/itex]
Wire length [itex]= L = 40km[/itex]
Resistance per unit length [itex]= R/L = .050 \Omega /km[/itex]
->Resistance for 40km wire [itex]= 2\Omega[/itex]
Voltage between wire and ground [itex] = 115x10^3V[/itex]

Homework Equations

Electric Power
[tex]P = IV[/tex]
[tex]P = I^2 R[/tex]
[tex]P = \frac{V^2}{R}[/tex]

Electric Current
[tex]I=\frac{V}{R}[/tex]

The Attempt at a Solution

I tried several of these and got all different answers.
[tex]I = P/V = \frac{1x10^9W}{1.15x10^5V} = 8695.7 A[/tex]
[tex]I = \sqrt{P/R} = \sqrt{(1x10^9W)/(2\Omega)} = 22360.7 A[/tex]
[tex]I = V/R = (1.15x10^5V)/(2\Omega) = 57500 A[/tex]

I couldn't even get the power to work out using the remaining Power equation, reliant on Volts and Resistance.
[tex]P = (V^2)/(R) = (1.15x10^5V)^2/(2\Omega) = 6.61x10^9W[/tex]

Please help me understand this:(

 

[Astronuc]

OK, one cannot use the line-to-ground voltage V (115 kV) with R in I=V/R because the voltage drop along the line is not 115 kV. The voltage drop along the line is IR << V. The V (115 kV) is the voltage drop across the load, not along the line.

Similarly P is not the power dissipated along the line. P = VI is the power generated and supplied (with some loss) to the load.

So find I from P/V and then use that I to find the voltage drop along the line IR, and compare to 1000 MW (1 GW). The power dissipated by the line is then I²R.

 

[xaer04]

ah... thank you very much:)

 

[christiem0269]

I still cannot figure out how to do this problem.
I have:
L=40 km
R = 0.050 ohm/km
P = 1000 MW
I = P/V ; at 40 km R=2 ohm; V= 115kV

I = 1000/115?

Am I going about this wrong? What should I do next?

 

[rwisz]

It seems like you have already found the correct value for the current, which is 57500 A. This can be calculated using Ohm's Law, I=V/R, where V is the voltage and R is the total resistance of the wire (2\Omega). Your other attempts at solving for the current may have used incorrect values for the voltage or resistance.

To calculate the power lost in transmission, we can use the formula P=I^2R, where I is the current and R is the resistance of the wire. Plugging in our values, we get P=(57500 A)^2 x 2\Omega = 6.61x10^9 W.

To find the fraction of power lost in transmission, we can compare the initial power (1.0x10^9 W) to the power lost (6.61x10^9 W). This gives us a fraction of 6.61/10 = 0.661, meaning that about 66.1% of the initial power is lost during transmission. This is not uncommon in power plants, as energy is often lost due to resistance in the wires and other factors.

I hope this helps clarify the solution to this problem. If you have any further questions, please let me know.