Current Flowing through High Voltage AC Transmission Lines

[Dave Johnson]

Homework Statement

Q1: A power plant produces energy at a voltage of Vi = 18667 V. Before being sent along long distance power lines this electricity is sent through a transformer with 143 turns in the primary coil and 8971 turns in the secondary coil.

Voltage is calculated to be 1171060.538V

If the wires have an efficiency of 99.60% and a resistance of 1096 Ω, what current flows through these wires?

Homework Equations

V = IR

The Attempt at a Solution

I = VR = 1171060.538 / 1096 = 1068A
1068A x 0.996 = 1064A

However, answer is wrong. Can anyone point out my mistake?

 

[haruspex]

I = VR = 1171060.538 / 1096 = 1068A

That calculation tells you the current that would flow if the wires were tied together at the other end, i.e. no other load in the circuit. The consequences would be most unfortunate.

1068A x 0.996 = 1064A

That makes even less sense. Inefficiency in the wires does not mean electrons disappear along the way. Current in = current out.

Any other ideas?

 

[Chandra Prayaga]

What is this thing called the efficiency of the wires?

 

[Vriska]

o

That calculation tells you the current that would flow if the wires were tied together at the other end, i.e. no other load in the circuit. The consequences would be most unfortunate.

That makes even less sense. Inefficiency in the wires does not mean electrons disappear along the way. Current in = current out.

Any other ideas?

what do you mean current when both ends are connected? what are they asking if not maximum current flow?

##spoiler
I thought the reason OP got his answer wrong was because he didn't take into account impedence scaling by transformer.
ie : R1/R2 = square of turns ratio.

 

[gneill]

what do you mean current when both ends are connected? what are they asking if not maximum current flow?

They did not mention maximum current flow, nor the maximum power transfer theorem. This problem hinges on an understanding of what is meant by "efficiency of the wires". The OP needs to root out a definition from his text or course notes.

 

[haruspex]

what do you mean current when both ends are connected? what are they asking if not maximum current flow?

No current flows unless there is a circuit. Nobody in their right mind connects the line directly to the neutral without a fat resistor in between. Somewhere out there in the grid there is a real load, with a big voltage drop across it.
The power lines have resistance too. With the efficiency as given, how much of the total voltage drop is caused by the wires?

 

[Vriska]

No current flows unless there is a circuit. Nobody in their right mind connects the line directly to the neutral without a fat resistor in between. Somewhere out there in the grid there is a real load, with a big voltage drop across it.
The power lines have resistance too. With the efficiency as given, how much of the total voltage drop is caused by the wires?

woh thanks, I didn't see the response but I was thinking of this problem again so I can back to see if OP got answered.

so they mean something like (voltage on thing being driven) /(voltage that should actually be there (eg 220)? ,if that were the case you could find the load?

What about generator impedence multiplication though?

 

[haruspex]

so they mean something like (voltage on thing being driven) /(voltage that should actually be there

yes, but not 220V. It's the voltage you calculated.

What about generator impedence multiplication though?

I don't think you have enough information to take impedance into account. But it would be more a question of impedance of the load, no?

 

[Alloymouse]

Perhaps the OP could consider using the power equations instead of just Ohm's Law. Also, a sanity check would be that the current flowing through wires is really small, so as to minimise power losses such as by Joule Heating.