Current Flowing through High Voltage AC Transmission Lines

• Dave Johnson
In summary, the conversation discusses a problem involving a power plant producing energy at a voltage of 18667 V and the efficiency of the wires used to transmit this electricity. The problem also includes the use of a transformer with 143 turns in the primary coil and 8971 turns in the secondary coil. The calculation for the current flow through the wires is incorrect and the conversation suggests considering the power equations and using a sanity check to ensure minimal power losses.
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?

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?

Last edited by a moderator:
Dave Johnson said:
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.
Dave Johnson said:
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?

What is this thing called the efficiency of the wires?

gneill
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haruspex said:
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.

Vriska said:
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.

Vriska said:
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?

Merlin3189
haruspex said:
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?

Vriska said:
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.
Vriska said:
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?

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.

1. What is the purpose of high voltage AC transmission lines?

High voltage AC transmission lines are used to efficiently transport large amounts of electricity over long distances. This is essential for providing electricity to homes, businesses, and industries located far away from power plants.

2. How does electricity flow through high voltage AC transmission lines?

Electricity flows through high voltage AC transmission lines in the form of alternating current (AC). This means that the direction of the current changes back and forth at a specific frequency, typically 50 or 60 hertz. The electricity is carried by conductors, usually made of copper or aluminum, that are suspended on tall towers to minimize energy loss.

3. What factors affect the amount of current flowing through high voltage AC transmission lines?

The amount of current flowing through high voltage AC transmission lines is affected by several factors, including the voltage level, the resistance of the conductors, the distance of the transmission line, and the load (i.e. the amount of electricity being used) at the receiving end.

4. How is the voltage level of high voltage AC transmission lines determined?

The voltage level of high voltage AC transmission lines is determined based on the amount of electricity that needs to be transported and the distance it needs to travel. Higher voltage levels are used for longer distances to minimize energy loss. In the United States, the most common voltage levels for high voltage transmission lines are 345, 500, and 765 kilovolts.

5. What are the risks associated with high voltage AC transmission lines?

High voltage AC transmission lines can pose several risks, including electric shock, fire hazards, and electromagnetic fields that may interfere with electronic devices. Proper safety measures, such as keeping a safe distance from the transmission lines and following electrical safety protocols, should always be followed to minimize these risks.

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