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I had a question in class that went :

$120$kW of power is generated at a power plant and is then transmitted. The resistance in the transmission lines is $0.4 \Omega$. Calculate the power lost as heat for the following transmission voltages.

a) $240$V

b) $24,000$V

What exactly is meant by the transmission voltages? Are they the voltage drop across the transmission lines or the voltage drop between the output end of the power plant and the receiving end?

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    $\begingroup$ It sounds somewhat ironic that the "transmission voltage" means the latter in this case - the potential difference measured directly across the terminals of the power plant. In other words, the "transmission voltage" is the voltage in the absence of transmission. $\endgroup$
    – Steve
    Commented Apr 24, 2020 at 13:26

3 Answers 3

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Transmission voltages mean what is the voltage of the live wire coming out of power plant. Two wires come out of the power plant, one is live wire and another wire is neutral/earth ("The earth is a pretty good conductor and it is huge, so it makes a good return path for electrons."Qouted).

There is some voltage given to the live wire (output end),while neutral wire (receiving end) is at 0V. So, the transmission voltage is the voltage difference between output and receiving end.

Now, power plant is generating 120KW of power. If power is generated it has to be stored or consumed, there is nothing about storing in the problem, so all power has to be consumed.

Voltage is constant across the line for particular case and we know

Power consumed(P) = Voltage(V) * Current(I)

So, you can calculate the current in the wire required to consume all the power generated using the above formula.

To calculate power loss in transmission line having resistance R = 0.4 ohm, you can use the following formula

P = I^2 * R

This power loss is in the transmission lines only, and only the leftover power can be used in houses, industries, etc.

Now, you can calculate and compare power loss in transmission lines for the cases and analyse the results.


Here I am considering single phase output from the power plant.


If you have any confusion or need clarification you can comment to this answer.

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  • $\begingroup$ Another part I was confused about is when you do V=IR. In part a) for example, when you do V=IR you get V=(500A)(0.4 ohms)= 200V which doesn't equal 240V. Is the 200V the voltage drop across the wire whereas the 240V is the voltage drop across the entire system. $\endgroup$
    – keeram
    Commented Apr 23, 2020 at 22:51
  • $\begingroup$ I'm temporarily deleting this in accordance with our homework policy. Please don't post complete answers to the underlying problem in homework-like questions. $\endgroup$
    – David Z
    Commented Apr 24, 2020 at 5:26
  • $\begingroup$ Editing out the details isn't enough to get it back right now -- the revision history still contains the complete solution and so undeleting it would still make the full answer available. The only choice is to wait awhile (several weeks, at least) and if you want it undeleted after it is no longer useful as a homework answer, you can raise a flag for us to look at it. See this discussion for more context. $\endgroup$
    – tpg2114
    Commented Apr 25, 2020 at 13:53
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The transmission voltage ist the voltage which is supplied at the beginning, if no current flows it will be the same at the end, but you want to transmit 120kW.

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The transmission voltage is the (nominal) potential difference between the transmission line and the earth. That is, it's the voltage you'd measure between an active transmission line and the ground, near the generator, assuming there's no other load on the line.

To solve your problem, you need to calculate the current, given the generated power and the transmission voltage, and then use that current and the resistance to calculate the power lost.

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  • $\begingroup$ I stand to be corrected, but I think what he's asking, is where do you measure the "transmission voltage"? 24kV at the far end of the transmission line, is not 24kV at the terminals of the generator. $\endgroup$
    – Steve
    Commented Apr 24, 2020 at 13:31
  • $\begingroup$ @Steve Fair point. I've added a little more detail to my answer. Of course, in reality, things are more complicated. Transmission lines don't normally just sit there with no load, and generator operators need to adjust the generator to compensate for load variations, and the power factor. Also, power stations normally produce 3 phase power, and quoted voltages normally refer to the voltage between phases, rather than from an active phase to ground, except when talking about the final low voltage supplied to the consumer. But all that stuff is irrelevant to solving the OP's problem. $\endgroup$
    – PM 2Ring
    Commented Apr 24, 2020 at 13:40
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    $\begingroup$ Agreed. Real power generation is a complicated balancing act. I suspect the OP has asked the question because he's trying to develop an understanding which is capable of solving this problem and others. Perhaps also, the educator who asked the question has unnecessarily complicated the setting of the problem - the same question could probably have been posed with a battery and a small table-top circuit, without the frippery of inviting students to think about real power generation situations. $\endgroup$
    – Steve
    Commented Apr 24, 2020 at 13:53

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