Electrical Network Problem: Power Transfer

In summary, when all three voltage sources are working simultaneously, the power dissipated is 450W (max) and 2W (min).
  • #1

cnh1995

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Homework Statement


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Homework Equations


P=V2/R
For maximum power transfer,
Rload=RThevenin

The Attempt at a Solution


I know the efficiency is 50% during maximum power transfer. So when all the sources are acting simultaneously and ( at the same time) R=Rth, maximum power will be dissipated in R.
I am not sure how to use the given values of power since both R and the source voltages are unknown. Plus, the voltage sources are connected across three different ports. This problem is from Circuit Theorems chapter, so I guess I need to use Maximum power transfer theorem along with Superposition theorem.
Any guidance is appreciated.
 

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  • #2
cnh1995 said:
For maximum power transfer,
Rload=RThevenin
I don't think this is relevant here. That equation says how to adjust the load to get maximum power transfer into it.
Consider that the direction of current might change between the three given power results.
 
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  • #3
haruspex said:
Consider that the direction of current might change between the three given power results.
Yes, but I don't know how to relate the three power results. I can't directly add/subtract the power results since I don't know the network inside the box. I think I need to set up an equation using some sort of proportionality (P∝V2 for instance).
The answer given is 450W (max) and 2W (min).
Do I need to use any specific network theorem here?
 
  • #4
cnh1995 said:
Yes, but I don't know how to relate the three power results. I can't directly add/subtract the power results since I don't know the network inside the box. I think I need to set up an equation using some sort of proportionality (P∝V2 for instance).
The answer given is 450W (max) and 2W (min).
Do I need to use any specific network theorem here?
Plus, when they say 'one source is acting at a time', do I open-circuit the other two sources or short them?
I now doubt if this problem is solvable with the given data.
 
  • #5
cnh1995 said:
Plus, when they say 'one source is acting at a time', do I open-circuit the other two sources or short them?
Presumably they mean to suppress the sources as is done in superposition analysis. So, short them since they are voltage sources.

Suppose that each individual source produces some potential difference across R. By superposition you know that these potential differences will sum linearly, and the resulting power will go as the square of that sum. But you are given individual power dissipations instead. How might you sum them?
 
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  • #6
gneill said:
Presumably they mean to suppress the sources as is done in superposition analysis. So, short them since they are voltage sources.

Suppose that each individual source produces some potential difference across R. By superposition you know that these potential differences will sum linearly, and the resulting power will go as the square of that sum. But you are given individual power dissipations instead. How might you sum them?
If E1, E2 and E3 produce voltages V1, V2 and V3 respectively across R individually, then in combined case,
P=V2/R,
where V=aV1+bV2+cV3.
Is that right?
 
  • #7
cnh1995 said:
If E1, E2 and E3 produce voltages V1, V2 and V3 respectively across R individually, then in combined case,
P=V2/R,
where V=aV1+bV2+cV3.
Is that right?
Yes. You can also say that the individual potential differences expressed across R will be proportional to the square root of the individual powers.
 
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  • #8
cnh1995 said:
If E1, E2 and E3 produce voltages V1, V2 and V3 respectively across R individually, then in combined case,
P=V2/R,
where V=aV1+bV2+cV3.
Is that right?
That looks reasonable, but there are limits on a, b and c.
 
  • #9
As per post 7, given the termination has some ## R_o ##, ## P_a=\frac{V_a^2}{R_o} ##, ##P_b=\frac{V_b^2}{R_o} ##, and ## P_c=\frac{V_c^2}{R_o} ##. A little algebra gives ## \sqrt{P_a}+\sqrt{P_b}+\sqrt{P_c}=\frac{V_a+V_b+V_c}{\sqrt{R_o}}=\frac{V_{total}}{\sqrt{R_o}} ##. It is a simple matter to compute ## P_{total} ## by squaring both sides. ## \\ ## Edit: One additional item though: What if the sign of ## V_b ## or ## V_c ## is different from that of ## V_a ##? The above equality doesn't always hold. That's apparently why there is a maximum and a minimum. ## \\ ## Additional edit: And yes, I get the answers of post 3 by selecting the appropriate relative signs for the 3 terms.
 
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  • #10
Sorry for replying so late!

Thanks a lot @gneill, @Charles Link and @haruspex for your clever hints. Turns out what I really need here is only the Superposition theorem. I got the correct answer now.
Thanks again!:smile:
 
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1. How does an electrical network transfer power?

An electrical network transfers power through the flow of electrons. When a power source, such as a battery or generator, is connected to a network of conductors, the electrons move from the negative terminal of the source to the positive terminal, creating an electric current. This current can then be used to power devices connected to the network.

2. What is the difference between AC and DC power transfer in an electrical network?

AC (alternating current) power transfer involves the flow of electrons that constantly changes direction, while DC (direct current) power transfer involves the flow of electrons in one direction. AC power is typically used for long-distance power transmission, while DC power is more commonly used for electronic devices and small-scale power transfer.

3. How can power loss be minimized in an electrical network?

Power loss in an electrical network can be minimized by using high-quality conductors with low resistance, reducing the length of the network, and minimizing the number of connections and junctions. Proper maintenance and regular inspections can also help to identify and repair any issues that may cause power loss.

4. What is the role of transformers in power transfer within an electrical network?

Transformers are essential components in an electrical network that help to regulate the voltage levels of the power being transferred. They can step up or step down the voltage to match the specific requirements of different devices and systems connected to the network. This helps to ensure efficient and safe power transfer.

5. What are some common problems that can occur in an electrical network and how can they be resolved?

Some common problems in an electrical network include power surges, circuit overloads, and faulty connections. These issues can be resolved by installing surge protectors, using properly sized circuit breakers, and regularly checking and repairing any damaged or loose connections. It is important to consult a professional electrician for complex network issues.

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