Calculating Power Dissipated in Sources

Discussion in 'Homework Help' started by CaptinKirk, Oct 12, 2016.

  1. CaptinKirk

    Thread Starter New Member

    Oct 12, 2016
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    Hello,

    I am asked to calculate the power dissipated in voltage sources in the following picture
    [​IMG]

    Firstly, I'm gonna need the current, using KVL I'll get that I = -2A
    Now, calculating the power ( P = IV) and following the passive sign convention I'll yield that
    P(-8) = -16W
    P(12) = 24W
    P(10) = -10W

    but comparing my solution to the solution manual
    p(-8) = 16W
    p(12) = -24W
    p(10) = 20W

    I am so confused, if any one could explain why I got those results that'd be appreciated.
     
  2. Picbuster

    Member

    Dec 2, 2013
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    calculate current = sum (batt's)/R = 8+12-10/3= 10V/3R Amp ( -8V is wrong should be +8V and 10V is opposite connected)
    P=I*U
    You do the rest.
    PB
     
  3. WBahn

    Moderator

    Mar 31, 2012
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    On what basis do you assert that the -8 V is wrong?

    The diagram clearly shows that the voltage of the bottom source is set to -8 V. What's wrong about that?

    I can easily take three suitable bench supplies and hook them up that way and set their outputs to those voltages and connect them to that resistance (though I would much prefer to work with something more along the lines of 300 Ω or 3 kΩ).
     
  4. WBahn

    Moderator

    Mar 31, 2012
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    There are two (dominant) interpretations of the passive sign convention when it comes to sources. On is that you simply ignore whether a component should be a source or a load and you assign the current for it to be such that positive current leaves the positive terminal. Thus if the power is positive it is absorbing power and if it is negative it is supplying power. In this interpretation the sum of all powers for all components is zero. The other is that you categorize each component as either a supply or a load (it doesn't matter if you are right or wrong, you just have to choose) and then you assign current directions for each component such that positive power for a supply means it is supplying power and positive power for a load means that it is absorbing power. In this interpretation the sum of the powers from the supplies equals the sum of the powers from the loads.

    So the real questions are:

    1) Which interpretation are YOU using? It appears that you are using the first.

    2) Which interpretation is the AUTHOR using? It appears that they are using the second.

    As for the numerical value on the 10 V source, you just need to review what the product of -2 A and +10 V is.

    A useful check is to see what the power being dissipated in the resistor is (which should be trivially easy to determine) and then see if the total power in the circuit balances out. Your sources have a net imbalance of 2 W. The author's solution has a net imbalance for the sources of 12 W. Which of these, if either, is consistent with the power being delivered to the resistor?
     
  5. WBahn

    Moderator

    Mar 31, 2012
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    MOD NOTE: Moved to Homework Help
     
  6. DGElder

    Member

    Apr 3, 2016
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    First could you quote exactly the text's question? This is what determines the sign. If it was phrased the way you wrote it then
    the text answers are wrong - the signs are reversed. (Yours are correct except the 10V source is dissipating -20W, not -10W) Your power signs (if for power flow) are following the passive sign convention. In that convention dissipation gets a positive sign, delivery gets negative sign. I don't know if that is the convention the text uses, but the question as you phrased it did not ask for power flow, it asked for power dissipation so it doesn't matter what convention you use.

    Clearly the 8 and 10V sources are delivering 16W and 20W of power respectively which is being dissipated in the 12V supply and the 3 ohm resistor. Regardless of what sign convention you use, dissipating has a clear physical meaning. If the text says an element is dissipating -24W then it is saying it is delivering 24W power - which is not what is happening here.
     
    Last edited: Oct 12, 2016
  7. WBahn

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    Mar 31, 2012
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    I agree with DGElder. I overlooked the fact that the question (as paraphrased by you) specifically asks for the power that each source is dissipating. This wording means that a positive answer means that the source is dissipating (absorbing) power while a negative answer means that it is supplying power. Since there is a resistor in the circuit we know that, overall, the sources must be supplying net power, so they are, overall, dissipating negative power. Hence the sum of all the power dissipated by all the sources must be negative.

    If the question wording only asks for the power in each source, then that is a different matter.
     
  8. MrChips

    Moderator

    Oct 2, 2009
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    Here are four symbols. Try to figure out what each one means, that is, is the left terminal more positive or less positive that the right terminal?

    upload_2016-10-12_18-49-19.png
     
  9. Picbuster

    Member

    Dec 2, 2013
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    not in line with drawing
     
  10. WBahn

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    Mar 31, 2012
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    What does that mean?

    The drawing clearly shows that the bottom source is outputting -8 V meaning that the left node (+) is 8 V lower than the right node (-). You stated that this is wrong and that it is +8 V. What is that claim based on?
     
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