Power Supplied by Current Source: Solution is Wrong?

Discussion in 'Homework Help' started by ElectronicGuru, Sep 26, 2014.

  1. ElectronicGuru

    Thread Starter New Member

    Sep 26, 2014
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    In this question, I have to determine the power supplied by the 1 A current source. So, using nodal analysis, I determine Vy to be 794/25 V, as given in the solutions.
    Screen Shot 2014-09-26 at 9.50.06 PM.png

    However, the solution for the power supplied by the current source is the following:
    Screen Shot 2014-09-26 at 9.50.15 PM.png

    Why is it negative? As I understand it, an element supplies positive power if positive current flows out of the positive voltage terminal. That's what I'm seeing: the current source is pointing upwards where Vy's positive terminal should be (since Vy was found to have a positive voltage with respect to the ground). Am I missing something incredibly obvious or is this solution incorrect?

    Thanks for any help in advance.
     
  2. JoeJester

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    What did your book state about why it's -Vy in the formula?
     
  3. t_n_k

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    One normally adopts the PSC - Passive Sign Convention.
    Google for details - Wikipedia for example.
     
  4. ElectronicGuru

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    Yes, I know about PSC. But this is about the power supplied by the current source, not delivered to it. So PSC doesn't apply here, no?
     
  5. ElectronicGuru

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    Unfortunately, there is no explanation given. And I can't ask anyone because I'm doing self-study (or review of my previous course, to be more accurate).
     
  6. t_n_k

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    It does apply .....
    For a source, the power delivered is the negative of the VI product with V & I marked according to the passive sign convention. So the answer given [the -ve sign part] is therefore incorrect, as you have suggested.
     
  7. The Electrician

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    It seems to me that there is an internal contradiction in the red phrase above.

    According to the passive sign convention (http://en.wikipedia.org/wiki/Passive_sign_convention) if an element supplies power, the sign of that power is taken to be negative, so an element can't supply positive power.
     
  8. ElectronicGuru

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    But you have to remember that PSC assumes that a positive current flows into the positive voltage terminal. So yes, using PSC, supplied power would be negative. However, in the case of this source, we'd have to flip the 1 A current direction to be going downward so as to satisfy PSC; therefore, this results in two negatives that cancel each other out.

    The statement I made (taken from my book) is simply another way of stating this.
     
  9. The Electrician

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    You asked "Why is it negative?". It's negative because power supplied by a source is negative.

    Then you offered a comment containing the contradictory phrase I pointed out earlier (which as I consider it further, contains another contradictory phrase): "As I understand it, an element supplies positive power if positive current flows out of the positive voltage terminal."

    About halfway down the referenced Wikipedia page we find:

    "Passive sign convention: Defining the current variable as entering the positive terminal means that if the voltage and current variables have positive values, current flows from the positive to the negative terminal, doing work on the component, as occurs in a passive component. So power flowing into the component from the line is defined as positive; the power variable represents power dissipation in the component. Therefore
      • Active components (power sources) will have negative resistance and negative power flow
      • Passive components (loads) will have positive resistance and positive power flow
    This is the convention normally used."

    If you use the PSC, it's contradictory to say : "positive current flows out of the positive voltage terminal". The reference direction under the PSC is that positive current is current into the positive voltage terminal. Current flowing out of the positive voltage terminal is, by definition, negative current.

    What should be said is : "As I understand it, an element supplies negative power if current flows out of the positive voltage terminal."

    You asked if the solution was incorrect. The solution obtained a result of -31.76 W. The power supplied by a source should be negative, which is what the book solution got. It appears that you agree that the power supplied by a source should have a negative sign. Now, it's possible that the book solution used an incorrect method to obtain that result, so let's consider that possibility.

    You don't flip anything to satisfy PSC. You just look at the direction of the current in the circuit element. In the case of the 1 amp current source, the current flows out of the positive terminal. This is opposite to the reference direction defined by the PSC, so it takes a negative sign (for the purpose of calculating power flow). The power associated with the 1 amp current source is given by I*V, which in this case is -1*794/25 = -31.76 W
     
  10. t_n_k

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    It seems to me this boils down to semantics - power "absorbed" or power "supplied". With respect to PSC one is specific about which term is applied. If the original question was what is the power absorbed or dissipated (rather than supplied) by the 1A source then I would agree with the negative sign.
     
  11. The Electrician

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    Of course it's semantics.

    If one says +1 watt is being supplied by a source, that could be the same as saying -1 watt is being absorbed by a source. If +1 watt is being absorbed by a resistor, is that the same as saying -1 watt is being supplied by the resistor?

    Consider a power of ±|1| watt (magnitude of 1). The sign of the power tells you the direction of power flow. Now, add in the effect of the words "absorbed" and "supplied"; they can be taken to reverse the effect of the sign.

    One shouldn' t use the words "absorbed" and "supplied" together with the sign. Pick one or the other usage, otherwise confusion ensues. Either use the words, with the understanding that the numeric value of the power is a unsigned magnitude, or use the sign (and don't use the words "absorbed" or "supplied" at the same time), to indicate the direction of power flow .

    That's why I said "power associated" (in accordance with the PSC) with the 1 amp source. Then the sign tells you whether the power is being absorbed or supplied.
     
  12. JoeJester

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    Here is an example .... From the prospective of supplying a power, I can see the 1 W as being negative, using electron flow. The 1W dissipated by the resistor certainly is shown as a positive 1 W.
     
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  13. t_n_k

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    "One shouldn' t use the words "absorbed" and "supplied" together with the sign."

    That certainly makes sense.
    Perhaps that point should be made to those textbook authors writing on PSC who fall into the "trap" of basing the sign on the nomenclature.
    Mind you, this apparent confusion existed in the writing of the eminent educator Ronald E. Scott.
    I quote from his text "Linear Circuits" second edition [1964] - chapter 6 "Power and Energy in Resistive Circuits" Section 6.1 page 195 ...

    "The net power absorbed by the sources is thus -52 watts, or the power supplied by the sources is +52 watts"
     
    Last edited: Sep 28, 2014
  14. MrAl

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    Jun 17, 2014
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    Hello there,

    The question was already answered in the first post where i (shorter) quote:
    "...the solution for the power supplied by the current source is the following: -31.76 amps"

    Following the book exactly, that means they are using the negative sign convention to indicate power supplied by a source. If that is the same wording as in the book itself, then i seriously doubt they would have went through the trouble to include the negative sign if they did not mean it.
    Following the book and proving that the source is really delivering power and not absorbing it, we can prove the books convention is negative to indicate power supplied.
    If there is still a question after this then the only way to find the answer is to look in the book and find out what their method states as to how to take this. They will probably be consistent, so if they use a negative sign now they probably did it before too and it might have been more obvious then why they did it that way.

    However, we can prove that the 1 amp source is really delivering power and not absorbing it by turning to the more physical view. The electrical view is just an interpretation of the real physical view, so doing this will eliminate the semantics because we can then apply our own.

    The way to do this is to simply add up the power from all the sources, and add up all the power being absorbed by resistive components. It does not matter what semantics you apply as long as you are consistent. The power supplied will equal the power absorbed.
    Doing this we see that all three sources are delivering power to the circuit, and that total power is around 300 watts. That means the resistances absorb around 300 watts and only the resistors absorb power, none of the sources absorb power.
    Because of this the book must be using the negative sign convention to indicate power supplied to a load.
     
    Last edited: Sep 28, 2014
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  15. t_n_k

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  16. MrAl

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    Hi,

    Haha, that's funny, no doubt to buy some positive products.. It's nice to see a little humor once in a while. Another little funny take on an old joke with this circuit is, if we ask a source if it is delivering power and it says "no", then we know it is because "Whoever denied it supplied it" :)
     
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  17. JoeJester

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    In double entry accounting, a debit increases the asset account. A credit decreases it. So debit your checking/savings account.
     
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  18. MrAl

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    Hi,

    In my checking account program i make all extractions (such as payments, checks written, etc.) show up as negative with the sign, and all deposits (or refunds) show up as positive but without the sign. So a check would appears as "-23.00" while a deposit would appear as "23.00".
    I could easily see doing it using the credit/debit way where then it would have another column to show credit or debit, so a check would show up as "debit 23.00" and a deposit as "credit 23.00", but i like the sign idea better simply because it's shorter and then adding all the entries gives the final balance without having to interpret any other text.

    I have always taken power absorbed and power delivered to be both positive, and so just holding them as one generated and the other consumed. I can see how signed power can come in handy, but i dont really like looking at it that way (see below). In a program though we might not have any choice if we wanted to sum them as a check for accuracy.

    Interestingly, in efficiency calculations they are always positive:
    Eff=Pout/Pin
    yet Pin comes from some source while Pout is absorbed Using the sign convention we'd end up with a negative efficiency :)
     
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