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Circuits question: Current

  1. Jan 29, 2013 #1
    I attached the circuit. I'm trying to solve for V_out, but I'm stuck.
    I can solve for it using mesh analysis, but there must be an easier way. I just don't see it yet. Can anyone give me a hint?
     

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    Last edited: Jan 29, 2013
  2. jcsd
  3. Jan 29, 2013 #2

    SammyS

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    attachment.php?attachmentid=55191&d=1359520682.png
    Use Kirchhoff's Laws.

    I don't know that it's any easier than mesh analysis.
     
  4. Jan 29, 2013 #3

    rollingstein

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    To me simplest seems using the Superposition Theorem.
     
  5. Jan 30, 2013 #4
    I used mesh analysis. Can someone verify if my answer at the bottom is correct?

    Here's what I did using mesh analysis:
    1. For the 3 closed loops, assume each loop has a clockwise current
    2. I1 is the left loop's current, I2 is the middle, and I3 is the right

    Given:
    R1=1000Ω R2=2000Ω R3=3000Ω R4=4000Ω
    V1=V3=10V, V2=5V

    For loop 1 (left):
    -1000*I_1-10=0
    -1000*I_1=10

    For loop 2 (mid):
    10-2000I2-3000I2+3000I3=0
    -5000I+3000I3=-10

    For loop 3:
    -3000I3+3000I2-10-4000I3+5=0
    3000I2-7000I3=-5


    Putting this in matrix form and solving gives:
    I1=-0.01A, I2=2.1mA, I3=1.923*10^-4A



    Vout-R4*I3+V2=0
    Vout=4000*1.923*10^-4 - 5
    = -4.2308V

    With the way Vout is drawn, it should be negative right?
     
  6. Jan 30, 2013 #5

    SammyS

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    Yes, that's correct.

    Notice that you didn't need to consider Loop 1 at all.
     
  7. Jan 30, 2013 #6

    rollingstein

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    This was how I did it. Same answer.

    wleJKO4.png
     
  8. Jan 30, 2013 #7

    gneill

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    If you recognize that R1 is "hidden" from the rest of the circuit by V1 (and so can be eliminated from the circuit entirely), and that V3 forms a supernode of Vout, you can write a single node equation and solve for Vout.

    attachment.php?attachmentid=55198&stc=1&d=1359558784.gif
     

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  9. Jan 30, 2013 #8
    Thank you everyone!

    The second part of the question asks what the power produced by each voltage source is.
    This is easy with the equation P=IV.

    The exact wording is "What's the power produced by each source."

    Generally speaking, if a current enters the positive terminal of the voltage source that means the power is positive, right?

    If a current enters the negative terminal of the voltage source that means the power is negative?

    For V_1, the net current enters the negative terminal of V_1.
     
  10. Jan 30, 2013 #9

    gneill

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    If current exits the + terminal of a voltage source it is producing power (injecting energy into the circuit). If current enters the + terminal it is absorbing power (taking power out of the circuit). Whether you call the power positive or negative depends upon your point of view: are you adding up power being dissipated or power being generated?
     
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