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Homework Help: Superposition Circuits Problem

  1. Sep 19, 2010 #1
    1. The problem statement, all variables and given/known data
    Find v0 and i0
    [PLAIN]http://img214.imageshack.us/img214/2051/superquestion.jpg [Broken]


    2. Relevant equations
    KVL and KCL


    3. The attempt at a solution
    I removed the voltage source and redrew the circuit with a short on the bottom left. I then used mesh current analysis with KVL and made a system of equations. My problem is that all of my current (i0, i1, i2, i3) come out to 0 which is definitely wrong.

    Am I approaching this problem correctly and setting up my equations right?

    my work:
    http://img530.imageshack.us/img530/4779/superosition.jpg [Broken]
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 19, 2010 #2
    Looks like your on the right track! :)
     
  4. Sep 19, 2010 #3

    Delphi51

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    With the 180 V source shorted, call the current through the 60 ohm resistor i1 (upward). Then the sum of the voltages around the loop on the lower left is 60i1 + 30(i1 + 7.5) = 0. This yields i1 = -2.5A straightaway. You can actually see that without the equations - clearly 2/3 of the current will go through the 30 ohm resistor and 1/3 through the 60. Looks like you forgot to use the 7.5 amps in that loop, and in the others. Very tough to find i0 . . .
     
  5. Sep 19, 2010 #4

    rl.bhat

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    To solve the circuit by super position method, you should not close the voltage source and open the current source. Keep them as it is and apply KVL and XCL.
     
  6. Sep 19, 2010 #5
    I'm having a hard time understanding this, is my circuit drawing correct? Because isn't the 60 not just i1?, isn't it 60(i1-i0)?
     
  7. Sep 19, 2010 #6
    Isn't that what the superposition method is though? Closing independent sources and solving circuits with only one source at a time.

    So don't I need two separate circuits with only a current source or a voltage source?
     
  8. Sep 19, 2010 #7

    rl.bhat

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    Not necessarily. Superposition method involves asigning a current in each loop and applying KVL.
     
  9. Sep 19, 2010 #8
    So I should just try solving the circuit as given originally?
     
  10. Sep 19, 2010 #9

    Delphi51

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    You have to be extremely careful about defining i1. I defined it as the current through the 60 ohm resistor because I thought your i1 loop on the diagram was ambiguous.

    There is an example of the superposition method here:
    http://circuits.solved-problems.com/936/superposition-problem-voltage-current-sources/#more-936 [Broken]

    Here is an article on doing it without superposition:
    http://en.wikipedia.org/wiki/Mesh_analysis
    I'm sure rl.bhat knows a great deal more about this than I do!
     
    Last edited by a moderator: May 4, 2017
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