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Homework Help: Sloving a depentant voltage source problem using node voltage

  1. Feb 24, 2012 #1
    Hi everyone,

    I currently stumped in the process of approaching a dependent voltage source problem using node voltages. Attached is the circuit.

    What I know:

    the Node north of the 60V supply with also be 60V

    there are four nodes, two when supernodes are used

    What I'm confused about:

    with the super node being the 6iψ, KCL states the sums must be zero

    when I try to solve, I end up getting the equation (using v2 as the junction of the dependent, and both 3Ω resistors):

    I am not sure how to calculate the current across the 60Volt source


    In addition, I end up having a recursion problem trying to solve for iψ

    Since V2 is 60+6iψ, and iψ is ([V2-V2]/3), I end up with


    any help would be greatly appreciated


    Attached Files:

    • 3.9.jpg
      File size:
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  2. jcsd
  3. Feb 25, 2012 #2
    Simply treat A and C as a one big (super) node.
    So we only have one unknown node Vb


    Current leaving the node is equal current entering the node.

    For node B

    Vb/24 + (Vb - 60)/2 + (Vb - Vc)/3 = 0 (1)

    And one additional equation

    Vc = Va + 6*Iψ = Va + 6*(Vc - Vb)/3 = 2Vb-Va = 2Vb - 60 (2)

    So we have

    Vb/24 + (Vb - 60)/2 + (Vb - (2Vb - 60))/3 = 0


    But we can remove the supernode from the circuit. We you can transform this circuit, legally, and get a new circuit which is equivalent to the old one


    Attached Files:

    • 3.9.jpg
      File size:
      18.9 KB
    • 3.9a.JPG
      File size:
      20.2 KB
    Last edited: Feb 25, 2012
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