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Circuits Question: Thevenin Equivalent

  1. Mar 18, 2010 #1
    1. The problem statement, all variables and given/known data

    Find thevenin equivelent of this circuit with respect to a and b


    2. Relevant equations
    Mesh Currents
    3. The attempt at a solution
    Here I will try to find V(open circuit) = Vth = Vab ((I think this anyways))

    I apply mesh currents (any faster methods are welcome if you know them)

    iA: -100/V/ + 10/ohm/(iA) + 40/ohm/(iA-iB)=0
    iB: 40/ohm/(iB-iA) + 50/ohm/(iB-iC)=0
    iC: 50/ohm/(iC-iB) + 20/ohm/(iC) + 200/ohm/(Ix) = 0
    iX: iX=iB-Ic

    I get the folowing values using solve function on calculator:

    And using ohms law with parallel resistors having equal voltages..
    Vab = 40/ohm/*(iA-iB) = -2000 = Voc = Vth

    Now is where I begin to have trouble finding Isc...

    I draw the short circuit between a and b (which I believe causes R3 and R4 to have no current through them thus making Ix = 0 and vs2 = 0 as well):


    Simplifying it you gain ((if my previous assumptions are correct reguarding the short circuit)):


    Now from here I am actually unsure what I should do. I do want to do mesh currents but I dont know if I will recieve a correct answer. I also wondered if I could use a closed surface... something like this perhaps:


    If I used that I would get an equation like -100/V/ / 10/Ohms/ + Isc = 0

    But then again it just doesnt seem quiet right to me. And i have no way to check my answer.
  2. jcsd
  3. Mar 18, 2010 #2

    The Electrician

    User Avatar
    Gold Member

    You could get rid of the 10 amp source (Is) right from the beginning; it does nothing to the circuit to the left of Vs2. It just adds 10 amps to the current in Vs2, which has no effect on Vs2's voltage.

    So, Is contributes nothing to the current in the short you've placed across a-b because Vs2 absorbs the entire 10 amps from Is, and the current in the a-b short is just 10 amps.
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