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Draw a Circuit based on the info and find the voltage values

  1. Jan 23, 2014 #1
    1. The problem statement, all variables and given/known data
    Consider a circuit containing four nodes
    labeled a, b, c, and d. Also, we know that
    vab= 12V,vcb=−4V,and vda= 8V. Deter-
    mine the values of vac and vcd. (Hint: Draw
    a picture showing the nodes and the known
    voltages.)


    2. Relevant equations
    ∑ voltages in a loop = 0


    3. The attempt at a solution

    I had no idea how to approach the problem, just a couple ideas. I tried sketching this out:

    HczRsAL.png

    This one didn't make much sense to me since applying the loop rule, I get differing answers for ##v_{ac}##

    So I tried a few other ways to draw it and this was the closest I could get:

    VsvrzhN.png

    This seems like it makes more sense, but I'm not entirely sure. Am I on the right track?
     
  2. jcsd
  3. Jan 23, 2014 #2

    collinsmark

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    Homework Helper
    Gold Member

    I recommend the first thing to change is you need to change your voltage symbol to indicate some sort of polarity. They blue squares alone are not sufficient. Either use a symbol with obvious polarity such as a battery symbol, or (and this is just as good too) label the '+' and '-' signs.

    What I mean by that is if you look at the 8 V element in the upper left. Imagine, hypothetically, flipping the polarity of that element, making it VAD = 8 V. If you did so, it wouldn't look any different than the way it is now with VDA = 8 V. You need some way of indicating the polarity. You need to know by looking at your picture that if VDA = 8 V, then VAD = -8 V

    Secondly, don't draw that stuff in the middle. It's not necessary. Just keep it as a square if you wish (or even three sides of a square), with nothing in the center. Note that VAC = VAB + VBC
     
  4. Jan 24, 2014 #3

    ehild

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    It is easier to work with potentials. If Vab means the potential of b with respect to a : Vab=Vb-Va=12 V. Write 0 at point a and 12 V at point b. Draw a battery between the nodes to ensure the given potential difference.
    Draw the batteries and determine the potential of each node. Calculate the potential differences Vac=Vc-Va and Vcd=Vd-Vc.

    You can connect a resistor between two nodes and an other one between the other two nodes, the potential differences would not change.

    ehild
     

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