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Mesh Analysis Problem

  1. Nov 13, 2007 #1
    1. The problem statement, all variables and given/known data
    For the following circuit determine:
    I, Vab, Vac, Vbd, Vcd

    See attachment for circuit diagram.


    2. Relevant equations
    Mesh Analysis method



    3. The attempt at a solution
    Using mesh analysis:

    -7V + I1 - I2 + 6V + 2I1 -2I3
    = 3I1 - I2 -2I3 ------------------mesh 1

    2I2 + 3I2 -3I3 + I2 - I1
    = -I1 + 6I2 -3I3 -----------------mesh2

    I3 + 2I3 -2I1 -6 + 3I3 - 3I2
    = -2I1 - 3I2 + 6I3 -6 -------------mesh 3

    Have I done this correctly? How do you get I from this and the voltages?

    Thanks.
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     

    Attached Files:

  2. jcsd
  3. Nov 14, 2007 #2

    Astronuc

    User Avatar

    Staff: Mentor

    The right hand side is missing the voltage. The sum of the voltages around each loop = 0.

    The polarity convention is reversed. I would have done it:

    7V - I1 + I2 - 6V - 2I1 + 2I3 = 0, for mesh 1.

    So, 7V - 3I1 + I2 + 2I3 = 0, and likewise with the others. One then has 3 equations and 3 unkowns (I1, I2, I3), for which one can solve. Simply add the equations together and eliminate all but one current so that currents are found in terms of voltage and resistance.

    Then Vab is just the voltage drop across the resistor (1 ohm) or Va - (I1-I2) 1 ohm = Vb or Va - Vb = (I1 - I2) * 1 ohm.
     
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