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Another mesh analysis

  1. Oct 11, 2016 #1
    1. The problem statement, all variables and given/known data
    pHJ8FSj.png

    1. Convert from time to freq domain
    2. Use mesh analysis to find I1, I2, I3
    3. Find Ve and convert it to time domain

    2. Relevant equations
    KVL
    V=IR

    3. The attempt at a solution
    Are these mesh equations correct?
    45cos(500t) -> 45V
    80mH -> 40j
    50mH -> 25j
    25uF -> -80j
    12.5uF -> -160j

    Mesh1
    (100+40j+25j+200)I1 - 200I2 - 400jI3 = 0
    Mesh2
    -45 + (200-80j)I2 - (200I1) + 80jI3 = 0
    Mesh3
    (-80j-160j+25j)I3 + 80jI2 -25jI1 = 0
     
    Last edited: Oct 11, 2016
  2. jcsd
  3. Oct 11, 2016 #2

    gneill

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    Staff: Mentor

    I don't see the 200 Ω resistor being affected by I1 in the first mesh equation.
     
  4. Oct 11, 2016 #3
    Can't believe I missed that. Do the other two look fine?
    Are there any "shortcut strategies" for solving a system of three equations with complex variables?
     
  5. Oct 11, 2016 #4

    gneill

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    Staff: Mentor

    The others look okay to me.

    No shortcuts other than using a software package to do the heavy lifting. I'm partial to Mathcad myself, putting the equations into matrix form and using the built in solver.
     
  6. Oct 11, 2016 #5
    For mesh1, it should be -25jI3 instead of 400jI3
    I used an online calculator and got this:
    upload_2016-10-11_10-59-40.png
     

    Attached Files:

    Last edited: Oct 11, 2016
  7. Oct 11, 2016 #6

    gneill

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    Staff: Mentor

    Your 1,3 entry of the matrix should be identical to the 3,1 entry.

    Here's a Mathcad version:
    upload_2016-10-11_14-1-3.png
     
  8. Oct 12, 2016 #7
    Is the voltage across Ve simply (I3-I2) * Impedance of 25uF capacitor?
     
  9. Oct 12, 2016 #8

    gneill

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    Staff: Mentor

    Make that (I2 - I3)*Z25μF. I2 flows into the top of the capacitor, so it'll produce a voltage drop in the correct direction.
     
  10. Oct 13, 2016 #9
    I ended up getting 9.988 < -43.347 volts.
    Converting to time domain would give: 9.988cos(500t - 43.347) right?
     
  11. Oct 13, 2016 #10

    gneill

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    Staff: Mentor

    That looks a bit small. Can you show that calculation in detail?
     
  12. Oct 13, 2016 #11
    (I2-I3) * (-j80)
    = (0.086 + 0.091j) * (-j80)
    = -6.88j - 7.248j^2
    =7.248-6.88j

    sqrt(7.248^2 + 6.88^2) = 9.99 < -43.5 degrees
     
  13. Oct 13, 2016 #12

    gneill

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    Staff: Mentor

    What values are you using for I2 and I3?
     
  14. Oct 13, 2016 #13
    I2 = 0.1188 + 0.1314j
    I3 = 0.0329 + 0.0408j

    EDIT:
    Are these the correct values?
    I2 = 0.52013055631408 +0.24535752634041i
    I3=0.15152422756397 +0.07991035923825i
     
  15. Oct 13, 2016 #14

    gneill

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    They don't match your results from post #5. Has something changed?
     
  16. Oct 13, 2016 #15
    Lack of sleep I guess :P
    I plugged in the wrong value to the calculator.

    New value for Ve: 32.3<65.88 degrees
     
  17. Oct 13, 2016 #16

    gneill

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    Staff: Mentor

    Better. Confirm the sign of the angle.
     
  18. Oct 13, 2016 #17
    Why is it -65.88 instead of 65.88? I recall this being covered in class but I forgot. The calculator spits out 65.88
     
  19. Oct 13, 2016 #18

    gneill

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    What are the Cartesian components of the complex value?
     
  20. Oct 13, 2016 #19
    Fourth quadrant.
    I get it now.
     
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