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Mesh Analysis

  1. May 27, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the three mesh current.

    12.jpg

    2. Relevant equations
    KVL

    3. The attempt at a solution

    I numbered the loop 1 with 2 and 3 ohms, loop 2 with 3, 5, and 212 V, and loop 3 with 3, 122V, and 5. All currents are clockwise.

    So for Loop 1: 2i1+3(i1-i2)=0
    Loop 2: 3(i2-i1)+5(i2-i3)-212=0
    Loop 3: 3i3+122+5(i3-i2)=0

    I solve the system and got i1=26.4878 A, i2=44.1463A, i3=12.3415 A.

    But when I plug them back in for power, I do not get 0 for every loop. So I know I must doing something wrong here. So would anyone please help me to see where I am doing wrong?

    Many thanks in advance!
     
  2. jcsd
  3. May 27, 2013 #2

    lewando

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    Gold Member

    KVL says nothing about power in a loop.
     
  4. May 27, 2013 #3
    From my textbook, I learned that if we add the powers for all the elements in the circuit, the result should be zero because energy is neither created nor destroyed.
     
  5. May 27, 2013 #4

    lewando

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    Gold Member

    Okay, then then power supplied by the active devices should equal the power consumed by the passive devices. What are you getting?
     
  6. May 27, 2013 #5
    I get a negative number.
     
  7. May 27, 2013 #6

    lewando

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    Gold Member

    I mean, what, specifically, are you getting for each element?
     
  8. May 27, 2013 #7
    2 ohms: P=i1^2*R=26.49^2*2=1403.44
    3 ohms: P=3(i1-i2)^2=3(26.49-44.15)^2=935.6268
    5 ohms: P=5(i2-i3)^2=5(44.15-12.34)^2=5059.3805
    3 ohms: P=3i3^2=3(12.34)^2=456.8268

    122 V: P=IV=122*12.34=1505.48
    212 V: P=IV=-212*44.15=-9359.8

    I got 0.9541. Unbelievable.

    I guess all the numbers are correct!
     
  9. May 27, 2013 #8

    lewando

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    Gold Member

    Good work by you!
     
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