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Mesh current equation in matrix form

  1. May 2, 2016 #1
    • Member warned to use the Formatting Template for homework
    7E3dGXN.png

    i3 -?




    This is how I tried to solve using cramer's rule (denominator is the determinant of the matrix, while numerator is the determinant of the modified matrix)
    Yo4LaQM.jpg

    I ignored the prefix Kilo, but the method is right. So I get a different value for i3.

    Does anyone know what's wrong?
     
  2. jcsd
  3. May 2, 2016 #2

    gneill

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    Staff: Mentor

    Your mesh equations do not appear to take into account the effects of the controlled current source in loop 1.
     
  4. May 2, 2016 #3
    But it does? You don't need to set up equation for it, because i1 = 0.001Vx
     
  5. May 2, 2016 #4

    gneill

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    Staff: Mentor

    So where are it's effects on the rest of the circuit? Hypothetically, suppose it was changed to i1 = 0.003Vx. Shouldn't that change be reflected in your mesh equations? Where would the changes appear?

    The controlled current source as a mesh current must create a potential difference across the 1 kΩ resistor in loop 3. You can't just ignore that.

    Big hint: To address this, insert an appropriate controlled voltage source in series with the 1 kΩ resistor.
     
  6. May 2, 2016 #5
    Why would I insert something just randomly??? I don't get these riddles!
     
  7. May 2, 2016 #6

    gneill

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    Staff: Mentor

    It's not random. The controlled voltage source expresses the controlled current source's effect on loop 3. Loop 1's mesh current flows through the 1k resistor of loop 3 and creates a potential drop across it. The inserted voltage source represents that potential drop.
     
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