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Writing Kirchhoff Rules for a Multi-Loop Circuit

  1. Apr 25, 2017 #1
    1. The problem statement, all variables and given/known data
    I need to write Kirchhoff rues for the following circuit. This is not for a physics class, but for a programming class. I can do that part, but I am not sure if the equations are correct.

    2. Relevant equations
    upload_2017-4-25_11-6-13.png

    3. The attempt at a solution
    V1-I1*R1-(I1-I2)R3-I1*R2=0
    V2-(I2-I3)R5-I2*R4-(I2-I1)R3=0
    V3-I3*R6-I3*R7-(I3-I2)R5=0
    These neglect R8, however.
    Should I also include:
    V1-I1*R1-(I1-I2)R3-(I1-I2)R4-(I1-I3)R7-I1*R8=0
    V2-(I2-I3)R5-(I2-I3)R7-(I2-I1)R8-(I2-I1)R2-(I2-I1)R3=0
    V3-I3*R6-(I1-I3)R8-(I3-I1)R2-(I3-I2)R4-(I3-I2)R5=0
    These last three equations seem really wrong. I am not sure how many currents there even are.
     

    Attached Files:

  2. jcsd
  3. Apr 25, 2017 #2

    cnh1995

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    Homework Helper

    Welcome to PF!
    For writing KVL, take no of currents= no of meshes (smallest loops). You can see 4 meshes here, so assume four currents.

    See this example.
    download (1).png
    You can now write the current through each resistor in terms of i1, i2 and i3. For example, current through the 25 ohm resistance is i1-i2 downward.
     
  4. Apr 26, 2017 #3

    ehild

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    Homework Helper
    Gold Member

    So they are wrong. Why did you write them?
    These equations are also wrong.
    Choose loops and loop currents and draw the currents clearly. Note that you have 4 independent loops, so you need to write 4 loop equations.
    This is a possible arrangement:

    upload_2017-4-26_7-34-43.png
     
  5. Apr 27, 2017 #4
    So these are the new equations that I came up with, but something still is not quite right:
    V1-I1*R1-(I1-I2)*R3-(I1-I4)*R2=0
    V2-(I2-I3)*R5-(I2-I4)*R4-(I2-I1)*R3=0
    V3-(I3-I2)*R5-(I3-I4)*R7-I3*R6=0
    I4*R8+(I4-I1)*R2+(I4-I2)*R4+(I4-I3)*R7=0
     
  6. Apr 27, 2017 #5

    gneill

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    Staff: Mentor

    In your third equation you ignored the defined current direction of I3. You did your "KVL walk" around the loop counterclockwise, which is fine, but you wrote the equations as though you were going in the direction if I3 rather than against it. For example, I3 should cause a potential rise as you pass through R5.

    Once you've defined the direction of a current and used it in other equations you must stick to what you've defined.
     
  7. Apr 27, 2017 #6
    Thank you! That makes sense.
     
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