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Kirchoff's law problem

  1. Mar 26, 2014 #1
    1. The problem statement, all variables and given/known data

    See attached image.

    Suppose I want to find the current through each resistor…how would I do so?


    2. Relevant equations

    Kirchoffs eqns … sum of voltages around every loop is zero


    3. The attempt at a solution


    1. The first problem I have with this, is that i am not sure how many currents there are. I put arrows in different colors the currents that I think there are. Could someone verify this step?

    2. If (1) is correct, then I think that the blue current = red + green current

    3. Next, I would attempt at using kirchoff's law on the smallest loop, and the loop which does not involve the top two resistors (the one with 5 resistors and 2 batteries in it). Then i would solve for current using a matrix.

    So generally speaking, is this a correct method?
     

    Attached Files:

  2. jcsd
  3. Mar 26, 2014 #2

    phinds

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    You have too many currents shown (red, blue, green = one too many). You have one little loop in the upper part another loop in the lower part. Just draw currents for those two loops.
     
  4. Mar 26, 2014 #3

    gneill

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    You've identified that there will be three different current values to be found. Three unknowns implies that you need three independent equations in order to solve for them.

    There are several possible approaches, the most basic of which is to write KVL around the obvious loops (yielding two independent equations), and writing KCL at one of the nodes in order to give a third equation. That is essentially the steps that you've described. :smile:
     
  5. Mar 26, 2014 #4

    phinds

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    Yes, that would work, but why would you want to go to 3 equations in 3 unknowns if he can just do what I suggested and have two equations in two unknowns?
     
  6. Mar 26, 2014 #5

    gneill

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    That would be the mesh current approach which, based upon the way the question was presented by the OP, is probably a chapter or two further along in his studies. I figured that he'd just been introduced to basic KVL and KCL at this point.

    Besides, you still need to write a third equation (essentially the same KCL equation) in order to determine the green current from the two mesh currents, even with the mesh approach :smile:
     
  7. Mar 26, 2014 #6

    phinds

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    Damn. You're right on both counts. Of course you already knew that didn't you :smile:

    Thanks for that correction ... I might have confused him.
     
  8. Mar 26, 2014 #7

    gneill

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    No problem, always glad to help where I can.
     
  9. Mar 26, 2014 #8
    Yes, I am just being introduced to Kirchoff's, so I have not heard about "mesh".

    sorry, but what is the difference between: KVL and KCL??

    For the 3 equations, I have the blue = red +green and applying kirchoff on both small loops.
     
  10. Mar 26, 2014 #9

    gneill

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    There are two Kirchhoff laws: KCL and KVL. The Current Law and the Voltage Law. One pertains to the sum of currents that enter/leave a node, the other to the sum of potential drops/rises around a closed loop. Your text should define both and provide examples.
     
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