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Kirchhoff's Current Law

  1. Sep 16, 2009 #1
    1. The problem statement, all variables and given/known data
    I have this diagram which asks me to find IL using the diagram.
    http://img183.imageshack.us/img183/6171/diagramq.jpg [Broken]

    2. Relevant equations

    According to Kirchhoff's current law, the sum of all currents entering and leaving a node must equal zero.

    3. The attempt at a solution

    I examined the currents that were entering and leaving each node, thus I came up with 8 equations (from the 8 nodes). I think that I am on the wrong track since I cannot find a way of solving 8 unknown variables since not all currents are given on the diagram.
    Any ideas on how to approach this problem?
    Thank you in advance.

    Attached Files:

    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 16, 2009 #2
    You also know Kirchoff's Voltage law, that the sums of the potential differences around a loop must equal zero

    What is the voltage across the 6k ohm resistor?
  4. Sep 16, 2009 #3
    You're going to have to solve it using simutaneous equations

    What are the circles and the diamond shapes in your diagram?

    I've never seen those before, are they supposed to be ammeters?
  5. Sep 16, 2009 #4
    Would I use Ohm's Law to find the Voltage across the 6k ohm resistor. If I do then what current is it linked to the resistor?
    Thank you for the quick reply.
  6. Sep 16, 2009 #5
    Yes use Ohm's law,
    the current you would use I am not to sure of because your picture shows a component with a circle around it, Is it some kind of bulb or resistor? or an ammeter?


    for each simutaneous equation, select a direction for the current in that loop to go,

    then use Ohm's law and sum all the potential differences around that loop to equal zero,

    e.g 3V-5I = 0 - a circuit containing a 3V source, a 5ohm resistor and current I


    after you have the equations for each loop solve them simutaneously if you can.
  7. Sep 16, 2009 #6
    http://img183.imageshack.us/img183/6171/diagramq.jpg [Broken]

    From your diagram, I am guessing that the two circles are two identical resistors, and that the centre component (the one with a square around it is a different resistor)

    Not sure though, is this all you're given? does the question come with any additional information other than this diagram?
    Last edited by a moderator: May 4, 2017
  8. Sep 16, 2009 #7


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    The circle with the arrow, is a 'current source', the diamond with an arrow inside is a dependent or 'controlled-current source'. In our present thread's example, it is controlled by another current in the circuit (see figure 2 in this http://en.wikipedia.org/wiki/Current_source" [Broken])
    Here is http://www.linearcircuitry.com/Kirchoff.html" [Broken] of how a current source is interpreted in a circuit (see Figure 7.1).

    Hint to jualin when applying KCL (Kirchoff's current law), a node that is shorted to another node is equivalent and nodes need not have a solid dot to call it a node. So the whole top of this circuit is one node.
    Last edited by a moderator: May 4, 2017
  9. Sep 16, 2009 #8
    Hello Ouabache
    Nice remark. Another thing is why the current through the 6kohm did not get a name; let us say I_6. So there a only two nodes and I think that somehow kirchof addition of currents in the one will give the same equations as in the other.
    greetings Janm
  10. Sep 20, 2009 #9
    Thank you all for the quick replies. They were very helpful!
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