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Linear Algebra Question on Calculating Current

  1. Sep 26, 2011 #1
    Hi everyone

    I am trying to find the current of a circuit using linear algebra.
    So far, I know that there are 6 loops, one on each side of the cube. However, I am not sure about how many equations I have to come up with to construct a matrix and thus solving the problem.

    The questions is to find the currents that are going through EACH resistor, and the DIRECTION that they are going in. There should be a total of 12 arrows indicating the directions of the currents, 1 on each side.


    ANY help/hint/suggestion is GREATLY appreciated.
     

    Attached Files:

  2. jcsd
  3. Sep 29, 2011 #2
    Are you referring to the application of Kirchoff's (and Ohm's) laws?

    In this layout, you have equations for each node and each loop in the circuit.

    Is that your layout?
     
    Last edited: Sep 29, 2011
  4. Sep 30, 2011 #3
    I'll post the layout, together with the solution for a specific circuit,( I'll do
    so if anyone is interested):

    Given a circuit with x nodes and y loops, we use the fact that (Kirchoff )

    i)At every node, the sum of incoming currents equals the sum of outgoing currents.

    ii) Around every loop, the (algebraic) sums of the increases in voltage equals the
    sum of voltage drops.

    Then, we must have , for a given node N in the circuit:

    c_N1 +..+c_Nj +...c_Nn =0

    ( I'm getting some cash back for that c_Nn plug, BTW.)

    where ci is the value of the current, and it is positive if the current is
    incoming, and it is negative otherwise.

    For every loop L , we use Ohm's law (E=iR ) to calculate voltage drops:

    iR_L1+..+iR_Lk+...+iR_Ln=0

    From this, you get a system of |L| +|N| linear equations, from which you get the
    currents.

    Is this what you're looking for?
     
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