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Circuits, linear algebra

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  1. Mar 12, 2015 #1
    Hi I got stuck at the following circuit problem which involves linear algebra, since I am not a physics major, I dont even have the basics to get started. Please shed some light, really appreciate it! Thanks a lot.

    1. The problem statement, all variables and given/known data

    Consider a long chain of resistors wired up like this

    circuit.jpg

    All the resistors have the same resistance R. The power rail at the top is at voltage V+ = 5V. The problem is to find the voltages V1 . . . VN at the internal points in the circuit.

    Using Ohm’s law and the Kirchhoff current law, which says that the total net current flow out of (or into) any junction in a circuit must be zero, show that the voltages V1 . . . VN satisfy the equations

    3V1 − V2 − V3 = V+,
    −V1 + 4V2 − V3 − V4 = V+,

    ... −Vi−2 − Vi−1 + 4Vi − Vi+1 − Vi+2 = 0, ...

    −VN−3 − VN−2 + 4VN−1 − VN = 0,

    −VN−2 − VN−1 + 3VN = 0.

    Express these equations in vector form Av = w and find the values of the matrix A and the vector w.


    2. Relevant equations


    3. The attempt at a solution

    I considered when N = 2, it gives me a "Wheatstone bridge" with V1 = V2 = V/2
    but then how should i continue? thanks a lot!
     
  2. jcsd
  3. Mar 12, 2015 #2
  4. Mar 12, 2015 #3
    please help thanks
     
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