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Solving a Simple Circuit involving Current Source by the Loop Current Method

  1. Mar 1, 2010 #1
    1. The problem statement, all variables and given/known data
    For the resistor network in the picture, use loop currents to find the current through the 4Ω resistor and the change in voltage E across the current source.

    Circuit Attached Below .

    2. Relevant equations

    • Kirchoffs Laws
    • Loop Current Method
    • V=IR


    3. The attempt at a solution

    Firstly I divided the circuit into 3 loops with 3 currents.
    1. Top left Loop, Current A
    2. Top right Loop, Current B
    3. Bottom Loop, Current C

    Looking For
    • Voltage Change,E, across the current source
    • Current A
    • Current B
    • Current C

    Now I apply Kirchoffs laws for every loop. I go around in a counter clockwise manner and get the total drop in voltage for each.
    • Loop A: -E+A+2(A-C)=0
    • Loop B: E+(B-C)+2(B)=0
    • Loop C: 12+(C-B)+2(C-A)+4C=0

    Now i have 3 equations, but 4 unknowns,

    So i need another equation coming from the current provided from the current source to get a system of equations and solve it.
    But i know that the current source provides a current of 1amp for the loop, however this is where im not sure how to proceed,
    does it mean that both A and B = 1 or A=1 only? How do i know which current the source affects?

    I proceeded with the assumption that both A and B both equal one, but got an overdetermined system with no solution.

    On second though maybe, both currents are related by lets say, the source gives out current = 1amp, so loop 1 and 2 share this current so, currents A+B=1 sort of thing? Proceed by substituting A=1-B into the system of equations and get 3 unknowns 3 equations?

    Just need some checking on this fact and the rest of the problem is pretty straight forward.
    Thanks in Advance.
     

    Attached Files:

  2. jcsd
  3. Mar 1, 2010 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member



    There are two Kirchhoff's rules, one for the currents at nodes, the other for voltages in a loop.
    You need to know them, and then it is not a possibility but the truth what your "second thought" is.

    ehild
     
  4. Jun 25, 2010 #3
    In case you want to check your answer, the currents are 6/11 A, 17/11 A and 23/11 A respectively. You have to use both Kirchoff's Loop Rule and Current Rule. At least that's what I did.
     
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