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Homework Help: Two-loop circuit using Kirchoff's Laws

  1. Sep 25, 2009 #1
    1. The problem statement, all variables and given/known data

    The circuit in the figure is composed of two batteries (ε1 = 10 V and ε2 = 5 V) and four resistors (R1 = 110 Ω, R2 = 40 Ω, R3 = 40 Ω, and R4 = 50 Ω) as shown.

    HELP: Because of the presence of batteries in more than one branch of the circuit, parts (a) and (b) of this problem can only be solved simultaneously. There is no way around this fact. Equivalent resistance tricks are of no help, but Kirchoff's Laws can provide simultaneous equations.

    HELP: Write two independent voltage loop equations by following I1 around the left-hand block of the circuit and, separately, I3 around the right-hand block. What is the net current through R2? What voltage drop will result from this current? Be careful with this point.

    A loop where I3 goes around the entire periphery of the circuit is another possibility, but this does not give independent information because the resulting equation is the sum of the previous two loop equations. In this case the current and voltage drop for R2 are simple, but you must be careful about the current and the voltage drop for both R1 and R4!

    Solve any two of the above three loop equations for I1 and I3, using standard algebraic techniques for solving two equation in two unknowns.

    2. Relevant equations

    I1 = I2 + I3

    left-side loop:
    E1 - I1R1 - I2R2 - E2 - I1R4 = 0

    right-side loop:
    -I3R3 + E2 + I2R2 = 0

    3. The attempt at a solution

    I tried substituting I1-I3 for I2 into both equations, and setting them equal to each other. For some reason whenever I'm solving these I always end up with 0=0

    Any help would be appreciated! thanks!

    Heres a link for the image of the circuit if you cant see the attachment: https://netfiles.uiuc.edu/ddwei2/shared/showme.pl.gif [Broken]

    Attached Files:

    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Sep 25, 2009 #2


    User Avatar
    Homework Helper

    HeyJohn, no one can see your attachment until it is approved - could be a while.
    I suggest you put your diagram up on Photobucket.com or some similar site, then post the link to it here. I see some people are able to put the diagram right in the post - I don't know how to do that but you might try putting and [Broken] around the link.
    Last edited by a moderator: May 4, 2017
  4. Sep 25, 2009 #3
    What about the link, does that work?
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