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Overlapping Loop Circuit

  1. Feb 25, 2008 #1
    1. The problem statement, all variables and given/known data

    Given the diagram:

    [​IMG]

    where R = 37 Ohms

    a) Find the current in the 37 Ohm resistor

    b) Find the potential difference between points A and B


    2. Relevant equations

    DV = IR, Kirchhoff's rules

    3. The attempt at a solution

    a) I = 25 V / 2 = 12.5 V (at the first (right) junction) , there for I thought I at the 37 Ohm resistor would be 12.5 V / 37 Ohms = 0.34, but it doesn't.

    b) I combined the middle resistor and the lower 5 Ohm resistor to get ((1/10)+(1/5))^-1 = 3.33 Ohms and made the V at "b" 12.5 V ... but I don't know where to go from there.

    Thank you so much for your time! -- I'm really stuck.
     
  2. jcsd
  3. Feb 25, 2008 #2
    Are you familiar with Thevenin's theorem? There are many ways to compute the current in the 37 Ohm resistor but this circuit lends itself to Thevenin's theorem. So:

    step 1) disconnect the R from the circuit.
    step 2) calculate the equivalent resistance looking into the circuit. There are a couple of ways to do this Vopencircuit/Ishortcircuit will give it to you. But I like the method of open circuiting all current sources and short circuiting all voltage sources (ideal) and then calculating the total resistance Rth. Now you have everything you need to replace everything to the left of the R with the Thevenin equivalent circuit which will be a voltage source with value Vopencircuit and a series resistance of Rth.
    step 3) reattach your load resistor R and calculate the current in the now trivial circuit.

    hope this helps you a bit....
     
  4. Feb 25, 2008 #3
    That's still beyond me at this point, but I do like the sound of it and should read about it. Thanks for your help!

    Meanwhile, I found an answer to this question in another book. What they suggested was turning the picture on its side to make 3 normal-looking horizontal loops, mostly in parallel but with R and 5 Ohm in series. Then the problem is simple an you don't even need Kirchhoff's rules (which I thought you must, and were confusing me).

    I "got the answers" by doing it this way but really need someone to help me visualize how this is possible, because I'm not really seeing it!

    Hope this helps anyone with a similar problem.
     
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