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Finding the equivalent resistance of this circuit?

  1. May 2, 2008 #1
    Hello

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

    **attachment of problem diagram at bottom**
    1)Find the current through R3
    2) Find the total equivalent resistance of the circuit

    2. Relevant equations

    Ohm's law, parallel resistances, series resistances, Thevenin's theorem, and all that jazz

    3. The attempt at a solution

    Okay, for #1, I actually got already. I thought the easiest way to do it would be to utilize Thevenin's equivalent method. So I was able to reduce the circuit down to just the thevenin "load" voltage (which I computed as (7E/15), the thevenin resistance (which I got (22R/15) for, and the load resistor R3. I found the current through R3 to be (7E)/(37R) and I'm pretty sure that's correct.

    The real problem is with finding the equivalent resistance of those 5 resistors. I don't see any easily attainable series/parallel resistor combinations thanks to that middle wire with the resistance on it, unless I'm overlooking something pretty badly. Being that there are no numbers given in this problem, what type of approach should I attempt to find Req of that entire branch?

    If you can't see the pic, it's basically a closed, looped rectangle located between the terminals of the battery. The rectangle is divided into 2 squares by a wire with a resistance on it, where there are 2 resistors "in a parallel configuration" with each other on both squares.
     

    Attached Files:

  2. jcsd
  3. May 2, 2008 #2
    You can't find the equivalent resistance with replacing series or parallel resistances. you have to compute the current through the whole circuit as a function of V and then if you find that I = (constant) * V, that constant is the equivalent resistance of the whole circuit.

    You can do it with Thevenin. I would use any resistor that isn't R_3 for the load, because if you have the current through any other resistance, you can find the potential of one of the nodes, and than other currents in that node with ohms law and kirchhofs current law, and the potential of the other node from that, and the currents through the other node from that.

    What I do to solve these is: There's one unknown voltage at every node. Call the potential between R1, R3, and R4: V_1 and the potential between R2, R3 and R5: V_2.
    The poles of the battery are at V and 0.
    given these unknowns you can calculate all the currents with ohms law
    I1 = (V - V1)/R1, I2 = (V-V2)/R2, I3 = (V1 - V2)/R3 etc.
    Then use Kirchhofs current law in both nodes to get two equations for the two unknown potentials. After you solve them, you can get the equations above to get all the currents.
     
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