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Res-monster Maze

  1. Jul 29, 2014 #1

    Zondrina

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    Homework Helper

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

    Res-monster maze. In the following figure, all the resistors have a resistance of ##4.0 \Omega## and all the (ideal) batteries have an emf of ##4.0 V##. What is the current through resistor ##R##?

    2. Relevant equations

    ##\sum V = 0##
    ##\sum I = 0##
    ##V = \epsilon##
    ##V = IR##

    3. The attempt at a solution

    See the attached image.

    When I look at it, I see two loops. The big loop to the left of ##R## and the smaller loop to the right of it. Would I just apply the equations in that sense?

    Left loop:

    ##\epsilon_1 - i_1R - i_2R' - i_3R'' = 0##

    Right loop:

    ##\epsilon_2 - i_4R''' + i_5R = 0##

    EDIT: Wait what if I just find an equivalent resistance for that one standout parallel resistor combination?
     

    Attached Files:

    Last edited: Jul 29, 2014
  2. jcsd
  3. Jul 29, 2014 #2

    NascentOxygen

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    Staff: Mentor

    The easy way is to see whether there exists a string of nothing but pure voltage sources between one end of R and its other end. Any other method will be many orders of magnitude more complicated. :wink:

    You know how to play snakes-and-ladders, right?
     
  4. Jul 29, 2014 #3

    Zondrina

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    I attached a picture of what I think you mean.

    Writing the loop equation now:

    ##iR + \epsilon_1 - \epsilon_2 - \epsilon_3 - \epsilon_4 = 0##
    ##i = \frac{- \epsilon_1 + \epsilon_2 + \epsilon_3 + \epsilon_4}{R}##
    ##i = \frac{8.0 V}{4.0 \Omega}##
    ##i = 2 A##
     

    Attached Files:

  5. Jul 30, 2014 #4

    NascentOxygen

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    Staff: Mentor

    That looks right.
     
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