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GR0877 Problem 68

PROBLEM STATEMENT: This problem is still being typed.

SOLUTION: (D) The total resistance of the circuit is equal to the resistance of three R+R = 2R resistors connected in parallel: \displaystyle \frac{1}{R_{total}} = \frac{1}{2R} + \frac{1}{2R} + \frac{1}{2R} = \frac{3}{2R}, \displaystyle R_{total} = \frac{2R}{3}. The current flowing through the battery is \displaystyle I = \frac{V}{R_{total}} = \frac{3V}{2R}.

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  1. WobbleWheel
    07.11.2011 at 03:14

    Because of the symmetry of the problem, there is no potential drop across any of the horizontal resistors. This means you can just yank them out of the circuit, which simplifies the calculations as noted above.

    • Eric
      08.10.2012 at 21:12

      I’m confused as to how we know there’s no potential drop across the horizontal resistors. If current I flows through the whole circuit, then I/3 flows through each arm after the first junction. Then, on the left and right, the current splits into two equal parts because the resistances after those junctions are equal. Now, we have I/6 flowing from the right arm towards the center and I/6 flowing from the left arm to the center. At the center, there are three paths of equal resistance, so the current into that junction splits into three equal parts of I/9. To me, it looks like there’s a net flow of current toward the center. Where have I gone wrong?

      Thanks!

      • Stevie
        16.10.2013 at 17:50

        I am not sure exactly where you went wrong, but I’m thinking about it like this: take one of the horizontal resistors — each is pulling the exact same amount of current from their left and right, so net current across either of the horizontal resistors is zero. In fact, it’s like they’re not even there (or the whole section of the circuit each is on). So the problem becomes three 2R resistors in parallel. …I hope this helps.

  2. Steve
    10.11.2011 at 03:17

    Makes sense now. How would you deal with it if there were no symmetry?

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