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Effective Resistance between 2 points

  1. Jun 16, 2016 #1
    Given that the resistance of each resistor is 1.0 ohm, find the effective resistance between P and Q.
    I do not know how to simplify the circuit.
    A little help on how to redraw the circuit such that the Reff can be calculated is appreciated.
     

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    Last edited: Jun 16, 2016
  2. jcsd
  3. Jun 16, 2016 #2
    You need to consider the symmetry.
     
  4. Jun 16, 2016 #3
    May I know a little bit more about that? I always have difficulties whenever I encounter questions that need me to redraw the circuit. I have been stuck in this question for 1 day and I still do not get it. @.@
     
    Last edited: Jun 16, 2016
  5. Jun 16, 2016 #4

    cnh1995

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    In this question, you can see that the circuit is symmetric about the line joining P and Q. You can replace the two horizontal 1 ohm resistors with parallel combinations of two 2 ohm resistors and then cut the circuit along the line PQ such that each part contains a 2 ohm resistor. This way, you'll have two exactly identical circuits which are connected in parallel in the original circuit. You can analyze any one circuit and get the result.
     
  6. Jun 16, 2016 #5

    NascentOxygen

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    Hi Abysmaltan. :welcome:

    It's always wise to look at the foot of this page to see what earlier threads identified as similar sounding might be of assistance. On rare occasions you might even discover your very problem has been solved!

    The technique of symmetry can be used here. Imagine P=+10V and Q=-10V and try to identify nodes in the circuit where the potential might be 0V.

    To confirm this, now imagine the voltage sources to be reversed so that P=-10V and Q=+10V and see whether the nodes you think should be 0V are those same nodes you identified in the step above.

    Once you have identified points of equal potential, you can simplify the drawing by showing those points connected together using a thick piece of wire to form a single node because you have shown they are all already at the same potential. (Connecting up points of identical potentials changes nothing because with the ends of each added wire being at the same potential then no current is going to flow through that added wire, anyway.)

    You then determine the resistance of this much-simplified circuit.

    To gain a good understanding of this requires that you work through practice exercises such as this homework problem.
     
  7. Jun 16, 2016 #6
    Thank you for your reply!
    However, sadly, I still do not quite understand the idea of using symmetry to solve complex circuits.
    Regarding the first part of the explanation (imagine P=+10V and Q=-10V then...), I do not know how to identify the nodes where the potential might be 0V. (I am still a beginner in circuits T___T)
    Also, you mentioned working through exercises. Unfortunately, I cannot find any similar question in my book, and I am not sure where to find on the Internet. Do you know of any websites that will allow me to understand more about solving circuit using symmetry and that have practice questions.
     
  8. Jun 16, 2016 #7

    cnh1995

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    Can you do series-parallel reductions? Have you studied Wheatstone's bridge?
     
  9. Jun 16, 2016 #8
    I can do series-parallel reduction, but have not studied Wheatstone's Bridge.
     
  10. Jun 16, 2016 #9

    cnh1995

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    So you can do this..
     
  11. Jun 16, 2016 #10
    I will still get 2 unbalanced brigdes (I just read it up), right?
     
  12. Jun 16, 2016 #11

    cnh1995

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    You'll get two balanced bridges.
     
  13. Jun 16, 2016 #12
    Oh, I see. So I just need to calculate accordingly, then.
    I am pretty sure there are other methods of doing it, like what @NascentOxygen suggested (Just that I do not understand). Thanks for your responses, though!
     
  14. Jun 16, 2016 #13

    cnh1995

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    Yeah. Only 3 steps are required...Good luck!
     
  15. Jun 16, 2016 #14
    How do I know that the two exactly identical circuits are connected in parallel in the original circuit? Is it linked to the concept of symmetry?
    Sorry, haha, I am an inquisitive but obtuse high-schooler, who is struggling to survive for physics. :(
     
  16. Jun 16, 2016 #15

    cnh1995

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    You can see the two configurations. They'll be exactly identical. The circuit is symmetrical about the PQ axis.
     
  17. Jun 16, 2016 #16
    So the idea is that when a circuit is symmetrical about an axis, the two identical circuits, separated by line of symmetry, are in parallel?
     
  18. Jun 16, 2016 #17

    cnh1995

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    If you are asking about the parallel connection part:
    When you separate the two circuits along the line PQ, their ends are still connected between P and Q.
     
  19. Jun 16, 2016 #18
    OOOHHHH, understood!!! Thank you!
     
  20. Jun 16, 2016 #19

    cnh1995

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    Not always. Here, the line joining the points between which the effective resistance is asked is the useful line of symmetry. If the line of symmetry coincides with the line joining the two points between which the effective resistance is asked, then the two circuits are in parallel. The circuit is symmetrical about vertical axis too. But that will not give two parallel circuits between P and Q.
     
  21. Jun 16, 2016 #20
    OK. Understood. Thanks a lot! :)
     
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