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Equivalent resistance between a and b -- Complex circuit

  1. Apr 1, 2016 #1
    1. The problem statement, all variables and given/known data
    tmp_4948-20160401_192356-639066610.jpg

    2. Relevant equations
    Req = [ ( 1 / R1) + ( 1 / R2) +. ....]^-1 (Parallel)
    Req = R1 + R2 +. . . (Series )

    3. The attempt at a solution
    I tried to simplify the circuit by spreading it out but I guess something is wrong with my simplification since I can't arrive at the correct answer (7 ohms)....Can someone please point me in the right direction?h
     
  2. jcsd
  3. Apr 1, 2016 #2

    phyzguy

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    You're taking the right approach, you just made a mistake. Look at the 10 Ohm resistor in the original drawing and in your first re-drawing. It is not just in series with the last 3 Ohm resistor, there is an extra connection that you left out of your re-drawing. Try doing the simplification again.
     
  4. Apr 1, 2016 #3
    Is this better? My answer is still a little off though... uploadfromtaptalk1459567179363.jpg
     
  5. Apr 1, 2016 #4

    NascentOxygen

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    Staff: Mentor

    In the original image you can see there is a piece of wire parallel to the 10 ohm resistor .... :wideeyed:
     
  6. Apr 1, 2016 #5
    Should I add a "dummy" 0 ohm resistor on that piece of wire...? Would it change anything? uploadfromtaptalk1459571894494.jpg
     
  7. Apr 2, 2016 #6

    NascentOxygen

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    The 0Ω is across the 10Ω, a parallel resistance of 0Ω.
     
  8. Apr 2, 2016 #7
    But then I'd have to compute [(1/0)+(1/10) ]^-1....and 1/0 is undefined....or do I just leave it out of the calculation?
     
  9. Apr 2, 2016 #8

    NascentOxygen

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    I see.

    It's 0/0 that is undefined; 1/0 is very large, infinity.

    How about just thinking about it: what would a resistance meter measure if you had it connected to a 10Ω resistor and then you held a piece of thick wire across the resistor?
     
  10. Apr 2, 2016 #9
    It would read 10 ohms....
     
  11. Apr 2, 2016 #10

    NascentOxygen

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    It would read 0Ω, the wire is a short circuit.

    If you had trouble using 0 in your computations, try instead a very small resistance, say 0.00001Ω and see where the calculations are heading....
     
  12. Apr 2, 2016 #11
    Please tell me more about short circuits. I haven't learned that yet....
     
  13. Apr 2, 2016 #12

    NascentOxygen

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    A short circuit is a piece of wire (a perfect conductor, ideally) that joins one node to another and causes all points along it to have the same voltage.
     
  14. Apr 2, 2016 #13
    Ooooh. So the ideal 0 ohm wire would kind of force the 10 ohm resistor to be null? How does that work?
     
  15. Apr 2, 2016 #14

    cnh1995

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    0 ohm in parallel with 10 ohm gives an equivalent resistance of 0 ohm between the two points.
     
  16. Apr 2, 2016 #15
    I just tried the computation with 0.0001 ohm resistor in parallel with a 10 ohm resistor and I got 0. Wow! How can that be possible? Does it mean that the 10 ohms resistor might as well not be there????
     
  17. Apr 2, 2016 #16
    Thanks everyone for your mentoring!!!! Appreciated from the bottom of my heart! uploadfromtaptalk1459655508530.jpg
     
  18. Apr 2, 2016 #17

    cnh1995

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    Yes.
     
  19. Apr 3, 2016 #18

    NascentOxygen

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    If you were an electron in a circuit and were given the choice, would you prefer to fight your way through a 10Ω resistance, or glide almost effortlessly along a copper conductor?
     
  20. Apr 3, 2016 #19

    epenguin

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    Yes. In future you can just recognise it, and just forget any resistor in a position that is short-circuited like that, eliminate it and not include it in your calculation.
     
  21. Apr 3, 2016 #20

    Second option! Thanks a lot for the image.
     
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