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Resistor puzzle

  1. Jun 8, 2003 #1
    If you have 12 resistors, each rated for 600ohms, how could you arrange them to make a total resistance of 500ohms?
     
  2. jcsd
  3. Jun 8, 2003 #2

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    The joyous algebraic method. :smile:

    Let 1/a + 1/b = 1/c

    c = a * b / (a + b)

    let a = 600 x and b = 600 y and c = 500

    (We are setting up a parallel circuit, one with x resistors, and the other with y resistors in parallel)

    we get then

    (x * y * 360000)/(600(x+y)) = 500

    Which simplifies to...
    x * y / (x + y) = 5/6

    Which we can turn into:
    x = 5y/(6y - 5)

    Now, set y = 1.

    x = 5 / 1 = 5

    So one easy possiblity is to have 5 resistors in series on one branch and 1 on the other.

    Multiply by two if you need to use all 12 resistors.
     
  4. Jun 8, 2003 #3
    I see how you get 500 ohms with 6 resistors but don't understand how you got it with 12?
     
  5. Jun 8, 2003 #4
    You could do it with only 5 resistors

    3 600 Ohm resistors in parallel (200 Ohms)

    In series with:

    2 600 Ohm resistors in parallel (300 Ohms)

    = 500 Ohms.
     
  6. Jun 10, 2003 #5

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    Oops.

    For 12 resistors, the solution is:

    3 in parallel, 3 in parallel and 6 in parallel joined in series.
     
  7. Jun 11, 2003 #6
    Ok I heard if you made a cube, which has 12 sides and put a 600 ohm resistor on them it would equal 500 ohms.
     
  8. Jun 11, 2003 #7
    Yeah but...

    How many cubes have twelve sides?

    [edit]
    Cheese, ok I drew it out and get it now,haha.

    I've forgotten what the question was as I edit this, but looking at my sketch I see that starting at one of the corners of such an array and assuming a current of '1', the flow would split in three equal 'parts' (each carrying 1/3). The three split again in two directions (each then carrying 1/6). Next the 1/6 branches would combine again into three (each now carrying 1/3), and these three combine again to bring us back to the original amount inserted at an opposite corner.
    Does that make any sense?
     
    Last edited by a moderator: Jun 11, 2003
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