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Equivalent electric circuit

  1. Oct 30, 2015 #1
    Given an electric circuit, with resistors R1 and R2, find the equivalent resistance R.
    Data: R1 = √2.R2

    Points M and N have the same electric potential so they can be connected with a conductor and this way we get the second circuit.
    222.png
     
  2. jcsd
  3. Oct 30, 2015 #2

    mfb

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    There is more you can do to simplify the circuit.
     
  4. Oct 30, 2015 #3
    In terms of what? I know i can solve the parallel ones below, however that won't solve it. There should be a way to proof that M and N are also equal to O.
     
  5. Oct 30, 2015 #4

    mfb

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    Sure, use symmetry again.
     
  6. Oct 30, 2015 #5
    It's symmetrical along MO, NO but that doesn't help us much.
     
  7. Oct 30, 2015 #6

    gneill

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    Temporarily remove the two vertical R2's. What are the potentials at M,N,O?
     
  8. Oct 30, 2015 #7
    On the upper side we will have a resistor with √2R2, but on the down side R2/√2. So they will be different.
     
  9. Oct 30, 2015 #8

    gneill

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    Really? What was your argument for M and N having the same potential in your first post?
     
  10. Oct 30, 2015 #9
    Equal amounts of charge will flow through the upper or downer R1, and since the resistance is equal the voltage will be too. However I don't understand why the points O and M or N will have the same potential as the resistance along the path is different.
     
  11. Oct 30, 2015 #10

    gneill

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    The potentials at M,N, and O are due to the voltage dividers comprised of the resistances in their branches. Here's the situation:
    Fig1.png
    All three branches have the same potential difference across them (whatever you imagine to be placed across terminals AB). All three branches have the same resistance ratios...
     
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