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Equivalent Inductance

  1. Feb 9, 2016 #1
    1. The problem statement, all variables and given/known data
    New Doc 11_1.jpg

    2. Relevant equations
    Adding inductors in series and parallel (same as resistors)

    3. The attempt at a solution
    This is the first time I ran into a circuit like this with diagonal wiring and I am not sure how to treat it. Do I add the inductors in the triangle in series? So for example, on the left would it just be 105uH? I don't think that is right. Then that would be in series with the 25uH. How do I do this?
     
  2. jcsd
  3. Feb 9, 2016 #2

    gneill

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    Component arrangement on the page doesn't matter. The only thing that matters is how they connect to each other (the topology). You can feel free to re-draw the circuit with only horizontal and vertical lines and components if you wish, just so long as you maintain all the same connections.
     
  4. Feb 9, 2016 #3
    As an indication, at the right end of the circuit 18 an 12 are connected in series and them together are in series with 38. the idea is tha the conductor lines between two connection points are ideal and you can modify their length and form as you wish.
     
  5. Feb 9, 2016 #4

    cnh1995

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    First identify the series and parallel combinations. The circuit collapses into a very simple form then! You will automatically get rid of the diagonal wiring once you spot the series and parallel inductors.
     
  6. Feb 9, 2016 #5
    I'm still not sure what would be in series and what would be in parallel. I want to say that the 60uH and 30uH inductors are in parallel, and once I get that would that equivalent be in series with the 25uH and 15uH?
     
  7. Feb 9, 2016 #6

    cnh1995

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    How are they in parallel? Do they have "common end points"?
    Start from the rightmost side. What can you say about 18uH and 12uH?
     
  8. Feb 9, 2016 #7

    gneill

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    Do they share the same two node connections? Can you draw a closed path that passes only through those two components (where wire doesn't count as a component) ?
     
  9. Feb 9, 2016 #8
    Those are in series, so 30uH.

    So if they have a common endpoint, they are in series? Like the 18 and 12?
     
  10. Feb 9, 2016 #9

    cnh1995

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    Remember these two points while checking whether two components are in series or parallel:
    1)Parallel components have common endpoints.
    2) While checking for series components, say R1 and R2, imagine some current flowing through R1. If the same current enters R2 after leaving R1, then R1 and R2 are in series.
     
  11. Feb 9, 2016 #10
    Ok, so whenever the current splits into different paths they are in parallel. So going through the 18 and 12 they would have the same current, but then the current would split at the bottom right corner. Current would go towards the 20 and 38. But then what happens?? It looks like current keeps splitting.
     
  12. Feb 9, 2016 #11

    cnh1995

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    Parallel components have common endpoint"s", both the terminals are connected between two points.
     
    Last edited: Feb 9, 2016
  13. Feb 9, 2016 #12

    cnh1995

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    18 and 12 will become 30uH. What can you say about this 30uH and the diagonal 20uH?
     
  14. Feb 9, 2016 #13
    It looks like the current splits right? So would they be in parallel? (sorry for the crappy drawing)
    14550444182375.png
     
  15. Feb 9, 2016 #14

    cnh1995

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    After splitting at one terminal, if all the split currents reunite at the other terminal, then the components are in parallel.
     
  16. Feb 9, 2016 #15

    cnh1995

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    They are in parallel because their terminals are connected between two common points.
     
  17. Feb 9, 2016 #16
    But what happens to the current after it goes through the 38? Wouldn't it split again?

    14550447666149.png
     
  18. Feb 9, 2016 #17

    cnh1995

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    It would, and it will continue to split. But in the end, all the split currents will reunite at the other terminal. Incoming current has to be equal to outgoing current. Isn't this what KCL is all about?
     
  19. Feb 9, 2016 #18

    SammyS

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    This is NOT correct.

    Yes, at the right end of the circuit, the 18 and 12 are connected in series, but that combination is in parallel with the 20. The combination of these three is in series with the 38.

    etc, etc.
     
  20. Feb 9, 2016 #19
    True. Im confused now. You said:
    Does this mean that the combined 30 is in parallel with the 20 and 38? Why is sammy saying they are in series?
     
  21. Feb 9, 2016 #20

    cnh1995

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    Combined 30 is in parallel with 20. Their parallel equivalent is in series with 38. This series-parallel stuff goes on and the circuit reduces to a single equivalent inductance between the given terminals.
     
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