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Thevenin Resistance question

  1. Jan 10, 2017 #1
    1. The problem statement, all variables and given/known data
    Determine the Thevenin and Norton equivalents at terminals a-b of the circuit in Fig. 4.125. The figure is uploaded.

    2. Relevant equations
    We know that the Thevenin resistance is the resistance between the terminals when the independent sources are turned off.

    3. The attempt at a solution
    1) We make the current source an open circuit, and then we find the equivalent resistance... The solution manual says that 10Ω and 20Ω resistors are in series, and that the 50Ω and the 40Ω resistors are in series, and that these combinations are in parallel to each other.
    However it doesn't make sense they can't be in series... because if they are in series the same current should pass through them and if a current passes from the 10Ω to the 20Ω resistor why can't it pass through the rest of the resistors as a path exists making them all in series..??

    2) I'm also wondering about what would happen in another configuration suppose we short circuit terminals a and b. How would the resistance be found then wouldn't the 10Ω and 20Ω resistors be in parallel. similarly the 50Ω and 40Ω would be in parallel and their combinations in series??

    Thank you for all the help
    it's highly appreciated
     

    Attached Files:

  2. jcsd
  3. Jan 10, 2017 #2

    gneill

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    Staff: Mentor

    You're only interested in paths from a to b since you're looking for the resistance between the open terminals a and b. There are two independent paths:

    upload_2017-1-10_8-20-50.png
    Resistance between what two nodes? If you short out a and b, they become the same node.
     
  4. Jan 10, 2017 #3

    cnh1995

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    Homework Helper

    When you are finding the equivalent resistance between a and b, it is the equivalent resistance "seen" by a voltage source placed between a and b. Put a battery between a and b and you'll see how the two currents flow.
     
  5. Jan 10, 2017 #4
    I know that they become the same node...
    My question is how would you combine the resistors in this case???
     
  6. Jan 10, 2017 #5
    Thanks got it
     
  7. Jan 10, 2017 #6

    gneill

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    Staff: Mentor

    Resistance is like voltage, you need two points to define the resistance between. What two points are you going to "view" the resistance between as you combine them?
     
  8. Jan 10, 2017 #7
    Between these two lines that I drew just now... I uploaded a pic
    The top and bottom
     

    Attached Files:

  9. Jan 10, 2017 #8

    gneill

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    Staff: Mentor

    You should be able to identify the parallel pairs of resistors. Once you've defined the two points between which you want to find the net resistance, you've also established the nodes where external current can flow into and out of the network. That in turn dictates what components have parallel connections:

    upload_2017-1-10_8-58-22.png
     
  10. Jan 10, 2017 #9
    well the 10Ω and 20Ω resistors are in parallel since they are connected to the same nodes. similarly the 50Ω and 40Ω are also in parallel for the same reason.
    Does it work like that??
     
  11. Jan 10, 2017 #10

    gneill

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    Staff: Mentor

    Yes.
     
  12. Jan 10, 2017 #11
    Thank you
     
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