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Norton's Theorem

  1. Jun 22, 2014 #1
    1. The problem statement, all variables and given/known data
    Obtain the norton equivalent of the circuit on terminals a-b. use the result to find the current i.
    see attached image.

    2. Relevant equations
    1.Shorting the terminal when finding norton
    2. Open current source and short voltage source when finding norton resistance


    3. The attempt at a solution
    By 2. We obtain
    Rn = 6+4=10.

    When Terminals a and b are short circuited we find current across it using nodal analysis
    2+((12-v)/6)=v/4
    v=9.6V

    So that
    In= (12-9.6)/6 =0.4A (current source facing upward)

    This is the part where i am confused.
    So connecting back the original components across terminal a-b (5 ohm and 4A in parallel) to the norton equivalent.
    By current division We obtain


    i = (10/(10+5))(4A + 0.4A) = 2.93A

    The real answer is 2.4A , it's kinda odd because 0.4A norton current source is facing downward with this answer.


    Edit. Pls move this to introductory physics
     

    Attached Files:

    Last edited: Jun 22, 2014
  2. jcsd
  3. Jun 22, 2014 #2

    ehild

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    Homework Helper
    Gold Member

    The short-circuit current flows downward if the source current points upward. You assumed the short-circuit current flowing upward, that means the Norton-current pointing downward, that is negative.

    ehild
     

    Attached Files:

  4. Jun 22, 2014 #3

    NascentOxygen

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    Staff: Mentor

    Hi, and welcome to the forums.

    Norton's Theorem does not involve Iin! His formula requires Iout.
     
    Last edited: Jun 22, 2014
  5. Jun 22, 2014 #4
    I can see it now.

    I've read the book and realized that whenever the short circuit current face upward, then the norton current which represent the rest of the circuit will face downward and vice versa.

    In this case, i made the short circuit current point upward.
    Then the norton current source should point downward.
     
  6. Jun 22, 2014 #5

    NascentOxygen

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    Staff: Mentor

    Well, okay. :wink: But aren't you going to be tripped up if ever the source is drawn horizontally?
     
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