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Thevenin Equivalent Resistance for a Black Box

  1. Mar 21, 2009 #1
    1. The problem statement, all variables and given/known data
    I am trying to find the theoretical Thevenin equivalent resistance for a black box that I used in a circuits experiment. The measured Thevenin equivalent resistance was roughly 4786[tex]\Omega[/tex], so the theoretical should be somewhere around that. However, I have tried several times to solve the problem, but keep arriving at a value of around 3511[tex]\Omega[/tex]. That just seems to be a little too low...

    I have attached the circuit schematic, with resistor values included.
    Could someone please look at the problem and see if I am on the right track. If so, any pointers on how I should finish it?

    2. Relevant equations
    R[tex]_{Th}[/tex]= V[tex]_{Th}[/tex]/I[tex]_{sc}[/tex]
    Resistors in Parallel: R[tex]_{eq}[/tex]= (1/R[tex]_{1}[/tex]+...+1/R[tex]_{n}[/tex])[tex]^{-1}[/tex]
    Resistors in Series: R[tex]_{eq}[/tex]=R[tex]_{1}[/tex]+...+R[tex]_{n}[/tex]
    Y to Delta Transformation:
    3. The attempt at a solution
    STEP ONE: R2, R3 in parallel
    R23 = [(1/R2)+(1/R3)]^-1 = [(1/9.97k[tex]\Omega[/tex])+(1/1.001k[tex]\Omega[/tex])]^-1 = .9096k[tex]\Omega[/tex]

    R235 = R23 + R5 = .9096k[tex]\Omega[/tex] + 10.0k[tex]\Omega[/tex] = 10.9096k[tex]\Omega[/tex]

    STEP THREE: Y TO [tex]\Delta[/tex] TRANSFORM R4, R6, R7
    Rc = [(R4*R6)+(R4*R7)+(R6*R7)]/R4 = 24.95k[tex]\Omega[/tex]
    Ra = [(R4*R6)+(R4*R7)+(R6*R7)]/R6 = 24.85k[tex]\Omega[/tex]
    Rb = [(R4*R6)+(R4*R7)+(R6*R7)]/R7 = 12.39k[tex]\Omega[/tex]

    [(1/24.95k[tex]\Omega[/tex] )+(1/10.9096[tex]\Omega[/tex] )]^-1 = 7.59k[tex]\Omega[/tex]

    From here, I have tried different combinations of source transformations, converting the delta back to a Y, etc. to try and get an equivalent resistance.
  2. jcsd
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