# Thevenin Equivalent Resistance for a Black Box

1. Mar 21, 2009

### jmcmillian

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$$\Omega$$, 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$$\Omega$$. 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$$_{Th}$$= V$$_{Th}$$/I$$_{sc}$$
Resistors in Parallel: R$$_{eq}$$= (1/R$$_{1}$$+...+1/R$$_{n}$$)$$^{-1}$$
Resistors in Series: R$$_{eq}$$=R$$_{1}$$+...+R$$_{n}$$
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$$\Omega$$)+(1/1.001k$$\Omega$$)]^-1 = .9096k$$\Omega$$

STEP TWO: R23 IN SERIES WITH R5
R235 = R23 + R5 = .9096k$$\Omega$$ + 10.0k$$\Omega$$ = 10.9096k$$\Omega$$

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

STEP FOUR: Rc PARALLEL to R235
[(1/24.95k$$\Omega$$ )+(1/10.9096$$\Omega$$ )]^-1 = 7.59k$$\Omega$$

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.