Thevenin Equivalent Resistance for a Black Box

[jmcmillian]

Homework Statement

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?

Homework 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:

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.

 

[Valkarie]

However, I keep arriving at a value of around 3511\Omega which just seems too low. Any help would be much appreciated!

 

[Mene]

However, I keep arriving at a value lower than the measured Thevenin equivalent resistance of 4786\Omega. Any suggestions?

I understand your frustration in trying to find the theoretical Thevenin equivalent resistance for your black box. It is important to note that theoretical calculations may not always match up exactly with experimental measurements due to various factors such as measurement errors and component tolerances. It is also possible that there may be other components or circuit elements present in the black box that are affecting the overall resistance.

That being said, your approach seems to be correct in breaking down the circuit into simpler components and using the appropriate equations for resistors in parallel and series. One suggestion I have is to double check your calculations and make sure all units are consistent. Additionally, you may want to consider using a different method for solving the circuit, such as using Kirchhoff's laws or nodal analysis, to see if you arrive at a different result.

Overall, it is important to keep in mind that the theoretical Thevenin equivalent resistance is just an approximation and may not match up exactly with the measured value. As long as your calculations and approach are correct, the slight discrepancy may be due to experimental factors. I would also recommend discussing your results with your instructor or peers to see if they have any insights or suggestions. Keep up the good work and don't get discouraged!