# Possible Explanations for Unexpected Results: Negative Resistance and Consistent Short-Circuit Current and Open-Circuit Voltage

My objective in this circuit is to find the value of RL that achieves maximum power transfer.

simulate this circuit – Schematic created using CircuitLab

To do this, find Voc and Isc, as shown below.

simulate this circuit

Upon performing the calculations, it is determined that $$\V_ \text{OC} = 4~V\$$ and $$\I_\text{SC} = -2~mA\$$, indicating that $$\R_\text{TH} = -8~k\Omega\$$.

Well, assuming that the calculations and simulations are correct, I agree that it doesn't make sense to talk about negative resistance. The direction of the short-circuit current and the polarity of the open-circuit voltage seem to be consistent. Now, what would be the theoretical explanation for this result or where could the error be?

$$V_{AB} = (1A + k V_{AB}) \cdot 1\Omega$$
$$R_{AB} = \frac{V_{AB}}{I_{AB}} = \frac{V_{AB}}{V_{AB}/1\Omega - k V_{AB}} = \frac{1}{1 \Omega^{-1} - k}$$