Normally, I would just assume that for a circuit with just a dependent source, I can treat it the same as as one with an independent source. Using Picture 1 Assume that I want to find the Thevenin wrt nodes A and B. I want to find Rth, so I zero out all sources, which makes I = 0A. The only resistance left is from resistor R. I call R my Rth. But this is wrong! Using Picture 2 Apparently, I have to attach an arbitrary voltage source with voltage Vx, which drives an arbitrary current Ix. Rth = Vx/Ix So doing KCL on Node C, I get Ix + I = i (1) I = 0.5i from the picture and plugging into (1) Ix + 0.5i = i. Ix = 0.5i (2) Node C is at potential Vx. i = Vx/R from the picture, then plugging into (2) Ix = 0.5(Vx/R) Rth = Vx/Ix Rth = Vx / (0.5Vx/R) Rth = 2R As you can see, the Rth obtained from both methods is different (the second method is correct), but why, for circuits with only dependent sources, must we apply an arbitrary voltage source to find Rth? What's wrong with the first method? If it's not clear, here is a video doing the same thing, but with arbitrary current source. He states that this is the ONLY way to solve for Thevenin Equivalent when there are no independent sources. Why?