Finding R_Thevenin involving dependent source

[Bishamonten]

Homework Statement

Homework Equations

Impedances:

Inductor = jωL; Capacitor = 1/jωC

The Attempt at a Solution

I attempted to excite the circuit with an I_o = 1A source, and then from Z_c = 1/jX₂ justify V_x = (1)(Z_c)

Thus, substituting our found V_x and then doing a source transformation, we find our V = g(V_x)(jX₁), and thus, our R_Th = V/I_o, which is not correct. The correct answer is #1 in the image.[/B]

 

[gneill]

I attempted to excite the circuit with an I_o = 1A source, and then from Z_c = 1/jX₂ justify V_x = (1)(Z_c)

Thus, substituting our found V_x and then doing a source transformation, we find our V = g(V_x)(jX₁), and thus, our R_Th = V/I_o, which is not correct. The correct answer is #1 in the image.

Exciting the circuit with a current source is good. I think that where you've gone wrong is after your source transformation.
The voltage source from that transformation is not the potential that appears across ab. There are now two components between that source and the "a" terminal, the impedance X1 associated with the transformed source and the capacitor's X2.