Electrical – How to simplify a circuit with ideal current source and ideal voltage source

It's actually quite straightforward to find the Thevenin impedance of this circuit.

The equivalent impedance looking into the port ab is defined by:

$$Z_{ab} \equiv \frac{V_{ab}}{I_{ab}} = \frac{V_{ab}}{i_{\Delta}} = Z_{th}$$

But you can write by inspection a simple KVL equation for \$V_{ab}\$ in terms of \$i_{\Delta}\$:

$$V_{ab} = i_{\Delta}(-jX_{1uF} + 10k\Omega) + 200 i_{\Delta} \cdot 100 \Omega) = i_{\Delta}(-jX_{1uF} + 30k)\Omega$$

Generally speaking, to find the Thevenin equivalent of a circuit with only dependent source(s), you must be sure to "activate" the dependent source(s) with a test source.

This is what was done above. We solved for the voltage across the port due to a test current source, \$I_{ab}\$ which, in this case, equals the controlling variable thus making this problem particularly easy to solve.

From what I understand the coil in the "sensor" is getting current induced by the AC phase I clamp it onto.

The current in the clamped AC circuit induces a voltage in the main coil (the secondary winding) of the CT. The current that flows in the secondary winding is only due to adding a burden resistor to the terminals of that coil.

Without a burden resistor, the voltage at the terminals of the secondary can be several tens of volts in amplitude because, in effect the primary is 1 turn and the secondary is (say) a thousand turns and although this makes a voltage magnification of 1000:1 the voltage at the primary is only a few several millivolts. That's the story without a burden resistor.

Just as the CT will magnify voltage by 1000:1 conservation of energy means that it reduces current into the secondary by 1000:1 but only when a burden resistor is added.

There are other subtleties related to how the burden (on the secondary) is transformed down into a very low impedance on the primary by the turns ratio squared and understanding this gives a real deep insight into the mechanisms at play but try and understand what I wrote above first.