I'm on this problem:
And I'm trying to use KCL to find Vth, my approach is:
Am I on the right path regarding KCL?
Thanks in advance!
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Hint 0: No your formula is not correct. The capacitor is not connected to the Vth node, so it won't be involved in the KCL equation for that node.
Hint 1: Anything in parallel with a voltage source has no effect on the rest of the circuit.
Hint 2: The Thevenin voltage can be calculated from the voltage divider formula.
You're almost there. I would reconsider the equation itself and more specifically the Vth/Zc part. It is also helpful to add +/- markers on the components to make sure you write the equation in a consistent manner. You are also using KCL, which KVL is much more applicable, and not even needed in this problem.
Using a voltage divider, you notice the Vth is simply (Zl V0)/(R+Zl) because V0 is in parallel to the entire branch.
Using KVL, you can write RI1 + ZlI1 - ZcI2 = 0, then Vth = ZlI1 where I1 and I2 are the currents in each branch.
KCL will give you the same result with more work.