Now that I look again at the final result in the image attached to post #1, I see immediately that it's incorrect. If the resistance "b" is not there its value becomes infinite. The final expression given says that if "b" is missing (becomes infinite), the bridge resistance becomes infinite...
I know you have Mathematica, so I figured you would have checked the post #1 result. :) I solved it with Mathematica, and the post #1 result appears incorrect.
There is an image attached to post #1 with the problem worked out. You, like me, tend to check results, Have you worked out the solution to the impedance seen at terminals 1 and 3, and compared to the result in the image attached to post #1?
Ratch, I think the final result in the image attached to post #1 is incorrect. Have you worked out the impedance seen at terminals 1 and 3, and compared your result with the result in the image?
Here's the oldest description of an RC network with gain I know of; page 40 of this old magazine:
https://www.americanradiohistory.com/Archive-Tele-Tech/40s/Tele-Tech-1947-04.pdf
Discussion about this topic:
Fialkow, A.D. & Gerst, Irving. (1953). The Maximum Gain of an RC Network. Proceedings of the IRE. 41. 392 - 395. 10.1109/JRPROC.1953.274389.
Also: https://ieeexplore.ieee.org/document/4050644
Also...
The 0.1 uF capacitor I have in my assortment is marked with the manufacturer--it's Jwco.I found the manufacturer's list of capacitor models here: http://www.jiaweicheng.com/en/productlist/products.html
They show several models whose capacitance range goes down to 0.1 uF. My capacitor doesn't...
If the measurement you got for your 0.1 uF was around 10 ohms then it must be ok, since extrapolating from the data you found of a 0.47 uF max impedance at 23 ohms, 0.1 uF max allowable would be much more than that.
Probably the reason you didn't find that value in tables is that 0.1 uF is an uncommonly small value for an electrolytic capacitor. Are you sure it's an electrolytic? You could just replace it with a 0.1 uF film capacitor.
I have some 0.1 uF electrolytics only because they were part of a full...
You used 3 equations (i1 and i2 are not asked for) and involved the current source.
For short and succinct, apply the voltage divider formula twice, obtaining expressions for the voltage across C3 and across Z, equate them and solve one equation. The current source needn't be involved...
You didn't read all the other responses to post #1, did you?
I made my careless mistake, and you failed to notice that the capacitors and inductor are not microfarads and microhenries, but rather millifarads and millihenries.
There's my mistake. In the table of component values, where it says w = 50 rad/s, I just mentally changed that to 50 Hz, not 50 rad/second. :( This is in Europe right, where the power is 50 Hz?
With that change both my solutions will get Z = 2.
I also did a mesh solution which also gets Z=2.