Hello panic mode,
before this goes any further, id like to apologize for being being harsh, wasn't my intention.
No problem - don't mention it.
i don't promote or defend any particular bridge not i get royalties from their use.
to me they are more of a curiosity or academic subject. can't say i've ever seen one outside school labs.
Nevertheless, as it was proposed by the questioner, I think we should comment it.
that is why i did not derive equations, because it sounds suspiciously like homework in disguise.
and that is why i stayed with choice of bridge OP mentioned instead of suggesting alternatives.
OK, instead deriving equations by ourselves we can use wikipedia. Unfortunately, a detailed treatment of the bridge under discussion in wiki is only in german. However, the formulas for equilibrium are the same. Look on pages 2 and three of the attachement.
As far as the frequency is concerned there was certainly a misunderstanding. By speaking on frequency-dependence, of course, I mean dependence of the measurement result from the selected frequency - not the problem of frequency uncertainties. The formulas in the attached document show what I mean.
My summary in short:
* To determine an Rx-Cx parallel combination a capacitive ac bridge (similar to the one under discussion) can be used if the frequency-dependent part of the bridge is also an R-C parallel combination. In case of a series R-C combination (as in the circuit under discussion) the formulas for equilibrium show that Rx depends on Cx and vice versa.
* Only if the valus of Rx is very large (small loss angle) there are approximative formulas which can be used. But this is an approximation only.
* However, the ac bridge containing a series R-C circuit can be used to determine the values of the device under test (tooth) in form of series R-C equivalent values. In this case, the series elements have to be converted into an equivalent parallel combination (as desired by the questioner).
However, this is not recommended.
* Why not use a bridge (as I have proposed earlier), which is well suited for the purpose?
W.