while studying this certain types of problems with capacitive displacement sensors I came across one in particular that I am pretty much stuck. The whole problem is explained in following text and screenshots. I am looking for useful tips on how to approach this kind of problem. Thanks!
Capacitive displacement sensor is shown in the picture below. (picture a). It has surface area of S_0 and starting distance d_0. It is connected (integrated) in bridge circuit which are shown in the pictures b and c.
a) Find the expressions for the output voltage U_0 for pictures b and c
b) In the cases when the displacement is very small (Δd/d_0 << 1) you must calculate the effective value of output voltage when R(resistance) = d_0/(ωSε_0), and when the indicator resistance is very high.