You have an industrial warehouse for which you need to design equipment

of liquid level measurement $($see figure $6.$ To carry out this measurement, two parallel metal plates have been placed inside the tank. These plates act as a

flat capacitor. The objective of this is to use the variation of capacity as a function

of the variation in the height of the liquid to determine the level. Calculate:

$($a$)$ The capacity C$1$ as a function of the height h reached by the liquid.

$($b$)$ The capacities Cmax and Cmin for: H $=10$m$,$ e $=10$cm$,$ d $=5$cm$,\backslash$epsi r $=3$