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A non-linear capacitive displacement sensor is constructed using three plates; two fixed and one moveable. Each plate is ‘Y' width and "L" length. The fixed once are separated by a distance "d" as shown below. Assuming that you can measure the capacitance of the total device, derive an expression giving the distance X1 and X2 in terms of the measured capacitance C. Also assume the permittivity of the dielectric materials between the top two plates is ε1 and the bottom two plates is ε2.

Hint: For Capacitors in series C = C1 C2/C1 + C2

966_capacitance of the total device.jpg

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