A circular capacitive pressure sensor has a 2 cm diameter diaphragm (density =4g/cm³) with 25 microns separation between the diaphragm and the fixed electrode. The sensor will be used to measure pressure difference from 0 to 10kPa. The Elastic modulus for the diaphragm is 8x10¹⁰ N/m². Assume Poisson's ratio is 0.2.

a) How thick should the diaphragm be if the capacitance change is to be limited to less than 1%?

b) What is the initial capacitance of the sensor without applying pressure? How much does it change for a pressure of 1 kPa using the thickness chosen in part a?

c) How thick should the diaphragm be if the diaphragm deflection is to be less than 1% of the diaphragm thickness?

d) Suppose the device is accelerated in a direction perpendicular to the surface of the diaphragm. This acceleration exerts a force on the diaphragm, which causes a deflection, just as if a pressure is applied. Using the thickness chosen in part c, what change of capacitance results from acceleration of 20g? Answer with C