Consider a fully-clamped circular diaphragm poly-Si with a radius of 250 μm and a thickness of 4 μm. Assume that Young’s modulus is 130 GPa and Poisson’s ratio is 0.3. A uniform pressure of 20 kPa is applied.
(a) What is the stress at the center of the diaphragm?
(b) What is the radial stress at the fully-clamped edge of the diaphragm?
(c) What is the transverse stress at the fully-clamped edge of the diaphragm?
(d) What is the amount of deflection at the center of the diaphragm?

An external consultant recommends that a plant installs a bank of capacitors for power factor correction. this will reduce the peak electrical demand charges by an average of 93 kw every month. the plant current pays $13 per kw in peak demand charges. the capacitor bank will include 223 kw of fixed capacitors, and 183 of variable capacitors. the fixed capacitors cost $59 per kw, and the variable capacitors will cost $65 per kw. the consultant charges 21% of the equipment costs to install the capacitors. because this project will reduce the demand for the electric utility, they are prepared to provide a one-time rebate of $42 per kw of reduced demand. what is the simple payback period for this project (in years)?