(Solved): (a) A capacitive transducer is constructed of two plates having an area of cross-section \( 600 \m ...

(a) A capacitive transducer is constructed of two plates having an area of cross-section \( 600 \mathrm{~mm}^{2} \) and are separated by a distance of \( 4 \mathrm{~mm} \) and is connected to a diaphragm gauge. When there is no pressure on the diaphragm, the output of the capacitor is \( 350 \mathrm{pF} \). If a pressure of \( 800 \mathrm{kN} / \mathrm{m}^{2} \) is applied to the diaphragm, the average deflection in the diaphragm is \( 0.5 \mathrm{~mm} \). Calculate the change in the capacitance of the system. (20 marks) (b) A parallel plate capacitive transducer has a plate area of \( 40 \mathrm{~mm} \times 40 \mathrm{~mm} \) and plate spacing of \( 0.5 \mathrm{~mm} \). Calculate: (i) the device capacitance (ii) the displacement that causes the capacitance to change by \( 5 \mathrm{pF} \). (20 marks)