A parallel plate capacitor with four silicon support beams is shown below. (a)The top plate has area of 1×1 mm2. Calculate the capacitance values for two distancesbetween the electrode plates: 2 and 0.5 ?m. The medium is air.(b) The four supportbeams are each 500 ?m long, 5 ?m wide, and 0.3 ?m in thickness. What is theforce constant Km experienced by the parallel plate capacitor? (diagram not drawn toscale).(b) If the support beams becomes 0.25 mm long (i.e. half as long as before), which ofthe following statement would be correct?(1) The pull-in voltage would increase by four times(2) The plate would pull in when the displacement of the beam exceeds xo/6 instead.(3) The electric force constant (ke) at the pull-in point will be increased by 8 times.(4) The resonant frequency of the device will decrease.
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