The pull-in voltage

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 distances

between the electrode plates: 2 and 0.5 ?m. The medium is air.(b) The four support

beams are each 500 ?m long, 5 ?m wide, and 0.3 ?m in thickness. What is the

force constant Km experienced by the parallel plate capacitor? (diagram not drawn to

scale).

(b) If the support beams becomes 0.25 mm long (i.e. half as long as before), which of

the 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.