A capacitive displacement sensor

1. A capacitive displacement sensor is used to measure rotating shaft wobble shown in the figure below. The capacity is 520 pF with no wobble. Find the change in capacity for a +0.035 to -0.035 mm shaft wobble. Show your calculations.

2. To measure the displacement, assume that the capacitive pickoff in problem 1 is used in an AC bridge constructed of only capacitors. Using 520pF for the bridge capacitors, find the offset bridge voltage for the two extremes of shaft wobble. Assume a sine wave voltage input having an amplitude of 5 Vrms and a frequency of 5 kHz. Rather than using an equation from the book, you are required to derive the offset bridge voltage using circuit analysis principles. Show all your calculations.
3. Using Multisim, construct and simulate the AC bridge of problem 2 for the two extreme conditions. Be sure to provide screenshots. Also, write a brief summary, noting if the results matched expected results.

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