# A capacitive sensor

The questions below are due on Wednesday March 04, 2020; 11:59:00 PM.

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A number of sensors use a variable capacitance. For example, the proximity sensor we built in lab is one such capacitor. Many of the accelerometers and gryroscopes that are found in automotive inertial measurement units and in your phone also use capacitive sensors. For the proximity sensor we will build in lab, we will use the RC time constant \tau to infer C and thus measure distance. Another way to turn a time-varying C into an electrical signal is to feed it with a constant voltage, as shown in the figure below: This is commonly used in an electret microphone, where sound causes a time-varying C. Imagine the time-varying capacitance is given by:

C(t) = C0 + C1 sin(\omega t)

Determine the capacitor current i(t).

Enter an expression for i(t) in terms V, C0, C1, t, and/or trigonometric functions. Use w for \omega.

i(t)=