Chapter 3, Problem 3.38P

A parallel-plate capacitor is used as a vibration sensor. The plates have an area of ${\text{100cm}}^{\text{2}}$ , the dielectric is air, and the distance between the plates is a function of time given by

$d\left(t\right)=1+0.01\sin \left(200t\right)mm$
A constant voltage of 200 V is applied to the sensor Determine the current through the sensor as a function of time by using the approximation $1/\left(1+x\right)\cong 1-x$ for $x<<1$ . (The argument of the sinusoid is in radians.)