Chapter 9, Problem 27P

An input voltage $v_{in}=10\sin \left(10t\right)\text{V}$ is applied to an Op—Amp circuit as shown in Fig. P9.27.

1. The relationship between the input and output of the Op—Amp is given by

$v_{in}=0.1\frac{d{v}_0}{dt}$ $\left(9.62\right)$ Suppose that the initial output voltage of the Op—Amp is zero. Integrate both sides of equation $\left(9.62\right)$ to determine the voltage $v_o\left(t\right)$. Also, sketch the output voltage $v_o\left(t\right)$ for one cycle.

(b) Suppose that the instantaneous power absorbed by the capacitor is $p\left(t\right)=100\left(1-\cos \left(10t\right)\right)sin\left(10t\right)\text{mW}$ and that the initial stored energy is $w\left(0\right)=0$. Knowing that $p\left(t\right)=\frac{dw\left(t\right)}{dt}$, integrate both sides of the equation to determine the total stored energy $w\left(t\right)$.