Chapter 10, Problem 22P

A constant voltage source $v_{in}\left(t\right)=10$ volts is applied to the Op—Amp circuit shown in Fig. P10.22. The output voltage $v_0\left(t\right)$ satisfies the following first order differential equation and initial conditions:

$0.01\frac{d{v}_0\left(t\right)}{dt}+v_0\left(t\right)=-v_{in}\left(t\right)$ $v_0\left(0\right)=0\text{V}$.

(a) Find the transient solution $v_{o_{\tau }tran}\left(t\right)$.

(b) Find the steady-state solution $v_{o_{\tau }ss}$, if $v_{in}=10\text{V}$.

(c) If the initial Output voltage is $v_0\left(0\right)=0\text{V}$, determine the total response.

(d)What is the time constant $\tau$ of the response? Plot the response $v_0\left(t\right)$ and give the values of $v_0$ at $t=\tau$, $2\tau$ and $5\tau$.