Chapter 9, Problem 31P

A current $i\left(t\right)=10e^{-10t}\text{mA}$ is applied to a $100\mu F$ capacitor, as shown in FigP9.31.

1. Suppose the initial voltage across the capacitor is $v_o=10\text{V}$. Knowing that $i\left(t\right)=C\frac{d{v}_o\left(t\right)}{dt}$, integrate both sides of the equation lo determine the voltage $v_o\left(t\right)$. Evaluate the voltage at times $t=\mathrm{0.0.1},0.2,$ and $0.5s,$ and use your results to sketch $v\left(t\right)$.
2. Suppose the stored power is $p\left(t\right)=0.2e^{-20t}$
3. pQ) = 0.2 r20’ W and that the initial stored energy is $w\left(0\right)=0.005\text{J}$. Integrate both sides of the equation $p\left(t\right)=\frac{dw}{dt}$ to determine the total stored energy $w\left(t\right)$.