The given circuit is modified as follows:
\begin{itemize}
\item Label the source voltage $v_s = 20u(t)$
\item The 0.5 F capacitor is replaced by a 2 $\Omega$ resistor
\item Terminal $(a, b)$ is connected to a load resistor $R_L$
\end{itemize}
1. Redraw the modified circuit, find its Thevenin
Equivalent, and tune $R_L$ so it absorbs maximum
power.
Hint: first find $v_x$ when terminal $(a, b)$ is OPEN hence $v_{ab} = v_{TH}$, then use nodal analysis. Think what happens when a
voltmeter is connected to $(a, b)$ to measure $v_{TH}$.
2. Suppose the modified circuit is connected to the series RL load circuit shown. Find $i_L(t)$, $t > 0$ when $u(t) =$
$u_s(t)$ (a unit step function), and $i_L(0^-) = 4$ A
3. Suppose the modified circuit is connected to a series RC load circuit (that is, the inductor is replaced by a
Capacitor) with $C = 0.1F$. Find $v_C(t)$, $t > 0$ when $u(t) = u_s(t)$ (a unit step function), and $v_C(0^-) = 4$ V
