(Solved): Consider the circuit shown in Figure 1 . Let eC1 be the voltage across the capacitor with capaci ...

Consider the circuit shown in Figure 1 . Let $e_{C1}$ be the voltage across the capacitor with capacitance $C$, and $e_{C2}$ be the voltage across the other capacitor. On paper, derive the state-variable equations for the circuit, briefly explaining each step, and show that they are $\begin{array}{rl}{\dot{e}}_{C1}& =\frac{1}{3RC}\left[e_{C2}-e_{C1}+R{i}_i(t)\right]\\ {\dot{e}}_{C2}& =\frac{1}{6RC}\left[e_{C1}-e_{C2}+2R{i}_i(t)\right]\end{array}$ Include, on paper, a copy of the circuit diagram indicating any voltages and currents required in the derivation. Note that, if you can't derive those equations, you can still attempt the next part of this exercise. Figure 1