2. Consider the circuit is shown in the figure below. The circuit comprises a voltage supply, v(t), resistor (R), inductor (L) and capacitor (C). Let x1=i and x2= v, be the state variables for this system, where i and v.are the circuit current and capacitor voltage, respectively. For this system, a) Derive the loop equation, involving integro-differential equations, from first principles b) Write the state differential equations Write the state-space equation in matrix-vector form Sketch the signal-flow graph. c) d) Show all your work. R + (1)

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