In the circuit below, the switch connecting the DC source to the network has been open...

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In the circuit below, the switch connecting the DC source to the network has been open for a very long time. The switch is closed at t=0, connecting the source. R Vin 402 8V is ↓ R www L 4Ω ele C 2mH 20 μF Ve a. Obtain the mathematical model of the circuit for Vc/Vin. b. Determine the value of the capacitor voltage at steady-state (t = ∞0). c. Obtain the mathematical model of the circuit for iL/Vin. d. Determine the value of the inductor current at steady-state (t = ∞). e. Determine the capacitor voltage as time passes t> 0 (V(t) = ?). f. Determine the inductor current as time passes t>0. (i (t) = ?). g. Is the circuit (for time t>0) underdamped, critically damped or overdamped? In the circuit below, the switch connecting the DC source to the network has been open for a very long time. The switch is closed at t=0, connecting the source. R Vin 402 8V is ↓ R www L 4Ω ele C 2mH 20 μF Ve a. Obtain the mathematical model of the circuit for Vc/Vin. b. Determine the value of the capacitor voltage at steady-state (t = ∞0). c. Obtain the mathematical model of the circuit for iL/Vin. d. Determine the value of the inductor current at steady-state (t = ∞). e. Determine the capacitor voltage as time passes t> 0 (V(t) = ?). f. Determine the inductor current as time passes t>0. (i (t) = ?). g. Is the circuit (for time t>0) underdamped, critically damped or overdamped?