1.) In the circuit below, the voltage source has been for a long ti...

1.) In the circuit below, the voltage source has been for a long time at Vs = 6V. At time t=0, the voltage source is set to Vs=3V and stays there. For R1 = 2KΩ, R2 = 1kΩ, C = 10μF: a.)Find and sketch the transient responses for vc(t). b.) Calculate the current through the R1 at t = 6ms clearly indicating the direction of the current. 2.) In the circuit below Vs = 1V, R1 = 1kΩ, R2 = 10Ω, C = 1μF, L = 10mH, and both switches S1 and S2 have been open for a long time. a.) At t = 0, only switch S1 is closed. Calculate the voltage across the capacitor vc(t) at t = 1ms. b.) At t = 1ms, switch S1 is opened: then at t = 2ms switch S2 is closed. Sketch the transient response of vc(t) from t=0, clearly indicating the types of response observed and the values of vc(t) at t = 0, t =1ms, t = 2ms, and t long enough. 3.) In the circuit below, the switch has been in position-1 for a long time. At t = 0, the switch is moved to position-2 and remains there for t>0. a.) Calculate the values of vc(t) at t = π/40 seconds. b.) Calculate the values of iL(t) at t = π/40 seconds. 4.) For the same circuit and switching sequence as described in Problem-2: a.) Derive the equations for the full transient response for vc(t) starting at t = 0. Plot the full transient response in MATLAB. b.) Derive the equations for the full transient response for i(t) starting at t = 0. Plot the full transient response in MATLAB.