4. (45 points) A circuit is shown in the diagram below. The circuit components have values Cl : 5uF, Cg : 10oF, R1 : 2 (2, R2 : 4 Q, and R3 : 19. Initially the battery is disconnected from the circuit. Figure 2: circuit diagram a. (15 points) The battery is connected to the circuit at t : 0 with both switches 81 and 5'2 initially open. What is the time constant of this RC circuit? What magnitude of charge is on Cl ve seconds after the battery is connected? b. (15 points) If 81 is, instead, initially closed when the battery is connected, discuss the qualitative behavior of the current owing through R2 as a function of time (1) after a short time has passed since the battery was connected, and (ii) after a long time has passed since the battery was connected. (iii) How much energy is stored in 01 after a long time has passed? 0. (15 points) Now consider the case where both switches are initially open and we connect the battery for a long time. We then disconnect the battery and then ip .32 closed. Find the current owing through R3 as a function of time. What is the potential diiTerence across R3 ve seconds after 32 is closed