1. The circuit shown below is a DC charging and discharging circuit.
a. At t = 0 sec, switch S1 is thrown to position 1 ("pos1"). Write the mathematical expressions for V_{c} (t) and I_{c}(t).
b. Find V_{C} at t = 15 msec ("millisec") and at t = 30 msec.
c. Find I_{C} at t = 0 msec and at t = 30 msec.
d. Find the time, t, in msec, that it will take for the capacitor to charge up to V_{C} = 3 Volts.
e. After t = 30 msec, the switch S1 is thrown into position 2 ("pos2"), as shown in the schematic below. Find V_{C} when the switch is thrown to position 2, and find the current I_{C} at the same instant.
f. Write the mathematical expressions for V_{c} (t) and I_{c}(t) for the time from the throwing of switch S1 to position 2 ("pos2").
g. Find V_{C} at t = 20 msec after S1 goes to pos2.
h. Find V_{C} and I_{C} at t = 8 msec after S1 goes to pos2.
i. How long does it take V_{C} to fall to 3 Volts.