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 and .

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  and  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.