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 Vc (t) and Ic(t).
b. Find VC at t = 15 msec ("millisec") and at t = 30 msec.
c. Find IC 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 VC = 3 Volts.
e. After t = 30 msec, the switch S1 is thrown into position 2 ("pos2"), as shown in the schematic below. Find VC when the switch is thrown to position 2, and find the current IC at the same instant.
f. Write the mathematical expressions for Vc (t) and Ic(t) for the time from the throwing of switch S1 to position 2 ("pos2").
g. Find VC at t = 20 msec after S1 goes to pos2.
h. Find VC and IC at t = 8 msec after S1 goes to pos2.
i. How long does it take VC to fall to 3 Volts.