For the circuit of given figure:
a. Determine the time constant of the circuit when the switch is thrown into position 1.
b. Find the mathematical expression for the voltage across the capacitor after the switch is thrown into position 1.
c. Determine the mathematical expression for the current following the closing of the switch (position 1).
d. Determine the voltage vC and the current iC if the switch is thrown into position 2 at t = 100 ms.
e. Determine the mathematical expressions for the voltage vC and the current iC if the switch is thrown into position 3 at t = 200 ms.
f. Plot the waveforms of vC and iC for a period of time extending from t = 0 to t = 300 ms.
