1. In the circuit shown below, the capacitor initially has a voltage across it 4 Volts (at t = 0).
a. Write down the expression for V_{C} (t) when the switch is closed.
b. Write down the expression for I_{C} (t) when the switch is closed.
c. Find the initial current when the switch is closed.
d. What will be the final voltage across the capacitor, and how long will it take the capacitor to reach that voltage?
e. What is V_{C} after one time constant has passed?
f. How long will it take for the capacitor to get to V_{C} = 20 Volts?