Assume that steady-state conditions exist before the switch is flipped, so the circuit at t=0- looks like:
You can find the voltage across the capacitor (which looks like an open) by finding the voltage across the 3Kohm resistor which is in parallel with the capacitor. (Try a voltage divider). Once you find the voltage at t=0-, that is also the voltage on the cap at t=0+.
The final condition circuit looks like:
Where the capacitor is back to steady-state. The voltage across the cap is again equal to the voltage across the 3Kohm. However, in this case, no current is flowing through the 3K ohm and you know what that means...(think Ohm's law).
In between the initial and final condition, the circuit looks like:
What equivalent resistance does the capacitor see? Use that to compute the time constant RC.
Back to Transient Analysis Examples