How do I calculate Vc and i for an RC circuit with a closed switch?

[CursedAntagonis]

Homework Statement

The switch in the following circuit has been opened for a very long time and then closes at t=0 (a) Calculate Vc(t) for t>0. (b) Calculate i(t) for t>0.

Homework Equations

The Attempt at a Solution

Here is my attempt of the problem. I have not dealt with a problem that has two voltage sources before. Also, I have not dealt with a problem that does not become source free after the switch is either opened or closed. I am not sure if I am on the right track, I have getting Vc for t<0 to be 24V, however, Vc for t>0 is 36V?... I thought the Vc for both t>0 and t<0 stays the same. Any tips and help is greatly appreciated.

 

[vk6kro]

Before you close the switch, there are 3 series resistors with 36 volts at one end and 12 volts at the other.
You have worked out the current, but you need to work out the voltage across the capacitor as this will change when you close the switch.

(Work out the voltage drop in the 2K and subtract it from 36 volts).

The capacitor will discharge or charge depending on the new voltage distribution when you close the switch, so you have to allow for the way that capacitors charge or discharge through a resistor.