so I'm trying to find the current I(t) passing through the node above the switch. I have already found the DC response of the RC circuit which is
in the form of:
so, after the switch closes a short circuit will be created, and here is the confusion, is the current going to take the shorter path ignoring the 4k resistor and the 12V source and no current will flow through them? with that being said, I don't know whether to consider them in my calculation of I(t) What should I do?