# How to find I(t)?

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

$Vc(t)&space;=&space;27+5e^-1.5t$

in the form of:

$x(&space;t&space;)&space;=&space;x(\infty)+[x(0)-x(\infty)]e^-t/RC$

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?

• why would you think that the 4 k resistor would have no current flowing through it if you applied 12 V across it? – jsotola Dec 27 '19 at 20:05
• @jsotola I think what he means to say is no part of his current of interest, i(t), flows through the 4k resistor when the switch is closed. – DKNguyen Dec 27 '19 at 20:29

You have an equation for the voltage across the capacitor as a function of time. After the switch closes, the 6kΩ resistor is in parallel with the capacitor. That should be enough information for you to find $$\i(t)\$$