At t = 0, the switch is at Position 1.

We note that

Using SNB to solve this differential equation, we have:

NOTE: By differentiating, this gives us:

We need to find :

.

Now, at , the charge will be:

At , switch at Position 2:

Applying the formula again:

NOTE: The negative voltage is because the current will flow in the opposite direction through the resistor and capacitor.

Once again, we solve using Scientific Notebook:

Exact solution is:

So the current transient will be:

This expression assumes that time starts at . However, we moved the switch to Position 2 at , so we need:

So the complete current transient is:

for

for

The graph is very interesting: