Basic RC Circuit but with parallel switch?

[anthonuc]

Homework Statement

I want to find i_x in the circuit below when the switch opens at t=0 after having been closed for a long time.

Homework Equations

v(t) = v(infinity) + (v(0)-v(infinity))e^-t/RC
i(t) = C dv(t)/dt
i_x = i_source - i(t)

v(t) = voltage across capacitor
i(t) = current through capacitor

The Attempt at a Solution

I just need to find v(t) then i(t) then i_x using the equations I have.

I transformed the circuit so that the current source and resistor in parallel become a voltage source and resistor in parallel. The voltage source = 4mA * 2kOhm = 8 V

v(infinity) = 8V

My only real problem:
v(0) = ?

When the switch is closed, how is the circuit affected? Seems so trivial but I'm really confused as to what happens to the circuit at t=0 and finding v(0).

When the switch opens it's easy - a simple RC circuit. But I'm having a hard time understanding what happens to the circuit while the switch is closed. My guess is all the current goes through the short closed switch and v(inifinity) = 0?

[PLAIN]http://sphotos.ak.fbcdn.net/hphotos-ak-ash2/hs399.ash2/67756_10150101801434992_712009991_7559768_7479272_n.jpg

 

[vk6kro]

Assuming a perfect switch with no contact resistance, the 4mA current will all go into the switch.
So, there is no voltage across the capacitor or the resistor.

When you open the switch, all the current will go into the capacitor, building up a voltage and hence feeding some current into the resistor. Eventually all the current will go into the resistor.

 

[anthonuc]

Ah thanks for the reply. Current taking the path of least resistance? I've been told not to believe it as it's not actually true but maybe that pertains to real life and not ideal circuits for problems i guess. Anyway thanks again!