Calculate voltage and current in time dependent circuit
Typical homework problem. I think of it as two steps:


Setup of Cap. Voltage via introduced energy
Discharge of Cap. Through Connected Impedance


The current division between R3 and R1 + R2 in series gives you the setup current (I label it I_0) (since R3 &lt; R1+R2, the most current should go into R3)

I0 * R2 Gives you the voltage in the node that is connecting R2, C1, C2 (I name the node n1 and the voltage V_0)

Total capacitance of two parallel caps is the sum C1 + C2 = C' 

the time constant is then R2*C' = tau

Classic RC-exponential discharge curve, R2 is the current path:

V(t) = V_0 * e ^ -(t/tau)

and V = R*I gives V(t)/R2 = i(t) 

easy as pie. 

All these tools are easily searchable in any electronics schoolbook or the internet.