Discharging a capacitor through resistor and uncharged cap

[sdfanm16]

Homework Statement

Given v₀ c_1c2 r₁ need to find the current on r₁ picture

switch 1 is closed for long time and on t=0 opened and switch 2 is closed

Homework Equations

The Attempt at a Solution

in the attached file

i was trying to use kvl assuming that q₀(charge on cap before opening switch 1) is v₀ adn the sum of q₁ and q₂ (the charge after switch 2 is closed) is equal to q₀
how to find cons c and I(t)?

 

[gneill]

Usually one uses known boundary conditions (initial, steady state) to solve for the unknown constants, plugging the known conditions into the general solution of the differential equation.

For this problem it might be easier to just look at the initial and final conditions and "connect" them with the known behavior of an RC circuit. That is, if you can determine the initial current that flows the instant after the switch S2 is closed and the final current at steady state, you know that the current must follow an exponential decay between those states. You've already determined the time constant, so the rest will be straight forward.