Simple RC Circuit question: how does a precharged capacitor interact with a lower voltage source?
For circuit 1: it will discharge until \$ V_C = V_{BAT} \$

$$ V_C = (V_{C0} - V_{BAT}) \times exp \left( \frac{-t}{R1*C} \right) + V_{BAT} $$

For circuit 2: it will discharge to zero but \$ V_{C1} \$ depends on the previous equation

$$ V_C = V_{C1} \times exp \left( \frac{-t}{(R1+R2)*C} \right) $$