2V
1kΩ
2µF
1V
1kΩ

vc(0-) = -2 V ; ic(0+) = -2 mA
vc(∞) = -1 V ; ic(∞) = 0 mA
τ = 2 ms

vc(t) = -1 - 1e-500t [V] ; t ≥ 0
time for vc to reach 0V: never

ic(t) = -2 - 2e-500t [V] ; t ≥ 0
time for ic to reach 0A: never, but 10ms is close