1V
5kΩ
2µF
-2mA
5kΩ

vc(0-) = 1 V ; ic(0+) = 0.2 mA
vc(∞) = 10 V ; ic(∞) = 0 mA
τ = 10 ms

vc(t) = 10 - 9e-100t [V] ; t ≥ 0
time for vc to reach 0V: never

ic(t) = 1 + 0.2e-100t [V] ; t ≥ 0
time for ic to reach 0A: never, but 50ms is close