-2.5mA
1kΩ
1µF
2.5mA
10kΩ

vc(0-) = 2.5 V ; ic(0+) = 0.25 mA
vc(∞) = 25 V ; ic(∞) = 0 mA
τ = 10 ms

vc(t) = 25 - 22.5e-100t [V] ; t ≥ 0
time for vc to reach 0V: never

ic(t) = 2.5 + 0.25e-100t [V] ; t ≥ 0
time for ic to reach 0A: never, but 50ms is close