On my E&M test I was given the circuit diagram below and asked to find the charge on the capacitor after a long time or as $ t \to \infty $. In class we had used Kirchhoff’s voltage rule on the same circuit except with a AC power supply instead of a DC one so I thought it would still apply. Making that assumption, I drew in the currents into the diagram and put a charge of CV on the capacitor and everything was consistent with Kirchoff’s voltage rule. However, apparently I was supposed to recognise that Kirchhoff’s rule doesn’t apply and get a different answer. If anyone could explain to me why and how this works and where my circuit analysis was wrong, I would greatly appreciate it.