Capacitor voltage continuity
= Capacitor voltage continuity
{title2=$\Delta V_C=C^{-1}\int I\,dt$}
Integrating the current-voltage relation shows that a finite <electric current> cannot change <capacitor voltage> instantaneously. An imposed impulsive current can make it jump. A prescribed instantaneous short-circuit discharge is an idealization of this exceptional fast process, not a counterexample for finite current.