Capacitor voltage ($V_C=q/C$)

The voltage across an ideal linear capacitor of constant capacitance C is its signed plate charge divided by C. With the passive current convention, $I=C{\dot{V}}_C$.

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.