If the voltage changes instantly from one value to another (i.e. discontinuously), the derivative is not finite. This implies that an infinite current would be required to instantly change the voltage. Since an infinite current is not physically realizable, that means that the voltage cannot change instantaneously.

Why capacitor does not allow sudden change of voltage?

Explanation: Capacitor does not allow sudden changes in voltage because these changes occur in zero time which results in the current being infinity, which is not possible. ... Explanation: When capacitors are connected in series, the charge across each capacitor remains the same whereas the voltage across each varies.

Can capacitor voltage change instantaneously?

Capacitors and inductors store electrical energy—capacitors in an electric field, inductors in a magnetic field. ... This isn't physically possible, so a capacitor's voltage can't change instantaneously. More generally, capacitors oppose changes in voltage—they tend to “want” their voltage to change “slowly”.