The voltage across a capacitor cannot change instantaneously due to its inherent property of storing electrical charge. When a voltage is suddenly applied or changed across a capacitor, it cannot immediately adjust to the new voltage due to the time it takes for the capacitor to charge or discharge. This delay is characterized by the capacitor’s capacitance (C) and the resistance (R) in the circuit, forming a time constant (τ = RC). During this charging or discharging process, the voltage across the capacitor changes gradually as it accumulates or releases charge, rather than instantaneously jumping to the new voltage level.

In an electrical circuit containing both an inductor and a capacitor, the currents and voltages in these components cannot change simultaneously due to their respective energy storage mechanisms. An inductor stores energy in its magnetic field, while a capacitor stores energy in its electric field. When the current through an inductor changes, it induces a voltage across the inductor according to Faraday’s Law of electromagnetic induction. Similarly, when the voltage across a capacitor changes, it induces a current through the capacitor due to the relationship Q = CV (charge equals capacitance times voltage). Thus, changes in current and voltage are staggered and cannot occur at the same time in these reactive components.

The voltage across a capacitor changes over time according to the RC time constant of the circuit it is in. When a constant voltage is applied to a capacitor through a resistor, the capacitor charges or discharges exponentially towards the applied voltage level. Initially, the voltage changes rapidly, and then the rate of change decreases over time until the capacitor reaches a steady-state where the voltage remains constant. The voltage across a capacitor thus follows a characteristic curve defined by its time constant, with the rate of change depending on the resistance and capacitance values in the circuit.

Unlike capacitors, resistors do not store energy in the same manner and do not have the ability to accumulate charge. Therefore, the voltage across a resistor can change instantaneously in response to changes in current or applied voltage. Resistors simply oppose the flow of current according to Ohm’s Law (V = IR), where V is voltage, I is current, and R is resistance. As such, resistors do not exhibit any time-dependent characteristics in terms of voltage change and can respond immediately to changes in the circuit.

A capacitor opposes changes in voltage across it by virtue of its capacitance. When the voltage across a capacitor attempts to change, the capacitor resists this change by either absorbing or releasing charge through its plates. This charging or discharging process occurs gradually over time, governed by the RC time constant of the circuit. The larger the capacitance, the more charge the capacitor can store for a given voltage, thus increasing its ability to oppose rapid changes in voltage. This property makes capacitors valuable in circuits for smoothing voltage fluctuations, filtering signals, and providing energy storage in various electronic applications.