Capacitors play a crucial role in inducing phase shifts in alternating current (AC) circuits by storing and releasing energy, which causes the voltage and current to become out of phase.

In typical AC circuits, current and voltage rise and fall in unison. However, the introduction of a capacitor disrupts this synchronization, resulting in a phase shift. This phenomenon occurs because capacitors can store and release electrical energy, which introduces a delay in the current’s response to changes in voltage.

When an AC voltage is applied across a capacitor, it undergoes a charging and discharging cycle in response to the alternating voltage. During the positive half-cycle of the AC signal, the capacitor charges, storing energy. As the voltage begins to decrease, the capacitor discharges, releasing its stored energy back into the circuit. This charging and discharging process is not instantaneous; it takes a finite amount of time for the capacitor to fully charge or discharge. This delay causes the current to reach its peak value before the voltage does, thereby resulting in a phase shift.

The extent of the phase shift is influenced by both the frequency of the AC signal and the capacitance of the capacitor. A higher frequency or a smaller capacitance results in a shorter time required for the capacitor to charge and discharge, leading to a smaller phase shift. Conversely, a lower frequency or a larger capacitance produces a greater phase shift.

In a purely capacitive AC circuit, the current leads the voltage by a phase angle of $90$ degrees, or $\frac{\pi}{2}$ radians. This occurs because the current achieves its peak value one quarter of a cycle prior to the voltage. This phase shift is often illustrated graphically, with the current and voltage waveforms plotted over time. In such a representation, the current waveform appears shifted to the left of the voltage waveform, clearly indicating that the current leads the voltage.