# Why does current lead voltage in a capacitor ?

In a capacitor, current leads voltage in AC circuits due to the phase relationship between the two. When an AC voltage is applied across a capacitor, the current that flows through it is not instantaneously in phase with the voltage. Instead, the current leads the voltage by 90 degrees in a purely capacitive circuit. This phase difference arises because the current initially flows to charge or discharge the capacitor, which takes time, whereas the voltage across the capacitor changes immediately with the applied AC signal.

Similarly, in an RC (resistor-capacitor) circuit, current can lead voltage depending on the frequency of the AC signal. At higher frequencies, the capacitor impedance decreases, allowing more current to flow, which causes the current to lead the voltage further.

Conversely, in an inductor (L), current lags voltage in an AC circuit because of the inductor’s property to oppose changes in current. When an AC voltage is applied across an inductor, the current does not change instantaneously. Instead, it lags behind the voltage by 90 degrees in a purely inductive circuit. This lag occurs because the inductor opposes the change in current by inducing a voltage that opposes the applied voltage.

The relationship between current and voltage in a capacitor also manifests in the way current decreases as voltage increases. Initially, when a voltage is applied to a capacitor, a large current flows to charge it quickly. As the capacitor charges up, the voltage across it increases, and the rate of current flow decreases exponentially. This behavior is governed by the capacitor’s charging equation, which shows that the current decreases as the voltage across the capacitor approaches the applied voltage or source voltage.

Understanding these phase relationships and behaviors is essential for designing and analyzing AC circuits involving capacitors and inductors, as they dictate how these components interact with AC signals and contribute to overall circuit performance and behavior.