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If you connect a capacitor to a battery, current rushes in for a fraction of a second and then stops completely. But plug that exact same capacitor into an alternating current (AC) supply, and current flows continuously.
Even stranger: if you look closely at the waveforms, the current peaks a quarter-cycle before the voltage even reaches its maximum.
Why would the electrical current rush in before the driving voltage gets there?

The 90-Degree Phase Lead

A capacitor stores charge QQ across two conductive plates separated by an insulator, governed by the relation Q=CΓ—VQ = C \times V, where CC is capacitance in Farads.
Because electric current is the rate of flow of charge (I=Ξ”QΞ”tI = \frac{\Delta Q}{\Delta t}), it depends directly on how rapidly voltage is changing: I=CΞ”VΞ”tI = C \frac{\Delta V}{\Delta t}.
When the AC voltage crosses zero volts, its waveform is at its steepest slope, creating the fastest change in voltage and therefore the maximum peak current.
Conversely, when the voltage reaches its peak crest, its slope is momentarily zero, meaning charge stops flowing and instantaneous current drops to zero.
Because the current wave reaches every peak 90∘90^\circ (or Ο€2\frac{\pi}{2} radians) before the voltage wave, we say current leads voltage by 90 degrees in a pure capacitor.
Electronics engineers remember this relationship with the classic word CIVIL: in a Capacitor, I (current) leads V (voltage); while V leads I in an inductor (L).
If a capacitor lets AC pass, does it offer any opposition to the current, and does that opposition change when the AC cycles faster?

Capacitive Reactance