• Current leads the voltage across the capacitor (is phase shifted by 90^o).
• Using a water analogy, the current is the water flow and the voltage is how full the bucket is.
• If you tip water into a bucket, there is a large water flow but it still takes time to fill the bucket.
• Once the bucket is full, the water flow stops. Capacitors are the same.
• A current is needed to charge the capacitor. Initially, the current flows while the voltage is still zero or low.
• Once the capacitor is charged, the current flow drops to zero and the voltage reaches its maximum.
• So current leads the voltage.

This concept can cause brain meltdown. How can there be a current wothout a voltage? It's because the capacitor voltage is not the one causing the current to charge the capacitor. There has to be an external voltage, fixed or alternating, causing the circuit current to flow. The capacitor voltage depends on how fully charged the capacitor is and it builds up as the capacitor charges.

In this simulation, the oscilloscope voltages are green and the currents are yellow. Notice the 90⁰ phase shifts in oposite directions.