Since between plates of a capacitor there is an insulator/dielectric, how is it possible that current flows in a circuit with a capacitor since according to Ohm's law, current is inversely proportional to resistance and an insulator by definition has a big resistance, so we basically have an open circuit?
Electric current is the flow of electric charge, which is what electrical components harness to light up, or spin, or do whatever they do. When current flows into a capacitor, the charges get "stuck" on the plates because they can't get past the insulating dielectric.
Capacitive reactance opposes current flow but the electrostatic charge on the plates (its AC capacitance value) remains constant. This means it becomes easier for the capacitor to fully absorb the change in charge on its plates during each half cycle.
Because the current changes throughout charging, the rate of flow of charge will not be linear. At the start, the current will be at its highest but will gradually decrease to zero. The following graphs summarise capacitor charge. The potential difference and charge graphs look the same because they are proportional.
The flow of electrons onto the plates is known as the capacitors Charging Current which continues to flow until the voltage across both plates (and hence the capacitor) is equal to the applied voltage Vc. At this point the capacitor is said to be “fully charged” with electrons.
When used in a direct current or DC circuit, a capacitor charges up to its supply voltage but blocks the flow of current through it because the dielectric of a capacitor is non-conductive and basically an insulator.