How does capacitor allow ac current when there is an insulator layer between the plates?
How does the current pass (AC) between the plates when there is an insulator or dielectric between the plates.


It does and it doesn't. This illustration may help a little.



Figure 1. A water pressure tank of the type used to even out water pressure supply. Image source: Pressure tank comparison on YouTube.

They're all doing the same job but I'll use the diaphragm pressure tank for illustration purposes. In this type of pressure tank a diaphragm separates the air from the water. This is analogous to the insulator in your capacitor. We'll say that the air represents the positive plat and the water represents the negative plate. When the water pressure rises water is pushed into the tank and when it falls the water is pushed out of the tank.

This is very similar to the smoothing capacitor in a DC power supply.







simulate this circuit &ndash; Schematic created using CircuitLab

Figure 2. The capacitor charges up when the voltage is high and discharges (into the load) when the rectifier voltage is low.

Now, how does the water go in and out of the pressure tank when there is no way through the diaphragm? It's because the pressure changes and energy is stored in the tank. In the same way charge can flow in and out of the capacitor because the voltage changes and energy is stored in the electric field of the capacitor.