Why Capacitor blocks DC current and Pass AC?

The answer I think is interesting, so I am posting it….. enjoy.
As we know capacitor is two conducting plates (which have free electrons) with insulating material in between. By sending dc current we are asking the electrons to flow thorough the inuslating material, which is not possible due to absence of free electrons. Hence Capacitor blocks DC.
When AC current is applied, during the first half-cycle of current we are “temporaryly” pushing external electrons onto plate-A, which inturn induce opposite charge on the plate-B (by stressing the dielectric in between) and thus to compensate push the free electrons out of the plate-B. This gives us the illusion of current passing from one side to other. However this illusion can not be sustained continuously in one direction, because after a while plate-A will be saturated with electrons and plate-B will be without further free electrons to contribute. Luckily, when the other half-cycle arrives the entire process reverses again giving us the illusion that current is now flowing from plate-B to plate-A.
Now, if the frequency is high the cycles are faster and thus the capacitor is happily performing its magic illusion of passing the AC current! But when we slowly reduce the frequency, the capcitor keeps getting close to fully charged and at further low frequency even show discontinuous currents…!!!

Explanation with an ANIMATION :

The voltage being represented by the graph has a  DC component as well as an AC component. We can see this by the fact that the voltage does not go below the 0v axis (x-axis) and you could say it represented a voltage of 7v, with a rise to 10v, and a fall to 3v.



We will now  show how the voltage enters a capacitor and emerges with the same wave-shape but with the DC component removed.
This is what we mean when we say a “Capacitor blocks DC but passes AC.” Take the case of the signal above (a signal is any type of varying waveform). Suppose the signal rises to 10v and drops to 3v. The frequency of the signal is not important. The animation below shows the result:

The shape of the signal is not altered by the capacitor. Whatever goes into the capacitor comes out. However the DC component (the height of the waveform above the X-axis) is removed and  the signal emerges as a positive and negative waveform based around the x-axis. Without an animation, this important concept could not be demonstrated. As the pointer moves across the graph from left to right, the rise in voltage (that is: the rise in voltage from the starting point of the graph) is passed to the capacitor and the output lead of the capacitor delivers this rise to whatever component is connected to the capacitor