Why capacitor pass AC and block DC current? We know that in circuit capacitor block the DC current and pass AC current. My question is how a capacitor block DC and pass AC?
 A: Consider a circuit with a capacitor, a voltage source, and a switch. Suppose the voltage source is DC and we flip the switch. If the capacitor is initially uncharged, then at the instant you close the switch current will flow as if the capacitor was not there. Instead of an electron crossing the capacitor, an electron will arrive at the negative capacitor plate and another electron will leave the positive plate. So, at first, current can flow, but as the charge builds up the capacitor begins to oppose the voltage placed on it and eventually there is no more current in the system because the capacitor is charged and at equal voltage to the DC voltage source.
Now suppose we did the same thing with an AC source. We close the switch, current flows, the capacitor starts building up charge to stop the current...but then the voltage flips around and the capacitor no longer opposes the current, so the current can flow the other way, the capacitor starts to change its polarity, but as it does the current changes AGAIN...etc.
In short, when a capacitor is placed in a DC circuit it very quickly becomes charged in such a way as to oppose the applied voltage and all current stops. When the power source is AC, however, the capacitor never has time to "adapt" to it and so won't build up a charge that opposes the current. It's like you keep flipping an hourglass back over.
A: Generally the work of capacitor is to store energy from the moving electric current. As DC flow of current is unidirectional, the current flows ant gets stored in the capacitors. Whereas ac current signals change there direction after every round so it is not blocked by the capacitors
A: The capacitor equation as we all know is Q=CV
Where the symbols denote the usual values
We know that the current I= (dQ/dt)
let V=v*sin(wt)
=> Q=C*(vsin(wt))
dQ/dt=I= wCv*cos(wt)  ----------------(1)
and we know that V=IR -------------------(2)
re-arranging the terms in eq (1)
v*cos(wt)= (1/wC)*I  ---------------------(3)
comparing eqs (2) and (3)
we can write resistance R=(1/wC)
notice that R is inversely proportional to frequency
which implies that for dc, w=0 
which gives R = infinity 
or it gives infinite resistance for DC, so completely blocks it 
