Hi
I Think this is why a Cap do not pass DC current...
The current Formula in a Cap is as Follow:
i=C dV/dt + v0
This formula indicates that we have current in a cap If the Cap Voltage Changes (The meaning of dV/dt). So If you just imagine DC voltage across a Cap, dV/dt = 0 ----> i=0
This formula also indicates why we have spark, when we short a charged Cap. when you do this, dt becomes very small so dV/dt increses so current will increase.
This Formula aslo indicates why small Caps are uses to remove small and fast changes in regulator voltage (i.e. before and after a 78xx regulator) but how?
Delta(v) = 1/C Integral ( i dt )
if dt become very small, Delta (v) becomes zero, it means the voltage across a cap do not accept fast voltage changes.
If you ask where did this formula came from, you can find it in Electronic Books.
HTH - Shahriar