When I was reading the section of "Teach Yourself Electricity and Electronics" (by Stan Gibilsco and Simon Monck) that discussed this, my brain fell out of my head and ran out of the room screaming 'STOP, STOP,,,STOP---!!!! It refused to return until I promised to put down the book and walk away from it. I guess there had just been many years since my high school math classes for me to grasp it. This presentation finally made sense of that section of the book!! I can now return to it without fear.Thank you ever so much for your cogent explanation of this matter.
My professor had a great analogy for this. Take a cylinder of some length. In the middle of that cylinder place a diaphragm. Now as voltage equals pressure, imagine the air pressure pushing against the diaphram to store energy. In an AC circuit the diaphragm will move in and out so the pressure on the opposite side will vary with the pressure applied to the other end. Its not the same air but it is equal to the applied pressure. So like the diaphragm a capacitor passes the effect of AC but not the actual current. The more you think about it, the more it makes sense...