why capacitance depends upon frequency physically irrespective of mathematical fact?
There is a barrier...
Capacitors block DC because there is a physical barrier (non-conductor) that prevents current flow. AC can pass simply because the charges on one side push (repel) and pull (attract) the charges on the other side during each half-cycle of the AC waveform.
The phantom current
This causes the charges to appear to circulate even though they are not actually circulating. This concept is called a phantom current because it appears that there is a current crossing the non-conductor at the center of the capacitor even thought there really isn't. What is crossing over is the electric field lines. A more intuitive way to grasp this is that the forces exerted by a concentration of like charges on one side applies across the gap on the charges of opposite likeness on the far side.
Reactance
Reactance is the opposition of a circuit element to a change of voltage. When at DC, there is no effort made by the signal to &quot;change the voltage&quot; and therefore a perfect ability of the capacitor to resist the change (ergo infinite reactance). Physically, the inability of the static charges to generate a phantom current means that the capacitor can perfectly resist the transfer of energy in the ideal case.