One of the properties of capacitors is its ability to hold a charge when a voltage is applied to it. The buildup of charges inside the capacitor generates a voltage across it and in opposition of the voltage that is driving the incoming charges, effectively resisting to their flow.
This effect of resisting current flow into and out of (an apparent flow "through") is called reactance and is measured in ohms, the same unit for resistance. This is because an ohm is a unit of opposition to electric current, so it makes sense that reactance is also measured in ohms.
With an alternating signal applied to the capacitor, some charge starts building up inside the capacitor opposing the flow of current, not enough to block it completely, so it appears to go through the capacitor; there's some opposition, but not as much as with a constant current, which it can block completely when fully charged.
As the frequency (number of times the signal completes a cycle of 0v > positive peak > 0v > negative peak > 0v) the charge that accumulates inside the capacitor gets smaller and smaller, up to the point where virtually no current is stored and all of the signal gets apparently through the capacitor.
With an increase in frequency, the capacitive reactance goes down in the same proportion. This has a more formal definition, given by the equation:
Xc = 1 / (2 pi f C)
where Xc is the capacitive reactance in ohms, f is the signal frequency and C is the capacitance of the component.
The 2 pi comes from the fact that reactance is actually dependent on the angular velocity of the incoming signal, but since the 2 pi is constant and increasing angular velocity leads to higher frecuency, it is sometimes better to think of reactance in terms of just variable frequency.
For all practical purposes, capacitive reactance follow the same rules as resistors when combined in series and parallel. This fact is particularly useful for understanding most filters, since they often rely on capacitive reactance as part of a voltage divider.
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