# Why does a capacitor decrease current amplitude

aaaa202
Suppose you run an AC-current through an RC-circuit. Writing it all up in terms of the complex impedance you find that the current amplitude is decreased due to the capacitor.
Physically I do not understand this. How does a capacitor decrease the amplitude of the current, when the current is alternating. Upon charging up the capacitor the current becomes less and less, but don't you get back this sink in the current when the capacitor discharges and works with you?

Mentor
Capacitor impedance varies inversely with capacitance and frequency. Impedance behaves as a resistance (it is, after all, measured in Ohms).

In terms of charging and discharging, a given capacitor can only hold so much charge for a given potential difference (you should know the formula). Suppose a given capacitor starts out "empty"; the capacitor potential begins at zero volts and rises as current flows into the capacitor. It takes only a tiny amount of charge (integral of current) to raise a big potential on a tiny capacitor; it takes a larger current to raise the same potential on a larger capacitor. So larger capacitor ---> lower impedance ---> more current. Smaller capacitor ---> higher impedance ---> smaller current.

aaaa202
I think you misunderstood me. I am asking why a capacitor component must necessarily decrease the current (which it does, seeing the impedance is a resistance).

I don't understand it from a sort of energy logic. When the capacitor is empty and charges up, then yes sure, your current amplitude will decrease because the battery must use some of the potential to fight against the electric field generated between the capacitor plates. But then when the voltage amplitude has peaked (remember the current is AC) there must be a point where the field between the capacitor plates starts "helping" the battery rather than fight against it - if this is not true I don't see why you can say alternating voltage => alternating current. And so for me it should be so that the current amplitude doesn't really get lowered, the current just switches phase such that the current amplitude is maximal at other times than when the voltage amplitude is maximal.
Where is my understanding wrong?

Mentor
Current is just the amount of charge flowing per second. Small capacitors take a relatively smaller amount of charge to develop a given potential difference than do larger capacitors. So for a given potential across the capacitor, smaller capacitors have less charge to "give back" in the form of current.

In terms of energy storage, smaller capacitors store relatively smaller energy per volt of potential difference.