You've spent your whole physics career saying that you can't have a current in a circuit unless the circuit is complete. Well, guess what? In the case of capacitors, that's not strictly true.
The simplest capacitors are big plates of metal close to each other but not touching. When connected to a potential difference (e.g. a battery), the battery tries to push electrons through the wire away from its negative terminal. Although there isn't a complete circuit, you can imagine that you can shove a few extra electrons onto a big sheet of metal . Let's face it, given the choice between being stuck at a negative terminal or going to a neutral metal plate, electrons will get up and move! So you get a flow of electrons to the plate i.e. you get a current without a complete circuit, but only for a short period of time.
What happens next?
As the electrons (the charge) build up on the plate, 2 things happen:
The plate becomes more negative and so becomes less attractive to the electrons, so the flow of electrons gradually reduces which means the current gradually reduces.
The electrons in the other plate are repelled by the build up of electrons in the first plate. So they move off the second plate. The electrons leaving the second plate complete the circuit.
If you plot a graph of the potential difference across the plates against charge stored on the plate you find:
As charge builds up, so does the pd across the plates Charged stored is directly proportional to the potential difference across the plates.
Also, if then,
= a constant.
We call the constant which relates the two, C, the capacitance because it is 'the charge stored per unit pd across the plates' - the capacity of the plates to store charge.
Capacitance is measured in farads, F.
1F = 1 C V-1 (A capacitance of 1 farad will mean a charge of 1 coulomb can be stored for each volt across the plates).
Warning: When you use capacitors in practical work you must connect them the right way round or they have a tendency of exploding, (not a pleasant occurrence and quite dangerous). There is normally an arrow on the case of the capacitor which points from high voltage to low, to show you which way around it should go.