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A capacitor is a device which stores energy, in the form of an electric charge. It is made of two sets of metal plates, separated by a thin insulator. It does have applications in both AC and DC circuits.
When a capacitor charges, one plate becomes more positive, and the other, more negative. It can retain this charge, even if removed from a circuit. For this reason, you should always discharge a capacitor before handling it, or you can get a nasty shock! (Although a resistor is safer for discharging, most electricians prefer a screwdriver :lol: )
The golden rule of understanding what a capacitor does, is that it OPPOSES a change in VOLTAGE. It does this by sinking or sourcing CURRENT. If you want to get mathematical, the current into/out of the capacitor is proportional to the rate of change in voltage, across the capacitor:
Ic = d(Vc)/dT (simplified, without constant multipliers)
In DC circuits, it is typically used for filtering, to maintain a (fairly) constant load voltage. Also used for timing, as the rate of charge/discharge is predictable (within tolerances).
In AC circuits, a capacitor is a load, but the current through the capacitor has a 90 degree phase shift, with respect to the voltage, ie, if:
Vc = sin t then Ic = cos t (where t is time)
This correlates with the first equation, ie:
d(sin t)/dt = cos t
In large electrical installations (factories etc) capacitors are used for power factor correction (if you want more info on power factor, let us know)