A simple, "parallel-plate" capacitor is a component composed of two sheets of conducting foil, called plates, and an insulating film sandwiched in between.  To save space, large "sandwiches" are rolled up like a jelly roll.

When a capacitor is in the path of an electric current, one of its plates accumulates electrons, making it negatively charged.  Since like charges repel, electrons are pushed off the facing plate, leaving behind positively charged ions (atoms missing an electron).

Charge is now trapped in the capacitor.  The electrons and the ions attract each other but they can't cross the insulator.  Their potential energy is instead stored in a surrounding electric field, appearing as a voltage across the capacitor plates.

Electrolytic Capacitors

An aluminum electrolytic capacitor has two, very thin aluminum foils, oxide coated to block current, and rolled up like a jelly roll.

The wound-up foils are immersed in an electrolyte, a solution containing both positive ions (cations) and negative ions (anions).

The cations are attracted to the foil that's gaining electrons and the anions are repelled toward the other foil.  In each case, the foil's oxide coating blocks conduction, thus trapping the charge.

Notice that the electrolyte serves as a common "plate" between the two foils and so the device is really two capacitors in series.

Capacitors are rated on a scale of capacitance, symbol C.  Capacitance is defined as the ratio of the charge q held in a capacitor to the voltage V across its plates :

A large capacitor has large plates with more room for charge to spread out than does a small capacitor.  As a result, the large capacitor must harbor more charge than the small one to reach the same voltage across the plates.

The unit of capacitance is the farad, abbreviated ‘F’, in honor of Michael Faraday.  The farad is an impractically large unit  so most capacitors are rated in one of the following subunits :

• the microfarad (μF or MF) = one millionth (10^-6) F
  
  
• the nanofarad (nF) = 0.001 μF = one billionth (10^-9) F
  
  
• the picofarad (pF) = 0.001 nF = one trillionth (10^-12) F
  
  

Capacitors In Power Supplies

The ability of capacitors to store electric charge makes them a common component in the power supplies of all kinds of gear.

Charged capacitors help keep a power supply's output voltage free of ripples and noise that could affect the gear's performance.

In rectifier circuits, where alternating current is converted to direct current, caps are used to store electrons while they flow in, then supply them when the alternating current reverses.

Capacitors & Tone

Sooner or later, the plates of any capacitor will fill up with charge and repel any additional electrons.

A small capacitor has less storage space than a large one and so fills up faster.  Hence, small capacitors block longer duration, low-frequency waves, allowing only shorter duration, high-frequency waves to pass through.

Since capacitors filter signals based on frequency, they're routinely used for tone control in musical instruments and amps.

As shown below, a capacitor wired in series with a circuit has the opposite tonal effect as the same capacitor wired in parallel with the circuit :

Series-Wired Capacitor

This guitar will sound trebly because only higher frequencies can go through the capacitor to the speaker.

Parallel-Wired Capacitor

This guitar will sound bassy because higher frequencies can go through the capacitor instead of the speaker.

Capacitance can exist between any two conductors, for example between the two wires in a guitar cable.

A long guitar cable has more capacitance than a short one and could siphon off higher frequencies.

In conclusion, take a look at the following hydraulic analogy to a capacitor.  It shows a flexible rubber membrane in a water pipe.  Although water can't cross the membrane, an alternating current of water (an AC signal) can.

The stretching of the membrane is analogous to the charging and discharging of a capacitor .  The amount of stretch is analogous to the amount of voltage stored by the capacitor.

A very stretchy membrane simulates a large capacitance while a stiff membrane simulates a small capacitance.