A common "parallel-plate" capacitor is made up of two sheets of conducting foil (called plates) and a non-conducting film sandwiched in between.  To save space, the sandwich is often rolled up like a jelly roll.

Each foil sheet has an attached lead so the capacitor can be wired into an electrical circuit.  (See illustration, below.)

When a capacitor is in the path of an electric current, electrons accumulate on the "upstream" plate, giving it a negative charge.  Since like charges repel, electrons are driven off the nearby plate, leaving behind positive ions (atoms missing one or more electrons).

Electric charge is now trapped in the capacitor.  The electrons and the ions attract each other but they can't travel across the insulator.  Their potential energy is stored in the surrounding electric field, registering as a voltage across the capacitor's plates.

Electrolytic Capacitors

An "electrolytic" capacitor comprises two very thin foil plates immersed in an "electrolyte" [a solution that contains both positive and negative ions (called cations and anions)].  In the capacitor, these dissolved ions function as charge carriers.

The Layers of an Electrolytic Capaciator

After an electrolytic capacitor is manufactured, the manufacturer applies a DC voltage across its foils (the electrodes) with the positive side of the voltage connected to the "anode" foil and the negative side to the "cathode" foil.

This voltage pushes electric charge from one electrode to the other, through the electrolyte.  Electrolysis, an electrochemical reaction, causes a tiny oxide coating to form on the anode foil.

After its formation, the oxide coating serves as the insulator (the "dielectric") between the capacitor plates.  To maintain the oxide coating, the capacitor must always operate with a net DC voltage across it, with the same polarity as the forming voltage.  The capacitor is "polarized", with a plus and a minus terminal.

Minus Terminal (Cathode) Markings on
Electrolytic Capacitors

When the capacitor is in an electric circuit, dissolved positive ions (cations) are attracted to its more negative foil (its cathode), and dissolved negative ions (anions) are attracted to its more positive foil (its anode).  But charge flow is dammed up by the anode's oxide coating – the potential energy is stored in the surrounding electric field.

Oxide Layer Blocks Anions from Reaching the Anode

If the capacitor is accidentally connected backwards, the anode's oxide coating is destroyed.  Oxide starts to form on the cathode but, meanwhile, charge flows unhampered through the capacitor.  This electric current heats up the electrolyte, which can boil.  The capacitor may puff up and eventually explode.  Or the electrolyte may leak out and degrade the capacitor.

Capacitors are rated on a scale of capacitance, symbol C.  Capacitance is defined as the ratio of the charge q 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.  So, a large capacitor has to accumulate more charge than does a small one to reach the same level of voltage across its 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
  
  

Power Supply Capacitors

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

Fender Princeton 5F2-A Guitar Amp

Charged-up, electrolytic capacitors help to keep a power supply's output voltage free of ripples and noise that could affect the equipment's performance.

In rectifier circuits, where alternating current is converted to direct current, electrolytic capacitors capture charge when it's flowing in.  Then, when the alternating current reverses direction, the stored charge is available to power the equipment.

Tone Capacitors

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.