[2]: 788 Electric currents create magnetic fields, which are used in motors, generators, inductors, and transformers.

Positive and negative charge carriers may even be present at the same time, as happens in an electrolyte in an electrochemical cell.

Introducing the constant of proportionality, the resistance,[14] one arrives at the usual mathematical equation that describes this relationship:[15]

In alternating current (AC) systems, the movement of electric charge periodically reverses direction.

Audio and radio signals carried on electrical wires are also examples of alternating current.

Direct current is produced by sources such as batteries, thermocouples, solar cells, and commutator-type electric machines of the dynamo type.

A biological example of current is the flow of ions in neurons and nerves, responsible for both thought and sensory perception.

When a changing magnetic field is applied to a conductor, an electromotive force (EMF) is induced,[21]: 1004  which starts an electric current, when there is a suitable path.

In other media, any stream of charged objects (ions, for example) may constitute an electric current.

In other conductive materials, the electric current is due to the flow of both positively and negatively charged particles at the same time.

For example, the electric currents in electrolytes are flows of positively and negatively charged ions.

Electric currents in sparks or plasma are flows of electrons as well as positive and negative ions.

With no external electric field applied, these electrons move about randomly due to thermal energy but, on average, there is zero net current within the metal.

As George Gamow wrote in his popular science book, One, Two, Three...Infinity (1947), "The metallic substances differ from all other materials by the fact that the outer shells of their atoms are bound rather loosely, and often let one of their electrons go free.

Thus the interior of a metal is filled up with a large number of unattached electrons that travel aimlessly around like a crowd of displaced persons.

The moment contact is made, the free electrons of the conductor are forced to drift toward the positive terminal under the influence of this field.

For a steady flow of charge through a surface, the current I (in amperes) can be calculated with the following equation:

However, once the applied electric field approaches the breakdown value, free electrons become sufficiently accelerated by the electric field to create additional free electrons by colliding, and ionizing, neutral gas atoms or molecules in a process called avalanche breakdown.

The breakdown process forms a plasma that contains enough mobile electrons and positive ions to make it an electrical conductor.

Due to their lower mass, the electrons in a plasma accelerate more quickly in response to an electric field than the heavier positive ions, and hence carry the bulk of the current.

These small electron-emitting regions can form quite rapidly, even explosively, on a metal surface subjected to a high electrical field.

Superconductivity is a phenomenon of exactly zero electrical resistance and expulsion of magnetic fields occurring in certain materials when cooled below a characteristic critical temperature.

It is characterized by the Meissner effect, the complete ejection of magnetic field lines from the interior of the superconductor as it transitions into the superconducting state.

The occurrence of the Meissner effect indicates that superconductivity cannot be understood simply as the idealization of perfect conductivity in classical physics.

The size of this energy band gap serves as an arbitrary dividing line (roughly 4 eV) between semiconductors and insulators.

The Pauli exclusion principle requires that the electron be lifted into the higher anti-bonding state of that bond.

[4]: 22 In linear materials such as metals, and under low frequencies, the current density across the conductor surface is uniform.

In such conditions, Ohm's law states that the current is directly proportional to the potential difference between two ends (across) of that metal (ideal) resistor (or other ohmic device):

For example, in a copper wire of cross-section 0.5 mm2, carrying a current of 5 A, the drift velocity of the electrons is on the order of a millimetre per second.

To take a different example, in the near-vacuum inside a cathode-ray tube, the electrons travel in near-straight lines at about a tenth of the speed of light.