Electric current

In an electric circuit, positive charges move spontaneously towards regions of lower potential, giving up energy along the way. A generator continually carries them back to their starting level, supplying energy from outside; along the way the charges experience a kind of “electrical friction”, resistance, which converts electrical energy into heat. This narrative picture is the same one used to describe a hydraulic circuit: the generator is the pump, the resistor is the narrow pipe that obstructs the flow, and the current is the flow of water running through the pipes.

Principle — Electric current

Current measures how much charge crosses a cross-section of the conductor per unit time. It is the quantity that quantifies the “flow” of the fluid of charges.

Definition

The electric current $i$ is the charge that passes through a cross-section of the conductor per unit time:

$i = \frac{\Delta Q}{\Delta t}$

It is measured in amperes (symbol A), a unit equal to one coulomb per second:

$\ev{[\,i\,] = \mathrm{A} = \frac{\mathrm{C}}{\mathrm{s}}}$

If in one second a charge of one coulomb crosses the section, the current is one ampere.

Conventional direction

Direction of the current

By historical convention the current is directed from the $+$ pole to the $-$ pole of the generator, i.e. in the opposite direction to the actual motion of the electrons.

In metals the charge carriers are in fact electrons, which have negative charge and move from $-$ to $+$. The convention was fixed, however, when the nature of the carriers was still unknown, assigning the current the direction in which positive charges would move. The two descriptions are entirely equivalent as far as effects go: a positive charge flowing in one direction is indistinguishable, in terms of the field and currents it produces, from a negative charge flowing in the opposite direction.

Conductor and free charges

A conductor contains free charges — in metals these are the valence electrons, weakly bound to individual atoms — which are set into ordered motion by an electric field. In a closed circuit this field does not die away: it is kept constant by the generator, which acts as a pump, continuing to push the charges and to resupply them with the energy dissipated along the way. Without a generator the ordered motion would quickly cease and the fluid of charges would return to equilibrium.

▶ The Big Misconception About Electricity — Veritasium

Links

Topics: Circuiti elettrici Concepts: Corrente elettrica

Related exercises: Problem — current as flow · Worked example — mixed series-parallel network · Worked example — network of capacitors