Hi, don"t post here very often, but as a practicing EE specializing in electromagnetics and having almost 40 years experience, I have an overwhelming urge to correct some of the misconceptions and patent nonsense I see in some of the answers here.
First, in answer to the original question, electrical current is the movement of charge carriers. In metallic conductors, the charge carriers are electrons; in some other materials, such as the electrolyte in some battery chemistry and some semiconductor materials, the charge carriers are actually positive ions. 1 ampere is defined as the movement of one coulomb of charge per second - there is nothing in this definition that says what the polarity of the charge carriers is.
An yes, Ben Franklin got it wrong. In a metallic conductor, the actual charge carriers move from negative to positive, however, from a practical standpoint it really makes absolutely no difference unless you"re working at a molecular level. The term "conventional current" is often used for the assumption that current moves from positive to negative.
In a good conductor, such as a metal, the outermost electrons are very loosely bound to the individual atoms. If I shove an electron into a conductor, it will displace an electron from one of the atoms. That electron will in turn displace an electron from another atom, etc., etc., etc. Insulators are insulators because the electrons are very tightly bound to their atoms, and it takes a LOT of force (voltage) to break them loose. There are some other mechanisms by which electrons move through materials, but these can be ignored unless you"re worried about things like how high energy electrons interact with materials in a spacecraft, or the physics of an arc, or other rather esoteric effects.
Here"s a relatively simple analogy for current flow in a wire. Think of a long tube filled with a fluid...if I force a small amount of fluid into one end, it will push a corresponding amount of fluid out the other end, even though the individual molecules haven"t moved very far. An analogous thing happens in a conductor...if I shove electrons into one end, a corresponding number will be forced out the other end, even thought the individual electron that I forced into one end is not the same electron that came out the other. This is how electrical signals move along wires at something approaching the speed of light, even though individual electrons only move along the wire (as I recall) at a few inches a second.
At DC, the current will distribute evenly through a conductor..."skin depth" at DC is infinite. At 60 Hz, unless you"re working with conductor dimensions measured in inches or 10"s of inches, it"s also safe to assume that current distributes evenly throughout the conductor. For the size conductors that most of us are concerned about, "Skin depth" is only a concern for things like RF transmission lines, which carry energy at much higher frequencies.
Stranded wire is used for mechanical purposes, not electrical. Fine strands are able to flex without breaking or work hardening in a vibration environment. For a given amount of copper, a single solid conductor can carry exactly the same amount of current as the same amount of copper made into a number of fine strands. Note that a stranded wire may be bigger in diameter than an equivalent solid wire because of the air spaces between the individual strands. There are also some minor thermal differences between stranded and solid conductors as a result of the way heat moves through the conductors.
There"s also an interaction between electrons and a magnetic field. An electron moving through a magnetic field experiences a force; conversely, a moving electron (as a result of an applied force) creates a magnetic field. This relationship between current and magnetic fields is the basis for all elecro-mechanical devices, such as motors and generators. For example, moving a wire through a magnetic field results in enough force on the loosely bound electrons to cause a current flow in the wire...note that this can be either a stationary wire in a changing magnetic field (such as in a transformer) or a moving wire in a stationary magnetic field, such as in a generator.
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