Electric Current · aiwiki.page

Electric current is the rate at which net electric charge passes through a specified surface, such as the cross-section of a wire. It can be carried by electrons, ions, or other charged particles, either within matter or through a vacuum. Current is a central quantity in electromagnetism and electrical circuit theory. Its conventional direction is the direction of positive-charge flow, which is opposite to the motion of electrons in a metal conductor. (openstax.org)

Definition and units

The average current through a surface is

I_{\mathrm{avg}}=\frac{\Delta Q}{\Delta t},

where $\Delta Q$ is the net charge crossing during the interval $\Delta t$ . Instantaneous current is the time derivative of the accumulated transferred charge:

I(t)=\frac{dQ}{dt}.

Current has a sign determined by the chosen reference direction. It measures charge transfer, not the amount of charge stored in an object or the speed of individual particles. (openstax.org)

In the International System of Units (SI), current is a base quantity whose unit is the ampere (A). One ampere equals one coulomb per second. The SI definition fixes the elementary charge at exactly $1.602176634\times10^{-19}$ coulomb. Consequently, a current of one ampere corresponds to approximately $6.2415\times10^{18}$ elementary charges crossing a surface each second. (bipm.org)

Charge carriers and conduction

In a metallic conductor, mobile electrons undergo rapid microscopic motion. Without an applied driving field, their motions do not produce a sustained net current. An electric field introduces a small average velocity, called the drift velocity, superimposed on that motion. Because electrons have negative charge, their drift is opposite to the conventional current direction. Scattering within the material limits their average drift rather than allowing indefinite acceleration. (openstax.org)

The charge carriers depend on the medium. In an electrolyte, positive and negative ions can both contribute: oppositely charged particles moving in opposite directions produce conventional currents in the same direction. Electron drift in ordinary wires is much slower than the propagation of the electrical disturbance that establishes current. A circuit therefore does not need to wait for an electron to travel from its source to a distant component before that component responds. (openstax.org)

Current density

Current through a selected surface is a scalar, whereas current density, $\mathbf J$ , describes the local magnitude and direction of charge flow. Its SI unit is amperes per square metre. The current through an oriented surface $S$ is the surface integral

I=\int_S\mathbf J\cdot d\mathbf A.

The dot product selects the component perpendicular to the surface. For uniform flow perpendicular to an area $A$ , this becomes $I=JA$ . For one carrier species,

\mathbf J=nq\mathbf v_d,

where $n$ is carrier number density, $q$ is the signed charge per carrier, and $\mathbf v_d$ is drift velocity. Contributions from multiple carrier species are added. (openstax.org)

Voltage, resistance, and energy

Current and voltage are distinct quantities. Voltage is a difference in electric potential, expressing energy transferred per unit charge; current expresses charge transferred per unit time. A battery maintains a potential difference through internal processes, while electromagnetic induction can generate a driving electric field when magnetic flux changes. (openstax.org)

For an ohmic component under fixed physical conditions, Ohm’s law gives

V=IR,

where $R$ is electrical resistance. This proportionality is not a universal law for all materials or devices. Locally, isotropic ohmic conduction is described by $\mathbf J=\sigma\mathbf E$ , where $\sigma$ is electrical conductivity. (openstax.org)

The instantaneous power absorbed by a component, using consistent voltage and current reference directions, is $P=VI$ . For a resistor, this yields $P=I^2R=V^2/R$ . The conversion of electrical energy into heat is called Joule heating. Charge is not consumed during this energy conversion: the source supplies energy, and the component transfers it into other forms. (openstax.org)

Direct and alternating current

Direct current (DC) flows in one direction; its magnitude may be constant or vary with time without reversing. Alternating current (AC) periodically reverses direction. A common idealized waveform is

I(t)=I_{\mathrm{peak}}\sin(\omega t+\phi),

where $\omega$ is angular frequency and $\phi$ is phase. A sinusoidal current averages to zero over a full cycle, but it still produces heating in a resistor because dissipated power depends on the square of current. (openstax.org)

Magnetic effects and displacement current

Electric currents produce a magnetic field. This connection is incorporated into Maxwell’s equations, which also describe how changing electric fields contribute to magnetic fields. (openstax.org)

Maxwell’s displacement current is distinct from ordinary conduction current: it represents the contribution of a changing electric field rather than charge transport through a material. In a charging capacitor, conduction current flows in the connecting wires, although charge does not cross an ideal insulating gap between the plates. The changing field in that gap supplies the displacement-current term, allowing the magnetic-field equation to remain consistent for surfaces passing through either the wire or the gap. (openstax.org)