Electricity and magnetism

Electric current

Electric current is the amount of charge passing a cross-section each second; conventional current flows from the positive to the negative terminal through the external circuit.

In a metal, free electrons acquire an average drift when an electric field is present. Conventional current is defined in the direction positive charge would move, so it is opposite to the average electron drift. A source sustains current in a closed circuit.

Current and drift speed

In a simple metal-wire model, $I=n|q|Av_d$, where $n$ is carrier number density, $A$ is cross-sectional area, and $v_d$ is average drift speed. Current can therefore be substantial even when electrons drift slowly: in ordinary copper wiring, drift speed is far below the propagation speed of the electrical signal.

Current has a conventional direction, but in basic circuit equations $I$ usually denotes its magnitude. For a changing current, $\Delta Q/\Delta t$ over a finite interval is only the average; instantaneous current is the rate at which charge crosses at that moment. If wire area increases while carrier density and drift speed stay fixed, more carriers pass each second, so $I=n|q|Av_d$ grows in proportion to area.

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