E2 Current, Resistance and Ohm's Law

Topic

Electric current is the flow of the charge established by the previous model through a conductor—specifically, the amount of charge passing through a cross-section per second. Ohm's law states that, in many materials, the potential difference established by the previous model is directly proportional to the flowing current, with the constant of proportionality representing the conductor's electrical resistance.

This resistance is not an arbitrary property of the conductor; rather, it depends on three simultaneous factors: the material itself determines intrinsic resistivity (very low in copper, extremely high in an insulator); greater length increases resistance because the charge has a longer path to travel; and a larger cross-sectional area reduces resistance because more parallel paths are available for the charge.

When current flows through a resistor, power is dissipated as heat—the Joule effect—and this dissipated power increases much more rapidly than the current itself; a moderate rise in current results in a significantly larger increase in generated heat. There is also a local version of Ohm's law that relates current density at any given point within a material to the local electric field and conductivity; this local version explains the internal behavior of modern semiconductor devices. In these devices, limits on permissible current density—dictated by heating and material degradation—are key factors constraining further transistor miniaturization, a topic revisited by a later model in this series.

Thus, this module—which begins with charge flowing through a conductor—concludes by demonstrating that Ohm's law, seemingly the simplest principle in electronics, takes on a new life at the local level within a material, where it now imposes one of the strictest physical constraints on semiconductor design.

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