Conductivity and Ohm's Law
In conducting media, an electric field drives a current proportional to it, with conductivity setting the ratio and resistive dissipation.
Definition
Ohm's law states that in many materials the current density is proportional to the electric field through the conductivity; conductivity quantifies how readily a medium carries current, and the resulting motion of charge dissipates energy as heat.
Scope
This topic covers steady and quasi-steady currents in conducting media: current density and charge conservation, the microscopic and macroscopic forms of Ohm's law, electrical conductivity and resistivity, the Drude model of conduction, Joule heating and power dissipation, and the relaxation of charge in conductors. It treats classical conduction, leaving quantum transport to condensed-matter physics.
Core questions
- How does an electric field drive current in a conductor?
- What microscopic picture underlies Ohm's law and conductivity?
- How is power dissipated as current flows through a resistance?
Key concepts
- current density
- Ohm's law
- conductivity
- resistivity
- Drude model
- Joule heating
- charge relaxation
- continuity equation
Key theories
- Ohm's law and conductivity
- In a linear conductor the local current density is proportional to the electric field, with conductivity as the constant of proportionality, leading to the familiar relation between voltage, current, and resistance.
- Drude model of conduction
- Treating charge carriers as a gas accelerated by the field and randomized by collisions yields a conductivity set by carrier density, charge, and mean time between collisions, recovering Ohm's law.
Clinical relevance
Conduction and Ohm's law govern all resistive circuits and power dissipation, the design of conductors and resistive heaters, electrochemical and bioelectrical impedance measurements, and the modelling of current flow in biological tissue.
History
Ohm established the proportionality between current and voltage in 1827. Joule quantified resistive heating in the 1840s, and Drude's 1900 electron-gas model gave the first microscopic account of conductivity, later refined by quantum theories of solids.
Key figures
- Georg Simon Ohm
- Paul Drude
- James Prescott Joule
Related topics
Seminal works
- ashcroft1976
- jackson1998
Frequently asked questions
- Is Ohm's law a fundamental law of nature?
- No; it is an empirical, approximate relation that holds well for many materials over a range of conditions but fails for non-ohmic devices such as diodes and at very high fields.
- Why do conductors heat up when carrying current?
- Charge carriers accelerated by the field lose energy in collisions with the lattice, transferring it as heat; this Joule heating is proportional to the resistance and the square of the current.