physics//electromagnetism//electric circuit//electrical resistance

Electrical resistance is how strongly a path opposes the flow of electric current, the voltage needed per ampere, and it decides how much current a voltage drives, how hot a wire runs and how much power is lost on the way. It is measured in ohms: one volt across one ohm drives one ampere (Ohm's law, \(V = IR\)).

Electrical resistance is how strongly a path opposes the flow of electric current, the voltage needed per ampere, and it decides how much current a voltage drives, how hot a wire runs and how much power is lost on the way. It is measured in ohms: one volt across one ohm drives one ampere (Ohm's law, V=IRV = IRV=IR).

Inside a metal the free electrons are pushed along by the electric field and keep colliding with the vibrating atoms of the crystal and with its defects; each collision costs them the speed they had gained. Resistance is the macroscopic sum of those collisions. It grows with the length of the path and shrinks with its cross-section, so a long thin wire resists more than a short thick one, and the material's own share is its resistivity (copper and silver are among the lowest).

Temperature changes it, in opposite directions for different materials. In a metal, cooling quiets the vibrations, the electrons collide less and resistance falls; in a semiconductor, cooling leaves fewer free carriers and resistance rises.

Some materials lose it entirely. Below a critical temperature, a few kelvin for classic metals and much higher for some ceramics, resistance drops to exactly zero: superconductivity, used for the magnets of MRI scanners and the sensors of classic MEG.

The energy lost to resistance is heat, P=I2RP = I^2 RP=I2R, developed in Joule heating.

The inverse, how easily a path conducts, is conductance (and for a material, conductivity): the same idea seen from the other side.