Georg Simon Ohm

Start with evidence, then build the model.

In his 1825 paper, Ohm studied how the electromagnetic effect produced by a wire decreased as the wire became longer. Rather than begin with a finished theory, he tabulated experimental evidence and searched for stable mathematical relationships.

In two important 1826 papers he modelled conduction in electrical circuits using ideas analogous to Joseph Fourier's mathematical treatment of heat conduction. In 1827 he assembled the work into the comprehensive theory associated with his name.

Current depends on both the source and the resistance.

A battery establishes an electromotive force or voltage across a circuit. The connecting wire and other components oppose current. Under stable physical conditions, an ohmic element follows V = I·R. The same relation can be rearranged as I = V/R or R = V/I.

At fixed resistance, doubling voltage doubles current. At fixed voltage, doubling resistance halves current. Resistance is not simply a synonym for a resistor: it is a property that depends on material, length, cross-sectional area and temperature.

The law has operating conditions.

Ohm's law often remains valid over a wide range, but it is not universal. Strong heating changes the resistance of a filament; diodes and vacuum tubes have nonlinear current–voltage behaviour. A useful calculation therefore asks whether the component is approximately ohmic and whether temperature and other conditions remain stable.