Current Flow and Ohm's Law

In 1827, Georg Ohm defined an empirical relationship between the current flowing through a wire and the voltage potential required to drive that current.*

Ohm found that the current, I, was proportional to the voltage, V, for a broad class of materials that we now refer to as ohmic materials. The constant of proportionality is called the resistance of the material and has the units of voltage (volts) over current (amperes), or ohms.

In principle, it is relatively simple to measure the resistance of a strand of wire. Connect a battery to a wire of known voltage and then measure the current flowing through the wire. The voltage divided by the current yields the resistance of the wire. In essence, this is how your multimeter measures resistance. In making this measurement, however, we must ask two crucial questions.

*Ohm actually stated his law in terms of current density and electrical field. We will describe these properties later. For one-dimensional current flow in a wire, his law is given as described above.