Ohm's law

Ohm's law is the simple, workhorse rule that ties together voltage, current, and resistance for a huge class of everyday conductors. Its everyday meaning: push harder and more flows. If you double the voltage across a plain resistor, you get double the current, in tidy proportion. It answers the most common question in circuit work: if I know two of the three quantities voltage, current, and resistance, what is the third?

Precisely, Ohm's law states that the current I through a conductor is directly proportional to the voltage V across it, with the resistance R as the constant of proportionality: V = I R. The same relationship can be rearranged as I = V / R or R = V / I. In its microscopic form it reads J = sigma E, current density proportional to electric field. A component that obeys this straight-line proportionality, so that R stays constant no matter the voltage, is called ohmic.

It is vital to be honest here: Ohm's law is not a fundamental law of nature like conservation of energy. It is an empirical rule that many materials happen to follow over a normal range of conditions, and plenty of important devices flatly disobey it. A light-bulb filament heats up and its resistance rises, a diode conducts one way but blocks the other, and a transistor is deliberately non-ohmic. So V = I R always defines resistance as V / I, but only for ohmic components is that ratio a fixed, voltage-independent number.