Ohm's law
/ OHMZ LAW /
Turn up the pressure on a garden hose and more water gushes out; the wider, smoother hose lets more through for the same push. Electricity behaves with the same plain bookkeeping: push harder with more voltage and more current flows, while a more resistant wire lets less through. That tidy proportionality is Ohm's law.
Ohm's law states that the current through a conductor is proportional to the voltage across it — double the voltage and you double the current — with the resistance being the constant of proportionality that links them. In symbols, voltage equals current times resistance. Underneath, it reflects something simple about the carriers: a bigger push gives them a proportionally bigger drift, as long as collisions keep happening at a steady rate. Rearranged, the law lets you find any one of the three quantities once you know the other two.
Ohm's law matters because it is the everyday workhorse of all electrical engineering, the rule used to size a resistor, choose a wire, or work out how hot a heater runs. The crucial caveat is that it is not a fundamental law of nature but an approximation that holds for many materials over a limited range. Push too hard, or heat the wire, or use a device like a diode or a light bulb's filament, and the neat proportionality breaks down — such non-ohmic behavior is the rule, not the exception, in modern electronics.
Plug a 12-volt source into a 6-ohm bulb and Ohm's law tells you 2 amps will flow. Swap in a stiffer 12-ohm bulb and the current drops to 1 amp — the same push, half the flow, because the resistance doubled.
Same voltage, double the resistance, half the current — the plain arithmetic of Ohm's law.
Resistance and resistivity are different things in Ohm's law. Resistance belongs to a particular object and depends on its shape; resistivity is the material's intrinsic property. Ohm's law uses the resistance of the actual component in front of you.