Ohm's law
Ohm's law is the first tool every electrical engineer reaches for, and it fits in one tidy line: V = I × R. Voltage equals current times resistance. Picture water in a pipe: voltage is the pressure pushing it, current is how much water flows past each second, and resistance is how narrow the pipe is. Squeeze the pipe (more resistance) and less flows; push harder (more voltage) and more does.
The real magic is that you only need to know two of the three values to find the missing one — just rearrange the line. Want the current? I = V ÷ R. Want the resistance? R = V ÷ I. Say you put 9 volts across a 3-ohm resistor: the current is 9 ÷ 3 = 3 amps. This single relationship lets you size a resistor, predict a current, or check a circuit — the everyday workhorse behind almost every design.
Ohm's law isn't a law of nature like gravity — it's a description that holds well for "ohmic" materials such as metal wires and ordinary resistors, where current stays neatly proportional to voltage. Many components break the rule: a light bulb's filament grows more resistant as it heats, and a diode lets current through in only one direction. Georg Ohm published the relationship in 1827, and the unit of resistance, the ohm (Ω), is named after him.