Ohm's Law, on a Live Circuit

The two laws behind the four boxes

Ohm's law says V = I × R: push harder or lower the resistance and more current flows. The power law says P = V × I: how much of that energy turns into heat. Rearranged, they answer any question you can ask about a simple circuit, and the wheel on the Ohm's law wheel page lays out all twelve arrangements.

Reading the diagram

The battery on the left sets the voltage, the zigzag is the resistance, and the meter reads the current that results. Change the resistor and watch the current move: half the resistance, double the current, four times the power. That last one is why a resistor that felt cool at 5 V can smell interesting at 10 V.

Picking a resistor that survives

The power figure this calculator returns is what the resistor has to shed as heat, and the rule of thumb is to buy at least double it. A resistor dropping 5 V at 20 mA dissipates 0.1 W, which a quarter-watt part handles comfortably. The same resistor at 60 mA dissipates 0.9 W and will scorch the board under a quarter-watt body. Power rises with the square of current, so doubling the current quadruples the heat.

Where Ohm's law stops applying

The law describes resistors, and plenty of parts are not resistors. An LED, a diode and a transistor junction all have a forward voltage that barely moves while the current changes by orders of magnitude, which is why an LED needs a resistor to set its current rather than a voltage to set it directly. Motors, filament lamps and batteries change resistance as they warm up or discharge, so a single measurement of any of them describes one moment, not the part.