A digital pin knows only ON and OFF — 5 volts or nothing. Yet it dims an LED and sets a motor's speed. The trick is switching fast and controlling the fraction of time spent ON: the load feels only the average. Scrub the duty cycle and watch the average move; scrub the frequency and watch it not move.
average voltage = duty × supply (5 V), independent of frequency — Node-verified at 100 Hz and 1 kHz to ±1%. Frequency only sets how smooth the average is (too slow and an LED visibly flickers). Built on the reusable probe.js primitive. · Institute for Physical AI @ BMI