Example 2
3. Filament Lamps
Ah, the incandescent light bulb. A classic invention, and another place where Ohm's Law is not obeyed. While they might seem simple, the resistance of their tungsten filament changes significantly with temperature. And temperature, as you might guess, changes with the current flowing through it! This makes the relationship between voltage and current decidedly non-linear.
When you first switch on a light bulb, the filament is relatively cold. It has a low resistance, so a brief surge of current flows through it. As the current heats the filament, its resistance increases rapidly. This higher resistance then limits the current, eventually reaching a stable operating point where the filament glows brightly. All of this happens in fractions of a second, but it's a dynamic process far removed from the static resistance assumed by Ohm's Law.
Think about how the brightness of a light bulb changes as you dim it. The voltage across the filament decreases, which lowers the current. This, in turn, cools the filament, reducing its resistance. The reduction in resistance isn't directly proportional to the voltage drop, because of the temperature dependence. Dimming the bulb reduces the temperature, which reduces the resistance, which impacts the resulting light output in a complex, non-linear way.
The filament's temperature dependence on resistance is due to complex interactions within the metal structure at higher temperatures. Electrons move differently, scattering and colliding more frequently, which hinders their flow. All this to say that incandescent bulbs are a prime illustration that Ohms Law is not a fit-all rule of thumb. The keyword, again, is that Ohm's Law is not obeyed.