Conceptual Physics (12th Edition)

There is less resistance in the higher-wattage filament. $Electric \; power = (current) \times (voltage)$. This is discussed on page 440. More power for the same voltage means that the current is greater. By Ohm’s law, more current for the same voltage means that the 100-W filament has less electrical resistance. It must be thicker. Thick wires have less electrical resistance than thin wires (page 443).