Final answer:
The filament of a lightbulb must have a greater electrical resistance than the wires to ensure the filament glows when heated by electrical current, while the wires remain cool, efficiently conducting electricity without energy loss or hazard.
Step-by-step explanation:
It is important that the filament of a lightbulb have a much larger electrical resistance than the supporting wires that carry current to and from that filament. The high resistance of the thin filament causes a significant amount of electrical energy to be converted into {heat}, which subsequently causes the filament to glow and emit light. In contrast, the wires connecting the lightbulb to the power source are designed to have a much lower resistance, ensuring that they can conduct electricity efficiently without heating up excessively, which would be wasteful and potentially hazardous.
Incandescent light bulbs work because the high resistance in the filament due to its small cross-sectional area causes it to heat up and ultimately produce light. This resistance changes as the filament gets hotter, influencing the amount of current that flows through it according to Ohm's Law. In the case of bulbs connected to a higher voltage than they are designed for, the increased current due to lower resistance at initial start-up causes them to burn out quickly.