How can a light bulb stay lit without a power source?

Light bulbs work by passing an electrical current through a thin wire. This thin wire has a high resistance. High resistance means more electrical energy is converted into heat. The heat causes the wire to glow, producing light. It stayed lit because the wire had yet to cool to a temperature below which it would not glow.

This only works in a vacuum; if you tried this under normal atmospheric pressure, the wire would burn. If you did it in helium or some other inert gas, too much heat would be conducted away from the wire for it to illuminate.

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