A circuit must be closed for a light bulb to light up because electricity needs a complete path to flow from the power source to the light bulb and back. When a circuit is closed, the electrons can move freely from the negative terminal of the power source, through the wire, through the light bulb filament, and back to the positive terminal of the power source. This flow of electrons is what causes the light bulb to light up.

If any part of the circuit is broken, the electrons cannot flow and the light bulb will not light up. For example, if the wire is cut or if the light bulb filament burns out, the circuit will be broken and the light bulb will not work.