Explain why the lightbulb lights up in the solution containing NaCl but not

in the solution containing sugar

Explanation:

Strong electrolytes are those solutions which undergo complete dissociation when dissolved in water.  The dissociation of strong electrolytes is given by a right arrow.

NaCl being an ionic compound dissociate in water to give sodium and chloride ions which help in conduction of electricity.

Whereas sugar being a covalent compound, do not dissociate into ions when dissolved in water and thus cannot conduct electricity.