Final answer:
Electric conductance is high in solid graphite, as it allows electrons to move freely, making it a good conductor of electricity. Sugar solution and solid nuclei do not have freely mobile charged species to allow for significant electrical conductance.
Step-by-step explanation:
Electric conductance is high in substances that contain freely mobile, charged species such as electrons or ions. Among the given options, solid graphite exhibits high electrical conductivity. In solid graphite, the structure allows electrons to move freely, which makes it a good conductor of electricity. On the other hand, while solid nuclei consist of charged particles, they are not free to move, and thus do not contribute to electrical conductance. Sugar solutions contain dissolved sugar molecules, which, because sugar is a nonelectrolyte, do not break down into ions and therefore cannot conduct electricity.
Solutions of electrolytes like KCl exhibit high conductivity because they contain dissolved ions that facilitate the movement of electrical charge. Solutions of nonelectrolytes such as ethanol, and by extension sugar, do not contain dissolved ions and thus are poor conductors of electricity. In contrast, graphite is an example of a non-metallic conductor due to the mobility of its electrons.