**Conductivity of Solutions**

**Introduction:**
Conductivity refers to the ability of a substance to conduct electricity. In solutions, the presence of charged particles (ions) enables them to conduct electricity. Substances that dissolve in water and dissociate into ions are known as electrolytes and are conductive. On the other hand, substances that do not dissociate into ions and do not conduct electricity are called non-electrolytes.

**Explanation of Options:**

a) Sugar in Water:
Sugar (sucrose) is a covalent compound that does not dissociate into ions when dissolved in water. Therefore, it does not conduct electricity.

b) Sugar in Ethanol:
Similar to sugar in water, sugar in ethanol also does not dissociate into ions. Ethanol is a covalent compound, and therefore, the solution does not conduct electricity.

c) Iodine in Ethanol:
Iodine is a nonpolar covalent compound that does not dissociate into ions when dissolved in ethanol. Hence, the solution of iodine in ethanol does not conduct electricity.

d) MgCl2 in Water:
MgCl2 is an ionic compound composed of magnesium ions (Mg2+) and chloride ions (Cl-). When this compound is dissolved in water, it dissociates into its constituent ions. This dissociation process allows the solution to conduct electricity. The magnesium ions (Mg2+) and chloride ions (Cl-) are free to move in the solution and carry electric charge, enabling the conduction of electricity.

**Conclusion:**
Among the given options, only the solution of MgCl2 in water conducts electricity. This is because MgCl2 is an ionic compound that dissociates into ions when dissolved in water. The presence of these ions allows the solution to conduct electricity. The other options (sugar in water, sugar in ethanol, and iodine in ethanol) do not dissociate into ions and therefore do not conduct electricity.