C

Step 1: Understand the process of electrolysis. In electrolysis, an electric current is passed through a solution or molten compound to produce a chemical change, primarily the breakdown of the compound into its components.
Step 2: Identify the role of particles in the electrolyte. In an electrolyte, the current is transported by charged particles.
Step 3: Analyze each option:

• Electrons: While electrons flow through the external circuit, they do not transport the current inside the electrolyte itself.
• Atoms: Atoms are neutral and do not carry electric charge, hence they cannot transport current.
• Positive and negative ions: In the electrolyte, positive ions (cations) move towards the cathode, and negative ions (anions) move towards the anode, thus carrying the electric current.
• All the above: This option implies that all mentioned particles contribute, which is incorrect.

Step 4: Conclude that the correct choice is option C, which correctly identifies that current is carried out by positive and negative ions in the electrolyte.