Step 1: Concept
A weak electrolyte is a substance that only partially ionizes or dissociates in aqueous solution.
Step 2: Meaning
$H_{2}SO_{4}, NaCl,$ and $NaOH$ are strong electrolytes because they dissociate almost completely into ions.
Step 3: Analysis
Carbonic acid ($H_{2}CO_{3}$) is a weak acid and therefore does not ionize fully, leaving mostly neutral molecules in the solution.
Step 4: Conclusion
$H_{2}CO_{3}$ is the weak electrolyte.
Final Answer: (A)