Final answer:
Montpelier is the capital of Vermont, known for being the state capital with the smallest population in the U.S., and is situated on the Winooski River.
Step-by-step explanation:
The capital of Vermont, which is located on the Winooski River and known for having the smallest population of any state capital in the United States, is Montpelier. Despite its small size, Montpelier serves as the center of government for the state and is rich in history and culture. Its unique status combines the charm of a small town with the responsibilities of a state capital.