Final answer:
The capital and largest city of Rhode Island is Providence, situated on the namesake river, at the head of Narrangasett.
Step-by-step explanation:
The capital and largest city of Rhode Island that is situated on the namesake river, at the head of Narrangasett is Providence. Providence is the capital city of Rhode Island and is located on the Providence River, which is an estuary of Narragansett Bay. It is known for its rich history, beautiful architecture, and vibrant arts scene.