There is no "capital of Philadelphia"—and for good reason. Philadelphia is a city, not a state or country. It's the largest city in Pennsylvania and the sixth-largest in the United States, but it doesn't have a capital.
The capital of Pennsylvania is Harrisburg, located ~105 miles west of Philadelphia along the Susquehanna River. Harrisburg has served as the state capital since 1812, chosen for its central location.
Philly is a consolidated city-county (Philadelphia County), a major economic hub (Fortune 500 headquarters, universities, healthcare, ports), and a cultural powerhouse—but administratively, it's one of Pennsylvania's 67 counties, governed by a mayor and city council, not a state capital.
Quick reference: Pennsylvania → Harrisburg (capital) | Philadelphia → largest city, former US capital, birthplace of American democracy.