The Battlefield Blog has system specifications for the PC editions of Battlefield Bad Company 2 and Battlefield 1943, which are the same, as the two military shooters share the same updated Frostbite engine:

Minimum Frostbite PC Specifications for BFBC2 & BF1943
Processor: Core 2 Duo @ 2.0GHz
Main memory: 2GB
Graphics card: GeForce 7800 GT / ATI X1900
Graphics memory: 256MB
OS: Windows XP
Free HDD space: 15GB for Digital Version, 10GB for Disc Version (BFBC2)
10GB for Digital Version, 4GB for Disc Version (BF1943)

Recommended Frostbite PC Specifications for BFBC2 & BF1943
Processor: Quadcore
Main memory: 2GB
Graphics card: GeForce GTX 260
Graphics memory: 512MB
OS: Windows Vista or Windows 7
Free HDD space: 15GB for Digital Version, 10GB for Disc Version (BFBC2)
10GB for Digital Version, 4GB for Disc Version (BF1943)