Hi Theodore,

I'm running a 6-3 Romex NM-B with ground for my new air conditioner
system. My main panel doesn't seem to have any spare (unoccupied) 3/4"
size punch outs left; but there is a 1/2" punch out. It is possible
for me to fit this 6-3 with ground in there, but does anyone know
whether this is prohibited by the NEC?

You can enlarge the 1/2" punch outs to accept a 3/4" cable clamp.

The ideal way to do this is with a knockout punch, but they tend to be
rather expensive for a one time job. Step drills will also work, but
they're almost as expensive as a knockout punch.

I went through this recently with my garage heater and used a metal nibbler
to enlarge the hole. You can see photos on this page ("Relocating the power
cord" about halfway down the page):

http://www.watsondiy.com/heater.htm

Be sure to turn off the main breaker before you start working in the panel,
and vacuum up any little metal bits that may fall inside the panel.

Good luck!

Anthony Watson
www.mountainsoftware.com
www.watsondiy.com