Tire/Rim sizes

I'm building two bikes. I have two 1.75" rims and was about to order another set, but am wanting a good size ballon tire. What is the max size I can run on the 1.75"? Do I need to go to 2 1/8th for the larger balloon tires?

Thanks. Was just kinda worried that 2.125" tires might be compromised a bit. Much of the choices of tires are in that size.
I'm building both bikes with 4 stroke power, coaster and disc, Sportscarpat sprockets, neither would need larger that 2.125" tires, although the Felt frame is much larger than the straight bar Schwinn.