So I have a bicycle that has a single front gear, but many back gears with a derailleur. I am wondering if I change the size of the front gear (like significantly), meaning if I get a bigger front gear without changing the back gears or derailleur, will the derailleur will still function and not cause the chain to go slack? If not can I adjust the rear derailleur to a larger front gear? I am trying to make a generator out my old bicycle, and in order to get a more efficient power output I need to have a higher front gear (since it is an old bike for smaller people so it has a rather small front gear). I am pedaling too fast on it as is right now. I do not know what gearing I have right now.
For a generator you will probably want two sets of gears. Cyclists normally pedal at about 90-110rpm, and getting a small generator to work efficiently normally means spinning at 1000's of rpm. I used a "drill pump" to make a pedal powered pump once and that was designed to spin at 1800rpm. But it used 500W or more at that speed, so I spun it at about 1000rpm using about 200W and that worked fine. Unfortunately I lost interest in taking photos after building the first, single-stage version.
Most of the bicycle generators I've seen use the bike wheel as the second gearing stage, typically having a generator drum 100-300mm in diameter for a ratio between 2 and 6 to 1. The bigger the drum the lower the ratio, but the less tyre deflection so the higher the tyre/drum efficiency.
Depending on what tools you have (mostly, do you have a lathe) you can either use the large cog on the cassette to drive a second cassette, or make an adapter to mount a full size chainring on the cassette. If you get a steel cassette and chainring you can just weld the chainring on, and it will probably not deform too much.
Doing that lets you have a road bike first stage with a maximum ratio of 50T:12T or ~4:1. If the cassette is a wide range one off a mountain bike it could be 12-36, say, giving you a 36:12 second stage or 3:1. That's 12:1 overall, so your 100rpm input becomes 1200rpm output.
You can get the same ratio with a single stage but it will be big and expensive. Assuming a 12T small cog, you will need a 144T chainring to get the same 12:1 ratio. There's one on ebay for $US500. A friend of mine sells large custom chainrings in Australia and could make you a 144T one, but a 90T one costs $AUS200 (about $US150 in April 2016).
I think the important thing is to start with the generator you want to use and work out its ideal spin rate. Then work backwards to the gearing. I suggest leaving at least one derailleur in your final build so that people can vary the gearing a bit to get the most comfortable combination of pedalling speed and load. Varying the generator output has much the same effect if you can do that.