If you have a crappy psu, you may want to look toward a 960, 950, or even a 750 ti if the power supply is that bad. Also, how big is the power supply (wattage) and what vendor?
It could be that your PC is using up all of the allocated ram for minecraft, which is 1 gb at default. I had a similar problem, with it dipping on my PC. You can change it through the minecraft launcher.