I am a college sophomore studying EE, I am currently working on making a simple battery charger circuit for an integrated device. The device has 3 Li-Ion batteries in series for my motors, and a single cell by itself for the circuitry. I have been doing some research on charging techniques. I have seen a couple charge controller ICs and some simple schematics. I am trying to square away all aspects of charging a battery. I currently understand that a battery should be charged at its rated voltage (say 4.2V for a single cell) and that you should try to limit the current so that the battery doesn't overheat.
I have some uncertainties about how exactly to charge batteries. I was thinking that I could try plugging in the a battery to my voltage supply, setting it to 4.2V, and limiting the current to something manageable, then when the battery gets to 4.2V there will be no potential difference and the battery will stop being charged.
I was wondering if all of that is true. If not, what is the best method to stop charging a battery?