Can I charge a large capacitor with a small resistor?
This question has not much to do with Arduino, but yes, you can. You only have to take into account the maximum amount of current that will flow. This current occurs when you start charging the capacitor and (as you will know) is V/R (where of course V is the supply voltage). The power supply, the resistor and the capacitor have to be able to handle this current (but only for a small time period).