Alright, so I got a circuit that charges a capacitor and I want to charge it to a fixed voltage in a longer time than than the current provided would have (as the current provided would have charged it several times faster).
I can drop the provided current by putting a resistor, but I don't want to create feedback to the circuit that provides the current.
Well, I like minimalistic solutions, so I decided I would simply let the capacitor leak. Basically, I'll be putting a resistor to redirect a good portion of the current.
-- where voltage potential 1 (V1), in respect to ground, may be less than or equal or greater than voltage potential 2 (2), in respect to ground.
I say "leaking" the capacitor because a lot of time, the capacitor wold be directly grounded and the redirected current would not be used anywhere, so it might as well be flowed back to ground. Hence, it's like placing a resistor in parallel with the capacitor, leaking it:
I have no idea if this is already being used, but my initial Googling didn't turn up a lot of hits. So I guess even if this is already being used, I don't know of any good sources that will guide me theoretically.
So my question is, given parameters
What are the equations describing this configuration, in ranges
V1 < V2
V1 = V2
V1 > V2
Or maybe just V1 = V2, as I'm using the configuration in figure 2.
I would hazard a guess that it's C = (I*t)/V ... But I don't know how to split the current (I) between the leaking resistor and the capacitor. Also (I'm not that sure) I think one has to take into account that the splitting of the current will change over time, as the capacitor gets more charged. Then again, one can simply assume that the charging is linear like we do with charging/discharging in smoothing capacitors.