Electronic – Help in finding capacitor and resistor value for discharging circuit

never really played with a PUT before (actually never heard of em) but i was interested and read the datasheet.

It looks like the current through the PUT is dependent on the resistance between gate and ground, which explains why when the cap is feeding the LED it doesn't get really mad about the LED not having a current limiting resistor. In this case the Rg gate resistance is your R3. My guess is that when you moved R3 up to 96k your limiting the current so much that your LED isn't getting to full brightness.

Additionally the low limit of this current combined with a really big cap means your capacitor discharges much slower. Combine this with the very small R1, which charges the cap quickly, and i'm betting you are getting some oscillation, but its happening very, very fast.

Try a larger R1, smaller R3 and whatever sized R2 you need to keep the divider ratio the same. Ideally track down a smaller cap, it would make finding the resistor sizes needed easier.

My contribution is to point out a circuit that suits your title: "A path for capacitor's charging, and another for discharging it". It is a solution commonly used to drive a N-channel mosfet/IGBT in the configuration high-side (load grounded). This avoids the use of P-channel mosfet, typically showing higher RDSon. But otherwise imposes a complication when designing N-channel gate drivers (except using a gate voltage larger than the drain voltage - a rare situation). The scheme shown below uses a capacitor as a "floating" gate voltage for the Mosfet. This solution is already integrated in most commercial gate drivers (pick a specific datasheet and note the presence of the diode and capacitor around the component). Motor control and power conversion are typical applications.

Note: When I started to answer, the author had not yet supplemented the question with the last figure (I took some time drawing my figures). The web page no mantain updated, when editing. I write this so the reader does not think I simply repeated that idea. It happens on forums.