Practical estimate for a capacitor discharge through a resistor and an LED in series
simulate this circuit &ndash; Schematic created using CircuitLab

Figure 1. The test circuit.

I haven't time to try to figure out your equations which seem to contain both variables and SI unit symbols (which makes it very difficult to read). I offer the following comments:


Assume that the LED Vf = 2 V.
When SW1 is closed C1 will charge up to about 2/3 of the way from VD1 to 5 V due to the R1 / R2 ratio - so about 4 V.
During discharge you can assume that  Vf will remain fairly constant although it will decrease with current.
Your RC discharge is now calculated from 4 V to 2 V. So your RC time constant is &tau; = R2C1 = 1.8 s so you should see a discharge of 63% from 4 V to 2 V (1.26 V) in 1.8 s.


Try that out and see if it clarifies anything.