This is a circuit which uses two pair of PNP transistors to create two current limiting circuits. The first limits the in-rush current on the supercap to prevent damage to a standard 5V USB power supply for charging. The second allows an appropriate amount of current to flow to power the LED. The four switches are for setting the current limits of each circuit with a short and for turning on an off the light and charger. The diode after the first circuit prevents the supercap from discharging back through the charger circuit.
I have included the equivalent series resistance of a real capacitor.
