How can you get 1/2 hr of light from only 50,000uF?
1) An array (10 LEDs) of high-powered (25mA ea) LEDs (3.5V white) needs a total of 250mA.
2) Charge the 50,000uF cap to 7.0V.
3) Use ten 140 ohm current limiting resistors for the LEDs, so that their current is 25mA ea when the cap is charged to 7.0V.
The LEDs' brightness will begin dropping immediately, and they will turn-off when the cap discharges to 3.5V or a little less.
The cap's voltage will discharge to 3.5V in 5 time-constants, which is 5 X 14 ohms X 50,000uF = 3.5 seconds. You would have useable light for about 2 seconds.
A 1/2 hr has 1800 seconds, doesn't it? :roll:
Lets try a 50F supercap.
1) Can't use white LEDs because the cap's recommended voltage is only 2.5V, so use ten 2.0V red LEDs operating at a starting total current again of 250mA.
2) Charge the cap to 2.5V.
3) Use ten 20 ohm current-limiting resistors for the LEDs, so that their current is again 25mA ea when the cap is charged to 2.5V.
Again, the LEDs' brightness will begin dropping immediately, and they will turn-off when the cap discharges to 2.0V or a little less.
Again, the cap's voltage will discharge to 2.0V in 5 time constants, which is 5 X 2 ohms X 50F = 500 seconds. You would have useable light for about 330 seconds. That's only 5.5 minutes, isn't it? :roll:
You'll have to spend a fortune on enough supercaps for the LEDs to last all night long. :lol:
I know, just use four AA Ni-MH 2500mA/hr rechargeable cells. Their voltage will remain at about 4.8V and they will power ten white LEDs at 25mA ea for about 10 hours (600 minutes) per charge! :lol: