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wiring led on power switch

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You might want a larger capacitor value. I would probably start with something like 100 uF. It really depends on the average current draw. More current would mean more ripple amplitude.

How much current do you want through the LED? A 2kOhm resistor won't give you much; maybe around 1.5 mA average. Something like 330 Ohms might give about 8 ma average.

With 2k and 1.5 mA, the 10 uF cap would give about 50 mV ripple, peak-to-peak, out of about 2.5 V across the LED. That should be fine, I guess.

But if you need more current, you can increase the cap value proportionately if you don't want more ripple amplitude.
 
It depends on how fast the LED is. TVs have rather slow phosphorous and don't toggle from on to off on every refresh. :) Some people get headaches from slow computer monitors.

I've used LEDs in situations like this where the flicker is noticeable, especially when sweeping my eyes across the room. Anyhoo...if you don't notice the flicker it's not a problem.
 
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