Some light switches run a small amount of current through the bulbs
even when off, usually to power small devices at the switch like a
timer, motion sensor, or night light. Do your switches have either of
those features, or something else like that?
The way those devices work is instead of having a hot/neutral pair
powering the switch, they just sit inline with the hot wire and draw a
very small amount of power. Old fashioned incandescent bulbs won't
light up if there's only a small amount of electricity running through
them, so you would never notice this current, but LEDs are much more
efficient and apparently are getting enough power to run.
If that is the cause of the problem, there are a few solutions:
Swap out the light switches for regular ones. You'll lose whatever additional functionality they have.
Upgrade your switches to ones that have both a neutral and a hot wire, instead of just the hot wire. This may be relatively
straightforward or extremely difficult, depending on whether the
neutral for the light goes through the same box as the switch. (Note
that even if you do have a neutral at the box it may be a little
tricky to wire it up, since you'll have to cut it and then probably
add a pigtail or two.)
Put back your old-fashioned incandescents.
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If we're talking a high voltage circuit, w high intensity LEDs: Many
high intensity white LED's use a phosphor that is in fact
phosphorescent, like glow in the dark paint. You just have to wait for
it to dim down. Switching to a different brand of bulb, with a
different phosphor may help, but it's hard to "try before you buy".
If we're talking a low voltage circuit, 5-12v: A capacitor in line
with an LED can power it for quite some time. You can limit this
effect by by using a power supply with a smaller filter capacitor.
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