---
L dI
E = ------
dt
Yabbut... inductance? Where? Can't see any possible need for that
in such a circuit,
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Not trying to be confrontational, but until you take one apart or
otherwise find out definitively how the thing works, your inability to
see why an inductance might be used is unimportant.
In a wind-up or a shake one, what do you think is generating the
electricity to drive the LEDs?
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and any stray should be minuscule. (It's not even
dependent on being a 'wind-up' unit -- the others I see advertised are
all battery driven.)
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Then I suspect that what might be happening is that, because of the
design, the miniscule inductance is generating a spike higher than the
reverse voltage of 7 volts or so allowed across the LED(s).
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Take one apart and post what you find in it?
Maybe eventually (:-)) but I don't really want to offend the present
giver that soon! I may try to write the supplier and see if they can
refer me to a useful source. [Some hope...]