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how long would a 3.7v, 1130mAh cell phone battery power a luxeon iii star at 350mA? Answered

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I say about two hours because the battery's voltage will gradually drop and eventually the LED does not have enough voltage to say on.

1130mAh/350mA=3.22h, not counting the loss of voltage as the battery becomes discharged.

about 3 h depending on battery condition