How long would it take to suck all the juice out of it?
I just ran an LED for about 8 days straight. Started off at 1.2v AA (dead to a digital camera), and wasn't noticeably dim until the 5th day. It just stopped last night at .58v.
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Alkaline batteries have a sloped discharge curve. What happens is when you first buy that 1.5V battery it will actually read more than 1.5V. When you use it over time the voltage will decrease. Digital devices and analog devices will be tolerant of this as long as it doesn't fall below the manufacturer's minimum voltage threshold. Usually once the battery hits around 0.9V it is considered dead. It still has some juice in it, not enough for most devices like a camera. If you look at the graph you can see that it is probably less than 10% of its full capacity. (the graph is a constant discharge so time can be related to capacity roughly)A well made joule thief can run down to 0.35V. See a Joule thief actually charges and inductor and switches it between charging and discharging. This is what allows you to have enough voltage to forward bias an LED and turn it on. What a lot of people don't know is the LED is not continuously on. It is actually flicker at a very high rate. Mine flickered around 250kHz when i measured it using a oscilloscope.In the end it depends what LED you are using and how dead is dead. If it is 'freshly' dead (~0.9V) it could last a day or so. The dead ones I had lying around the house only lasted ten hours.The thing about the digital camera ones are a limitation in the chemistry. Alkaline batteries should never be used for digital camera or high end electronics. Digital Cameras and other similar electronics require a very high current draw. This kind of current draw damages an Alkaline. It will cause it to drop rapidly in voltage since the chemistry does not support a high current draw. Rechargeable NiMHs have a better chemistry for cameras. Also Lithium batteries also do better. If you use Alkaline batteries for cameras they will appear dead long before their full capacity is used.Well good luck. I recommend the boost circuit in my instructable if you want a really good voltage boost converter. It is designed to go down to 0.8V much farther than most joule thief can.https://www.instructables.com/id/SPVWXYUFT7PUSX8/
My joules thief in my energy seed lamp discharge the battery to 0,5V and last more the 24Hours.
I don't think it was a truelly dead battery.
It really depends how dead the battery is... the joule thief can last for from about an hour to a few months.
In a really really really "dead"( one even dead for a remote control)lasts 29 hours straighI think a "dead" (for a digicam) will last about 3 days or more!