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The other night, I found myself crashing at a friend's house without a MicroUSB charger handy. As such, my phone (Nokia Lumia 920) died before I went to bed - attempting to boot would simply yield a "low battery" screen. When I awoke about 6 hours later, I decided (in a moment surely befitting the definition of insanity) to try turning the phone on again. The phone booted this time, showing about 12% battery remaining. Aside from the expected "low battery" warning messages, I was allowed to use the phone normally for awhile before I finally got back into my car and was able to charge it there.

I'm pretty sure I've seen this phenomenon in other small electronics (usually phones). A device will have drained its battery to the point of being un-bootable but, after a few hours or so, I'll later try again and find it coming to life as if nothing was wrong.

What causes this?

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  • \$\begingroup\$ Reaction rate limits. \$\endgroup\$ – Ignacio Vazquez-Abrams Jul 15 '13 at 15:47
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    \$\begingroup\$ @IgnacioVazquez-Abrams I suspect if I understood the meaning of that phrase, in this context, I wouldn't be asking this question - care to expand upon that a bit in a proper answer? \$\endgroup\$ – Iszi Jul 15 '13 at 15:56
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Batteries work by way of a redox reaction. The reaction can only occur so fast, thus limiting the current the battery can provide. As more current is drawn from the battery, the voltage decreases.

As the battery becomes depleted, there are less of these reactants available to drive electric current. However, if the battery is left to sit for a while, the reaction can proceed a bit, building up an excess of electrons at one terminal, and a lack at the other.

As soon as the battery terminals are connected with a conductor, a current results as the electric charge imbalance attempts to reach balance. However, pretty soon all that imbalance that was developed as the battery sat on the shelf has been used, and the chemical reaction must continue to create more imbalance to continue driving the current from the battery. If the battery is nearly dead, this reaction can't happen very fast, as nearly all of the reactants in the battery have already reacted.

So, the battery on the shelf isn't "recharging", because it's not gaining any more energy. You are simply giving the chemicals inside the battery more time to react, converting more of the chemical energy that was already there into electrical energy.

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In a battery (rechargeable or not) ions must migrate to the two poles to exchange electrons with the poles, which makes the electric current flow between the poles (= the battery delivers power).

This ion migration does not happen instantly: ions can take some time to migrate to their respective poles an do their work. When the region around a pole is depleted of ions the battery will appear empty, but after a while the ions will spread out again, there will be ions near the pole, and the battery will appear charged again.

A similar effect can be caused by the remains of the charged ions: once discharged they can block the intended process near the poles. They take time do diffuse away from the poles.

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A battery may be loosely modeled as a bunch of capacitors interconnected by resistors of various values. For simplicity, assume two capacitors--#1 is attached directly to the load, and #2 is connected to #1 via high-value resistor.

When the load isn't drawing any current, a small amount of current will flow from whichever cap has the higher voltage into the one which has the lower voltage. This will cause the two caps to approach an equilibrium where there voltages are equal.

When the load does draw current, however, charge may flow from #1 to the load faster than it can flow from #2 to #1. If this happens, the voltage on #1 will fall below that of #2. The greater the difference in voltage, the more current will flow from #2 to #1, but the voltage on #1 may fall below the minimum operating voltage of the phone even while the voltage on #2 is substantially higher. Once the phone shuts down and stops drawing power, the flow out of #1 will no longer be faster than the flow into it from #2, and consequently it will start to be recharged from #2 until the batteries again reach equilibrium.

Note that in practice batteries are a lot more complicated to model than capacitors; among other things, the resistances that connect the various capacitances are not fixed but vary as the battery is charged and discharged. Nonetheless, the interconnected-capacitors model provides a simple intuitive picture of what's going on.

PS--Both batteries and caps may be thought of as containing some charge-storing material and some material to connect it together. The more interconnecting material a battery or capacitor contains, the lower the effective resistances that connect everything together. The interconnecting material doesn't hold any useful amount of charge, however, so low-ESR batteries and caps have to be physically larger than higher-ESR batteries and caps with the same capacity.

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