IPhone – the best replacement battery for iPhone 5s

There is a general tips page on maintaining great battery life, as well as general terms about battery replacement.

Personally: This sounds like a bad battery. It sounds like it just plainly is not holding a charge after a certain discharge point. Remember that iOS multitasking is not true multitasking. Barring streaming audio (actually persistent audio in general), there is (almost) NOTHING that your phone can constantly do for more than 20 minutes at a time.

I've streamed audio for hours (hours being... maybe 5?) during the day at ~40% and it did get under 20% by the time I was done, this was both on an iPad, and roughly equivalent on an iPhone 4. Connected WiFi, 3G (on the iPhone) enabled but not being the active radio in use, of course.

I don't know that you're able to see what's draining the battery, Apple forbids "task management apps". A possible workaround to see if it is app involved or a bad battery, is to drain your phone to a similar level, open the fast app switcher bar (double tap the home button), tap-hold on any application in the task bar until they begin to "jiggle", then press the white minus inside the red circle on EVERYTHING. This will kill any and all tasks that aren't first-party. (For example, it will not stop the occasional housekeeping/tasks that Mail, Phone, Safari, or other built-in apps are allowed to do.)

Having said that, to properly test, ensure that mail's auto-fetch is off (or in push only mode at best), make sure that you have no tabs in Safari with "live" or automatically refreshing content. Safari IS ALLOWED TO BACKGROUND, and has always been able to, to the best of my knowledge. At least since iOS 2.something (where I started with an iPhone 3G).

Final Conclusion Given the sources and explanations below. I am officially going to do the following to optimize my battery life:

1. Keep my battery as cool as possible.
2. Don't worry about whether it's plugged in or not. When it doubt, keep it plugged in so it uses AC power instead of battery, unless getting hot.

It turns out that the two methods I originally posited are largely moot. The only thing that really matters is temperature.

"Temperature was the most significant factor contributing to the cell degradation, with state-of-charge (SOC) and discharge pulse length of secondary importance." (Liaw et al.2)

Furthermore, it turns out that the decay can be accurately mathematically modeled:

(See Ramadass et al.1 for explanation of terms)

However, the dominant model is that of the Arrhenius formula, which generically predicts time-to-failure as a function of temperature.

The figure below shows the capacity at various cycle counts. Just look at the capacity on the x-axis. The top graph is at 25ºC, the bottom at 50ºC.

After 600 cycles, the cooler battery had ~2x the capacity

While I could still find no evidence on the behavior of Mac power circuitry, there was helpful information on the official Dell website. Two items specifically stood out.

Q. When docked or AC adapter is plugged into a wall outlet, am I using my battery charge?

A. No.

http://www.dell.com/content/topics/global.aspx/batteries_sitelet/en/batteries_faq?c=us&l=en&cs=19#faq9

Q. Should I totally discharge, then recharge my Dell laptop battery occasionally to make it last longer?

A. No, discharging and charging does not increase the life of a Lithium Ion technology battery.

http://www.dell.com/content/topics/global.aspx/batteries_sitelet/en/batteries_faq?c=us&l=en&cs=19#faq27

However It is important to note that Apple and Dell charging circuits may be different. Although, given that Dell does this, I assume apple does as well. On this assumption, unless someone can provide sources to claim otherwise, I will assume that the Apple charging circuitry is smart enough to know this.

I encourage anyone to continue exploring this question and challenge my assumptions. Please see the sources below if you're curious for a more detailed explanation.

Sources

1 Ramadass, P., Bala Haran, Ralph White, and Branko Popov. "Mathematical Modeling of the Capacity Fade of Li-ion Cells." Journal of Power Sources 123.2 (2003): 230-40. Web. http://www.che.sc.edu/faculty/popov/drbnp/WebSite/Publications_PDFs/Web33.pdf.

2 Liaw, B., R. Jungst, G. Nagasubramanian, H. Case, and D. Doughty. "Modeling Capacity Fade in Lithium-ion Cells." Journal of Power Sources 140.1 (2005): 157-61. Web. http://electrochem.org/dl/ma/204/pdfs/0253.PDF.

[3] Ning, G. "Capacity Fade Study of Lithium-ion Batteries Cycled at High Discharge Rates." Journal of Power Sources 117.1-2 (2003): 160-69. Web. http://www.che.sc.edu/faculty/popov/drbnp/website/Publications_PDFs/Web38.pdf.

[4] Ramadass, P., Bala Haran, Parthasarathy M. Gomadam, Ralph White, and Branko N. Popov. "Development of First Principles Capacity Fade Model for Li-Ion Cells." Journal of The Electrochemical Society 151.2 (2004): A196. Web. http://www.che.sc.edu/faculty/popov/Publications/Premanand1.pdf

[5] Zhang, D., B. S. Haran, A. Durairajan, R. W. White, Y. Podrazhansky, and B. N. Popov. "Studies on Capacity Fade of Lithium-ion Batteries." Journal of Power Sources 91 (2000): 122-29. Web. http://www.che.sc.edu/faculty/white/2000studiesoncapcaityfadeofzhangharandurairajanwhitepodrazhanshkypopov.pdf.