Electronic – recharging zinc-carbon batteries? (if an “AA R6P” is a zinc-carbon anyway)

1. What they said

2. Single chip custom IC based.
   Various manufacturers make single IC LiIon / Lipo chargers that need no external transistors to function. One sich is Maxim's MAX8=8934A / 8934E. This is not necessarily the best solution available, but is very flexible and very competent. It allows USB or mains (via power pack) input, charge and discharge control, low power inbuilt LDO 3V3 regulator and much more. Cost is about $US5.20 /1 from Digikey in stock. This is about 4 x the complete parts cost of my "simplest possible" solution below - but it is far more capable. It's in a beginner unfriendly 28 pin TQFN package.
   Datasheet
   Pricing
   A typical circuit diagram is provided at the end of this post.
   Block diagram only:

3. Simplest possible (almost) that will work well enough is a supply that is current limited to 930 mA and voltage limited to 4.0 to 4.1 V. I say 930 mA based on a 1C max charge rate. If you are SURE that the manufacturer says you can charge this at > 1C then consider doing so BUT as a general rule, 1C is a safe max rate for LiIon of various flavours. SOME LiPoly allow you much faster rates, but there is no guarantee without specific data.

The constant current supply works when the cell is below 4.0V and the constant voltage take over thereafter.

If you are happy to operate it from a 9V supply then 2 x LM317 would do.

2 x LM317 , 3 x resistors, a few caps. See below.

LM317 pricing Digikey from $US0.64/1 in stock.
LM317 datasheet

1st LM317 = constant current 900 mA.
Vin to In
Vout from Adj
R from Adj to Vout = Vref/Ilim = 1.25/0.9 = 1.4 ohms. You may need to combine some standard R values to get this.

2ns LM317 = constant voltage at say 4.0V.
Rlow = say 1k Rhigh = (4.0-1.25)/1.25 x 1k = 2k2.
Scale resistors in that ratio as desired to suit data sheet requirements

LM317 constant current:

LM317 constant voltage

(3) My answer here gives some good related background re what capacity you can expect for what end voltage etc. DO NOT use 4.2V. No need. shortens life risks going too far.

This shows capacity achieved with Voltage and time

Be aware of LM317 dropout voltage = necessary drop across IC to operate it. Shown below. The constant current will drop dropout + Vrsense = say 2.3 + 1.25 = 3.55V.
The constant V will drop Vout + dropout = 4.0 + 2.3 = 6.3V.
So notionally you will need 3.55 + 6.3 = 9.85V = 10V.
In practive you can probably use slightly less, but not much.

MAX8934x typical circuit diagram.

I chose to go ahead and give it a try.

Result: The battery got hot to the point that I could not keep it in my hand for more than a few seconds, but not so much to melt the case.

Voltage dropped to 0.1 in about ten minutes, and that was the point where the temperature was at its highest.

The wires did not get as warm as I expected, probably because their resistance is negligible compared with the internal battery one.

Unfortunately I did not have a digital thermometer, so all of this test was very rough. A graph comparing temperature raise and voltage drop over time would have been cool. After dropping below 0.1V, voltage kept dropping, while temperature dropped as well - battery got less warm.

So to answer my own question: it was safe, at least in my case.

The author of the book, for what matter alkaline batteries, recommends wearing protective glasses (and I would add, gloves) just in case the battery is defective, so I advise to do the same in case you want to reproduce this.

If you do, and have more accurate measurement instruments (and patience) than I had, it would be interesting to see the behavior pictured (and compared with a test with an alkaline cell.)

By the way, in the minutes I took to write this the battery is still providing current into the short circuit. It is at 45mV right now.