I was given an electric drill that uses 12V lithium ion batteries
because the charger didn't work and the batteries died and the owner
lost interest. I hack sawed the transformer case open and found that the
primary winding was open somewhere that I couldn't see, so I didn't try
to repair it.

Also the charge adapter that the battery slides into has a burnt out
resistor on the circuit board. It's a very simple circuit board, there
are 4 diodes on the input side which I assume is a full wave bridge
rectifier. After the rectifier there is a small series resistor (R1)
powering an LED across the dc power lines coming out of the rectifier,
and a larger resistor (R2) which got hot enough to char the circuit
board near it as it was blowing up. I'm guessing it was over-voltaged,
or maybe more likely the outputs were shorted together. The V+ output
voltage passes through R2.

I don't have a schematic, and would like to repair the ct. board if I
can choose a replacement resistor that doesn't unsafely charge the
batteries. If I get a transformer with the same V and I ratings (14.5V
200mA) I'm wondering what value Resistor to replace R2 with.

I am including a picture.
http://tinypic.com/m/k2ck8j/3

I read this, "Most consumer orientated lithium ion batteries charge to a
voltage of 4.2 volts per cell and this has a tolerance of around ± 50 mV
per cell. Charging beyond this causes stress to the cell and results in
oxidation that reduces service life and capacity. It can also cause
safety issues as well."
https://www.electronics-notes.com/ar...n-charging.php

Since the batteries are labeled "12V", if it uses the same LiIon
technology the article is referring to, I assume it has 3 cells totaling
12.6V. The transformer was clearly labeled 14.5V 200mA.

Also from the web page, "Charging lithium ion batteries can be split
into two main stages: Constant current charge: In the first stage of
charging a li-ion battery or cell, the charge current is controlled..."

It seems like it might be a simple matter of trial and error, power the
charge adapter attached to the battery, and find a value of R2 that
leaves 12.6V on the output side, when the battery is fully charged. The
adapter has no current regulation, other than the series R2. Is that a
safe approach?

Would a 12V car trickle charger work safely, with a maximum charging
current of 2A (based on the web page)? The transformer had a much lower
current rating.

I'm surprised the charge circuit is so simple after reading this web page!

TIA, Mike