The circuit was to charge a 1.2V NiCd battery which was in a beard trimmer. Below is a drawing of what I could make out from the toasted circuit board.



A wall adapter supplying 3V & 150mA to charge the circuit. The path went through a 5819 diode and a, now unknown, 1/8W resistor.
Can anyone figure out what the resistor value was given the battery capacity was 800mA. And if so what would the resistor be for a 2000mA
NiMH battery in it's place?

The circuit must have disconnected the charger portion via a DPDT switch as this was also part of the circuit.

 

The 1N5819 is a 1 amp diode that uses up .3 to .4 volts at 800 ma depending on its temperature.
A single Ni-cad is 93% discharged at 1.13 volts
so 3V - 0.4V - 1.13V = 1.47V
Working from PR=E^2
and assuming the resistor is derated by 50%
Minimum R = 34.57 ohms and that's 42.5 ma at the start of charging, which is pretty slow for a AA Ni-cad.

That's the math.

If you want to build this so the resistor doesn't smoke when the battery is shorted, change the voltage to 3 volts and change the wattage of the resistor if you want to.

There is no point in figuring out the resistor for 2000 ma when the wall wart is rated for 150 ma.

 

Take #12 advice with one exception:
For 2000 mAH cell the charger is the same, it just takes longer time to fully charge.

 

Take #12 advice with one exception:
For 2000 mAH cell the charger is the same, it just takes longer time to fully charge.

It's obvious that I read that wrong. Oops.
But the problem as I see it is that the original design is such a low current rate that changing the battery from 800 maH to 2000 maH just makes the charging time longer. I gave the math because I would change the design to limit the current to 150 ma into a short and not smoke, then figure out what the charge rate will be, based on the resistor required to make the charger idiot proof.

If I can read a calculator correctly, that's 20 ohms @ 1W and about 74 ma at start of charge into an empty battery (which is not damaged).

 

My guess is that the resistor was 2.2 ohm (or lower) ,0.125W. At 150mA the resistor will get hot but survive.
We don't know what the 3V really is under load because it is not loaded with the resistor being burnt (oc). My guess is that the 3V is 2V under load. The internal resistance of the charger determent the current. The purpose of the burnt resistor is not to set the charge current, it is used as a very slow fuse to protect the charger from over heating when the cell is sc. It is a common design practice. Most NiCad go sc after 3 years and you don't mind the burnt resistor when you buy a new trimmer.
My advice to iONic is to stand to the feminists, throw away the trimmer and let his beard grow wild.