The simplest battery charger
One has to be very brave to make and sell things like that the simplest battery charger ever. Actually these are probably not sold any more as have too many disadvantages. But despite of it, I find this design very charming in its simplicity.
This is how they did it:
The capacitor is used to limit current to few milliamps. The bridge rectifier (Gretz) transforms AC to DC current. And that is about it you connect your battery to the output terminal and the charger will start charging at some fixed current.
As I said, this simple battery charger circuit has many disadvantages. Two of them are particularly nasty.
First, there is no galvanic separation to the power grid meaning that it can really strike you if you dare to touch output terminals. Even few milliamps that are allowed by the capacitor are enough to give you something to remember. It is clear that output terminals must not be easy reachable by fingers. True, you could use a transformer to feature the galvanic separation but then all of the simplicity would be lost.
Second, there is nothing that would stop the charging process. If you dont take the battery out on time, the charger will overcharge it and may also damage it. Due to the high input voltage (the power grid voltage) compared to the battery voltage, the charger will keep pushing current invariably on the battery voltage (actually you may as well charge several batteries at once if you connected them serially). True, you could use some timer that will automatically disconnect the battery, and this is sometimes done, but it also affects the simplicity.