Here is a basic description of the circuit. The fist part of the circuit is the transformer. One side(the primary) is hooked up to the wall plug. The transformer takes the 120V AC from the outlet and steps it down to about 12.6V. Both the input and the output from the transformer will look like the wave shown in fig1, with the difference being that the input will have a magnitude of 120 volts, while the output will have a magnitude of 12.6 volts. The next stage of the circuit is the rectifier, which internally consists of an arrangement of 4 diodes. The the output of the rectifier is the absolute value of the input, and looks like fig B. The purpose of the rectifier is to convert the AC from the transformer to DC. As you can see in fig B, the rectifier output is a series of pulses, which need to be smoothed out into a continous wave to be of use. This is the job of the capacitors. They act sort of like a tank for electricity. when the voltage is on, thye take in electricity. When the voltage drops, they provide power. Finally we end up with soemthign that looks like fig C., a steady relatively clean(ripple free) 12 volts. When plugged in, the circuit will power whatever is hooked up to is, as well as charging the battery(up to 12V). When it is unplugged, power will come from the battery. This circuit is one of the most basic types of power supplies and is a bigger version of what you would find if you cracked open a "wall wart"( the big annoying things that use more plug space than they should). This circuit has only 1 problem, an it is that it will only charge batteries up to 12V. A fully charged battery is normally about 13.8V. This van easily be fixed by replacing the 12.6 volt transformer with a 14-15volt transformer.