What happens electricity being produced by the alternator if the car battery is fully charged ?
Go waste? Where does it disappear to?
It doesn’t get produced. The alternator’s output is based on demand. It will produce only the amount of electricity that the system call for, up to the limits of the alternator. So, if you have a 120A alternator, but your car’s system, battery, modules, lights, radio, etc. is only asking for 40A, the alternator will only produce 40A to match the load. If the system needs 130A, however, the alternator will produce 120A and the remaining 10A will be pulled from the battery, causing a discharge. The voltage will drop when this happens, because the battery will only discharge if the voltage drops to less than it’s static state, which is around 12.5V for a healthy battery.
The alternator converts rotational energy from the drive belt to electricity. As the electrical demand goes up, the alternator puts an increased load on the belt, and therefore the engine, to make that juice. At 120A max load, the stress on the belt is high, but at 40A, it’s not so much.
To add to what BustedKnuckles said, if your battery is fully charged, and there isn’t much electrical demand, the voltage regulator, which in all modern cars is a function of the PCM, or car’s “computer”, decreases the voltage applied to the alternator’s field windings. When this happens, the magnetic field that the rotor is spinning against decreases, and instead of power being generated, you just have a belt driving a spinning piece of metal which isn’t acting on anything. In a sense it’s like coasting down a hill with your engine still spinning, but no fuel is being fed to it so it’s not making any power.
does my mechanical voltage regulator work the same way? I can get either mechanical or electronic volt. reg. for my truck.
I have the mechanical one put away in case of EMP… 
Yep, no ‘extra electricity’. Otherwise you’d find something like a toaster glowing under the hood…
In the 50s a lot of cars had adjustable voltage regulators, you just took off the cover and turned a screw. Generators wouldn’t put out much charge at idle. If you did a lot of driving in the dark or at slow speeds you turned it up. If you had to add water frequently to your battery, you turmed it down.
interesting…
The mechanical voltage regulators of the 50’s (and early 60’s) were relatively simple, on/off devices. They energized or de-energized the generator’s (and the early alternator’s, too) field windings, turning the output on or off.
When the battery was fully charged the contacts connected and disconnected, just keeping the battery topped off, then turning the generator / alternator off, then back on when the battery voltage dropped a little.
When did the VR move into the ECM? I’ve worked on (early) 21st century cars, and they were still in/bolted to the alternator.
AS a bit of trivia to OP and others, this works because the magnets are electromagnets, and thus adjustable in strength. Motorcycles (well, the older ones I’ve worked on) used permanent magnet alternators and therefore were “Full on” all the time–the VR acted to dump the “excess” charge to ground. Heck, “bottle generators” on bicycles are PMAs, and they would blow out the headlights at high speeds–the “voltage regulator” principle employed there is to limit the total mass of ferrous metal in the alt, which somehow (I’m not an EE) “saturates” at a certain output.
Those familiar with older British bikes may be familiar with their voltage regulators which were nothing more than a large Zener diode mounted on a finned heat sink attached to the front forks.
Excess voltage would bleed off through the diode and prevent overcharging. What could happen (and I’ve seen it happen) is that the Zener would sometimes fail and allow unregulated voltage to go through the lighting.
The lighting was welder bright; for a limited number of seconds. After that the bulbs would all pop and Lucas induced darkness would set in… 
@meanjoe75fan, Dodge/Chrysler as been doing this since the 90’s. I had a neighbor with a early 90’s Caravan that quit charging and it appeared the ECM ciruit for the VR died. I managed to retrofit an electronic regulator to by-pass the ECM VR and get it back on the road.
Newer cars I’ve seen still have a regulator in/on the alternator, but there is a line from the ECM that can change the regulators set point.
The ECM can also see how hard the alternator is working (field voltage).