Of course the second one will work why refer to ground at all ? it's just +ve / -veNo I dont think so, you should look at this:
Rectifier circuits : DIODES AND RECTIFIERS
The middle of a center tap transformer is always ground. You can rectify each of the other two leads with just a diode as illustrated in my link and this will give you a full wave. Your second picture will not work because there is no ground. Perhaps you do not understand how a center tap transformer works and should look it up.
I have a 24V transformer and two 12V transformers. I need some 24V current and as much 12V current as possible.Yes it will work though I'm not sure why you would want to.
If you have separate transformers, why are you showing a schematic with just one transformer?I have a 24V transformer and two 12V transformers. I need some 24V current and as much 12V current as possible.
I need a common ground. If I connect the grounds, is it still going to work? I'm a bit paranoid, because a cap just blew up in my face the day before yesterday, though I don't think the circuit was exactly like this.
Jeez! I'm really rusty, to have missed that!The two bridge rectifiers on the 24 V transformer combine to give you 24 V on the 12V line.