soda,

What is the VA of the transformer you running there ?

 

I'd guess at least 24*4 = 96VA

 

It is a multitap transformer and this tapping is 96va. The white led is for a back light on a panel meter, the red one is for a extra diagram i add to clear the memory on a ni-cad battery and the blue is for the mains indicator

SODA

 

If I get a 2 x 12VAC - 12VA rated transformer (0.5Amp output per winding), Is it possbile to put the secondary windings in series to get 24VAC giving me 1Amp output ?

 

No not quite, you could if it was 24VA.

If you were drawing 1 ampere from the 24V - 12VA transformer you are drawing 24W of power. But the transformer can only handle 12W (12VA)

Center taps are usually used when you want multiple outputs. With a 2x 12V transformer you can rectify and get -12V and +12V and a virtual ground (COMON) at 0 voltage. But you can only draw 0.5A at each output. Let's say you were drawing 0.5A from both the -12 and the +12. That'd mean that total current trough the transformer was 0.5+0.5 = 1A.
Which is just what the transformer can handle. (0.5A*12V + (-12V*-0.5A)) = 12W = 12VA.

If you connected the windings in series you'd have 24V across it. If you drew 1A you'd be drawing power (24V*1A) = 24W = 24VA. Which exceeds the transformers capabilities. So if you connect them in series you can only draw 0.5A.

The transformer can only handle so much power per turn of winding. Let's say it had 24 turns on the secondary(most likely ALOT more). And was rated 12VA. That would mean each turn of winding could handle 0.5V per 1 Ampere current.
A center tapped transformer has the secondary windings divided in two. That mean each winding has 12 turns. So each winding can handle 12*(0.5V per ampere)= 6VA. That is you can draw 12V/6VA = 0.5A from each winding at maximum.
Let's say you now series connect the windings. That means you are now applying 24V across 24 turns of wire. Each turn can only handle 0.5V per ampere. You have 24*(0.5V per ampere) = 12Va. So now you can still only draw 24V/12VA = 0.5A total.
So you see according to calculations. Series connecting them doesnt change the amount of current the transformer can handle because the voltage per turn of wire stays the same. And thus you can't draw any more current without exceeding the transformer's specifications