I have read that putting 2 transformers in parallel or in series will increase the output power, how does this work?

I have questions about transformers placed in series and parallel and how they are able to amplify voltage for series and current for parallel without decreasing current/voltage as the case for a step up or step down transformers. From my understanding, the power has to be constant when switching between voltage and current. I know if batteries are placed in series, the voltage adds up, and if the batteries are in parallel, the Ah capacity adds up. Is there an analogy between series and parallel transformers that is related to this? Say if I have a 12VAC going at 2A from an inverter or an AC source and that goes to two transformers in series. I set the diagram as shown below. If I used a multimeter to measure the potential difference between the two open circles at the right side of the picture, apparently I would get 24VAC at 2A. I also know the Tesla coil uses voltage amplification using this method. I am working with low voltages (120VAC Max)so I would assume that the coils wouldn’t overheat or short circuit. Wouldn't the conservation of energy be violated if that was the case? Do the two transformers have to be exactly identical and how would voltage be amplified without decreasing current from the picture? • Don’t forget that there’s double the input current, so there’s no magic happening. Dec 9 '21 at 4:04

Two identical transformers may be interconnected to operate at rated voltage or double the rated voltage and deliver double the rated power at either double the rated voltage or double the rated current.

The primary windings of two identical transformers may be connected in series, should the supply voltage be double the rated voltage. The secondary windings may be connected in series to deliver the rated current at double the rated voltage. They may be connected in parallel to deliver double the rated current at the rated voltage. If you have a 12V 2A transformer, it can deliver 24W. Ignoring losses, it will draw 24W from the supply.

Wire two transformers in series and you get 48V 2A. In parallel you get 12V 4A. Either way, that's now 48W total. If wiring two transformers in parallel, make sure that they are the same way round or something will go bang.

Conservation of energy is fine, simply because you're connecting two transformers to the supply. If each draws 24W, then the pair draws 48W total.

If I used a multimeter to measure the potential difference between the two open circles at the right side of the picture, apparently I would get 24VAC at 2A.

No — power in equals power out. Assuming the turns ratio for each transformer is 1:1, you would get 24VAC on the right side, but the current on the right side will be half as much as the current on the left.

The two transformers have their secondaries wired in series, so each transformer's secondary current equals the output current. They're 1:1 transformers, so each transformer's primary current equals the secondary current. The primaries are wired in parallel, so the current flowing into the two transformers taken together is twice the output current.

Look at the way the turns add up. All this is is a different way of constructing a 1:2 transformer.