210520-1310 EDT
Consider a 1 to 1 isolation transformer, with two identical windings. Suppose the input rating is 120 V 10 A, and the transformer is used and rated as an isolation transformer.. Assuming an ideal transformer the output is also 120 V 10 A.
Now connect this transformer as a step up autotransformer. The output is now 240 V and you know that the upper half of the transformer can handle 10 A. Thus, output power is double or 240*10 instead of 120*10. No change in the transformer size, weight, or power loss.
Then the question is about the lower half of the transformer. Will that winding overheat? In other words what is the current in the lower winding. Note the current going into the lower half of the winding via the center tap is double the current coming out of the top winding.
The current in the lower winding is the same as the current in the upper winding. Thus, no increase in the power dissipation in the lower winding compared to use as an isolation transformer.
This means that using the transformer as an autotransformer doubled its power output capability compared to use as an isolation transformer. If I do not need isolation then a less costly device can do the job.
Had the transformer been wound as an isolation transformer, physical size and primary the same, and to produce 240 V from the secondary, then its secondary current capability would have been cut in half.
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