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Let's try another approach.

Visualize a transformer with the primary connected to a 120 volt DC, current-limited power supply through a switch, and with the secondary left open-circuit. The current limit on the power supply is set for one ampere to keep from blowing things up.

At time t = 0 the switch is closed. What is the time response of the current in the primary?

It will not rise immediately to one ampere, but will do so after the core is saturated.

The core switches its magnetization to provide the back-emf that prevents short-circuit current from flowing. The product of 120 volts and the time it takes to saturate the core should be greater than the integral under the half-wave sine curve if the transformer is to work properly at the sine wave frequency, whatever it is (25 Hz, 50 Hz, 60 Hz, 400 Hz).

I've greatly oversimplified here to get the basic point across. Transformers are designed to avoid core saturation for maximum expected primary voltage at some particular frequency. The lower the frequency, the more magnetic flux the core must contain without saturating. This is why the transformers in switching power supplies are so small.

This is only the beginning of the design. The maximum current determines the size of the wire, which determines the size of the coils, and on and on. It may be cheaper to just design the thing for 50 Hz and sell it into both the 50 Hz and 60 Hz markets (so-called "World" transformers as carried by Mouser, etc.), so a device that uses one of these would be perfectly safe to use in either area. However, this is not guaranteed.


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