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Electrical Engineering/Transformer

Question
Sir, how do you calculate the maximum size wire guage of a transformer. Supposed, you wanna built a transformer  whose primary current and voltage are 220V  and secondary current and voltage are 12.5V and 3.5A. What is the size wire guage for both primary and secondary? You can assumed the primary current if is needed. Sir, all i just wanna know is,how to calculate "size wire guage'' for any transformer!

It is not such a simple matter. There are many, many variables to consider in the design.

The size of the wire and the length of it determines the I**2R losses. Large size wire and a short number of turns means the losses will be low but the transformer will be large and heavy.

Decreasing the size of the wire can allow more wire to be placed on a given bobbin, for example, and the inductive coupling will be very tight but the losses will be high and the regulation will be low.  (Regulation has to do with the drop in output voltage as the load current increases.)

Also, the type of housing for the transformer is important.  Mostly EI shaped laminations are used with power transformers being used at 50 or 60 Hz, but there are many power applications at different frequencies.

Mostly, the design is accomplished by experimentation, given the specifications and the application intended.

For the hobbyist and the DIY enthusiast it is almost always a better choice to purchase a transformer that is manufactured by a reputable firm.  Only in unique applications would I suggest you make your own.  Whenever connecting to the mains of your power source you must think of safety, fire and other calamities when the transformer is not designed to withstand the temperature, humidity, emf kickback voltages, etc. that may come upon it during its service.

Efficiency and regulation are usually important specifications for a transformer as well.  These will alter the design accordingly and dictate the number of turns, size of wire, kinds of laminations to be employed, form factor and heat loss, etc.

The design you mentioned in your question, an output of 12.5v at 3.5a or 44w can be a fair amount of heat production in the transformer is the losses are great.

This youtube may be of help to you:

All the best.  Cheers.

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