A transformer is not 'necessary'. The human race evolved, and developed
cultures, societies, disease resistance, and technology, without ever
seeing a transformer.
But there are specific situations in which desirable things can be accomplished
much more effectively and efficiently with a transformer than with any other
device or method. Here are a couple of examples:
-- If the voltage you have available is not the voltage you need, then you can
use a transformer to make the change. (But that only works for AC.)
-- You can use a transformer to change the output impedance of an amplifier
to the impedance of the speaker or earbuds you want to use with it.
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no transformer is not necessary for rectification today most of power supplies have been made without using transformer in order to reduce weight and size of power supply.for example SMPS(switch mode poqwer supply)
TO INCREASE END-OF-LIFE EXPECTANCY OF THE UNIT AND MAXIMIZE CAPACITY AND TO HANDLE OVERLOAD UP TO 40%.
If rating is correct, terminal connections are correct, if safety devices are in place, if device is a standard with necessary requrement, it should not be problem to connect a transformer first time.
A transformer has two coils coupled via the magnetic field, and when it has no load all you see is the inductance of the primary coil, which has to be fairly high to create the necessary amount of magnetic flux. When the transformer supplies a resistive load, the input looks much more resistive.
Center tap transformer is the such kind of transformer that is made to a point half way along a winding of a transformer.