Verified answer

First thing first. A transformer is an AC device. When wire is coiled up, it is an inductor. It is wrapping around the core. When frequency is applied to the inductor, it creates something called inductive reactance, XL. Which is an AC resistance. Though voltage is applied, current flowing, impedance also exists. That's why the transformer doesn't get short circuited.

Since DC has no frequency, that also means impedance doesn't exist. That's why transformer is not to be operated with DC.

The basic definition of an inductor is that it is a device that opposes a change in current. A transformer is an inductor, actually. So if the starting current is zero, then when you plug it in, it opposes a change of current, which is zero, so it has no current when you first plug it in. Ergo, no short circuit!

the transformer offers inductance

X (L) = wL

X (L) - voltage drop

w - omega = 2 pi f , f -frequency of input voltage

L - inductance offered in henrys

Inductance.