...actually was a challenge to find something suitable to help you. All booked up and still with no understanding of what is really simple: been there myself.
Check this LINK out. The entire page describes everything you will need to know. Especially in answering why DC applied to a coil heats up the wire and AC applied to a coil acts very differently. I tried to steer away from web sites that had too much theory and crap diagrams and did not answer your question directly.
You will need to understand words such as inductance, resistance, magnetism, current etc. to get a handle as to what is actually happening behind the scenes with a transformer. This whole page given in the link above describes these things and other internal links are worth a look. It would be impossible to answer your question concisely in one sentence and a link to another website was in my view needed.
Some people use analogies of water in a hose and I think the description is good for DC but not very applicable for AC in providing a clear understanding with regards to transformers/coils etc..
You must have learnt- a changing magnetic field intuces an electric field (or current). The DC do not have this changing magnetic field (at least when it is stabilised, you have a bit on the switch on) - hence no induced electric field and hence no transformer action.
In other way also this is explained - when a conductor cuts flux lines
Or A conductor (like the mechanical momentum) tries to retain its magnetic state- so when a magnetic field is applied on it it tries to resist it by passing a current which resists the applied field- but when it is a constant field, then (like a constant velocity in no-friction- so no force)
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