Why transformers don't work on DC supply?

Before we get into topic, we have to know about some basic concept related to Transformers.

    As you know that the transformer work on Faraday's law of electromagnetic induction that's why we will discuss about flux linkages and EMF first.

"Faraday's law states that, whenever there is relative space or time variation between magnetic field and set of conductors and EMF will be induced in the conductors."

     By this definition we know that the generation of EMF is possible only if there is space time variation between magnetic field and set of conductors, as we know that this principle applies in motors and Transformers. In dc generators the EMF induced in set of of conductors due to relative space variation with respect to steady magnetic field is called dynamically induced EMF. And for Transformers the EMF induced in the set of stationary conductors due to relative time variation with respect to magnetic field called statically induced EMF.

EMF in Transformer = -N(dΦ/dt) and

Inductance= -N(dΦ/di)

As we know that in DC supply there is no alternating or changing flux. That's why there is ideally zero EMF and inductance in transformer coil under DC supply, because of there is no change in flux and change in current.

As there is no EMF and alternating flux, therefore no flux linkages to secondary coil. (So not useful as power transfer device under DC supply.)

Because of low impedance value in primary coil which causes to maximum current flow in primary winding. As the current in primary winding is maximum so flux in primary winding is also maximum.

This large amount of current in winding and flux in core, which result into heating and saturation of core. Under DC supply Transformer maybe get damaged by over-heating. That's why Transformers should not operate on DC supply.