Okay let's start with the changing magnetic field. We know that in the region of time varying magnetic field , electric field is induced and ( they have some energy released by the source and it depends on the process involved in bringing the change) and when a coil is placed in this region then the electrons experience a net force as shown in the figure.
Since the force is acting tangentially, the induced electric field does a net work on those charges and hence the energy of the electric field is transferred to those electrons . Since there is an attractive force between the atoms of the coil and the moving electrons ( i.e. resistance of coil ) , energy is released out by the electrons in the form of heat.