Magnetic reconnection is one of the most efficient ways of transforming magnetic into kinetic and thermal energies. We prove a general identity relating the energy transfer in a neighborhood of a current sheet, where reconnection is assumed to occur. With some reasonable hypotheses regarding the geometry of stream and field lines, we prove that for a constant rate of transformation of magnetic energy, the width of the current sheet must grow with the plasma conductivity. Hence an enhanced diffusivity seems necessary for certain classical models of fast reconnection to work.