Let's use an electron and a 1V potential difference as a mode.
In school I learned that if the electron is at the negative end of the electric field, its potential energy is equal to the work that could be done on it by the electric field (analogous to standing on a building and having gravity-mediated potential energy). In this case the P.E. is 1 eV. Once the electron is moved across the 1V, that potential energy is converted into kinetic energy (just like the P.E. on top of the building being converted entirely to K.E. at the ground) and now the electron has K.E. of 1 eV. However, I just learned that accelerating charges emit EM radiation. If all the P.E. is converted into K.E., where does the energy for the radiation come from?