The necessity for experimental verification of leakage currents using Sm-doped ceria electrolytes (SDC) in solid-oxide fuel cells (SOFCs) has been indicated. This paper describes the theoretical limitations of Wagner's equation and details the analytical work that has been performed to support the experimental results. These limitations cannot be solved, even considering polarization voltage losses. Globally, there are several research groups working on SOFCs to solve the current-voltage relation with mixed ionic electronic solid conductors (MIECs). However, this problem must be solved considering the electric field (E) in MIECs. Thus, even though articles have already been published in similar areas, no approach has been taken within this body of work that considers the E in MIECs. In this report, a new calculation method considering E is expressed only from Wagner's equation, with continuity expressed using the Choudhury and Patterson style. The calculated results match the values from conventional models. The constant field approximation is verified using the conventional definition of E. However, the definition of E should be changed when there is a large voltage drop in the thin area of the electrolyte compared with the lattice constant. In this study, the electric field near the cathode is sufficiently large to cause dielectric breakdown, which has never been reported.