For electric-vehicle and hybrid-vehicle applications, it is expedient to determine what factors are likely to limit battery performance and determine cell designs that optimize operation for a particular application. This paper provides a derivation of the governing equations and an analytic solution useful for thin-film battery design. Specifically differential equations consistent with a two-dimensional representation of a thin-film battery are developed based on the underlying physical chemistry. A perturbation approach is used to derive a simpler set of governing equations, and associated analytic solutions for cell energy, power, and thermal characteristics are constructed. The analytic solution of this work assumes a secondary current distribution and linear kinetics for the porous electrodes; the associated system of model equations is thus linear. These assumptions should be valid for short times after the start of charging or discharging from a quiescent state.