In this work we study the effect of internal relaxation in a (Bu4N)2Ru(dcbpyH)2(NCS)2 (N719) dye molecule in a dye sensitized solar cell. Experimentally measured light intensity dependencies of short circuit current and open circuit voltage for two different types of photoanodes, ZTO (Zn2SnO4) nanorods and nanoparticles, are explained in the framework of the proposed microscopic theory. This theory is based on a density matrix equation with a Markovian relaxation term. The computational results are in favor of the fast relaxation inside the unoccupied and occupied bands rather than slow interband electron-hole recombination. The difference in experimental dependencies for ZTO nanorods and nanoparticles is explained by the difference in the electron transfer matrix elements, and therefore, the electron transfer injection constants for the different morphologies of the photoanodes.