This　paper　is　concerned　with　the　convergence　of　the　time-dependent　and　nonisentropic　Euler-Maxwell　equations　to　compressible　Euler-Poisson　equations　in　a　torus　via　the　nonrelativistic　limit.　By　using　the　method　of　formal　asymptotic　expansions,　we　analyze　the　nonrelativistic　limit　for　periodic　problems　with　the　prepared　initial　data.　It　is　shown　that　the　small　parameter　problem　has　unique　solutions　existing　in　the　finite　time　interval　where　the　corresponding　limit　problems　have　smooth　solutions.　Furthermore,　the　convergence　of　solutions　is　rigorously　justified.