A reactor for carrying out a chemical reaction using multiphase alternating current, includes a reactor chamber surrounded by thermally insulating reactor walls and multiple substantially straight reaction tubes. The reaction tubes run between at least one tube inlet opening and at least one tube outlet opening in opposite reactor walls and consist of a material that permits electrical resistance heating. Two electrically conductive bridges spaced apart along the reaction tubes are provided, each of which electrically conductively connects the reaction tubes to one another. Electrically conductive power input arrangements are provided extending through one or more input openings in one of the reactor walls. Each reaction tube is electrically conductively connected to one of the power input arrangements. Each power input arrangement is electrically conductively connected between the bridges to one of the reaction tubes and is connected or connectable to one of the phases of the alternating current.