A lamp assembly adapted to operate as one of a total number of lamp assemblies that are connected together in series and connected to a ballast. The lamp assembly comprises an electrodeless, closed-loop, tubular lamp envelope enclosing mercury vapor and a buffer gas, and a transformer core disposed around a portion of the lamp envelope. An input winding is disposed on the transformer core so that it has a particular number of turns, Ninput. An auxiliary winding is disposed on the transformer core so that it has a particular number of turns, Nauxiliary. The auxiliary winding is adapted to connect to the ballast and to couple with the input winding. The ratio of the particular number of turns Ninput to the particular number of turns Nauxiliary is substantially proportional to the total number of lamp assemblies that are adapted to operate in series together.