Methods and apparatus for simulating resistive loads, and facilitating series, parallel, and/or series-parallel connections of multiple loads to draw operating power. Current-to-voltage characteristics of loads are altered in a predetermined manner so as to facilitate a predictable and/or desirable behavior of multiple loads drawing power from a power source. Exemplary loads include LED-based light sources and LED-based lighting units. Altered current-to-voltage characteristics may cause a load to appear as a substantially linear or resistive element to the power source, at least over some operating range. In connections of multiple such loads, the voltage across each load is relatively more predictable. In one example, a series connection of multiple loads with altered current-to-voltage characteristics may be operated from a line voltage without requiring a transformer.