Methods and apparatus for providing power to devices via an A.C. power source, and for facilitating the use of LED-based light sources on A.C. power circuits that provide signals other than standard line voltages. In one example, LED-based light sources may be coupled to A.C. power circuits that are controlled by conventional dimmers (i.e, “A.C. dimmer circuits”). Hence, LED-based light sources may be conveniently substituted for other light sources (e.g., incandescent lights) in lighting environments employing conventional A.C. dimming devices and/or other control signals present on the A.C. power circuit. In yet other aspects, one or more parameters relating to the light generated by LED-based light sources (e.g., intensity, color, color temperature, temporal characteristics, etc.) may be conveniently controlled via operation of a conventional A.C. dimmer and/or other signals present on the A.C. power circuit.