A dimmable electronic ballast for an electrodeless discharge lamp comprises an inverter circuit, a resonance circuit, an induction coil and a start circuit. The start circuit has a variable time constant. The start circuit sweeps a drive frequency of the inverter circuit through a time constant for start or restart so that the voltage applied across the coil is raised from voltage lower than start voltage and restart voltage for starting and restarting the lamp to voltage higher than the start voltage and the restart voltage. The time constant for start during a start period for starting the lamp is larger than the time constant for restart during a restart period for restarting the lamp.