An inductively powered lamp unit (500) that uses an inductive power pick up comprising a resonant circuit including an inductance (401) and capacitance (402), the induced current circulating in the resonant circuit is limited to a maximum value by a shorting switch (503) that closes a connection across the inductance (401) shorting the resonant circuit. The shorting switch (503) is controlled by a comparator (506) that compares the sensed current with a reference value (510). Voltage control maybe similarly implemented. Power is supplied to LED's (405), control data may also be conveyed through the inductive link. Applications include roadway markers, fire escape indicators, underwater or explosive environmental lighting.