How can I use an Arduino to detect a burned out light bulb? Is there a simple circuit that can detect this?
If you want to detect the lack of current, that will depend on the voltage. If it's household AC voltage, you'll need isolation.
I would like to detect lack of current for 120V
Hall effect current sensor, works on AC or DC. Has complete isolation from the AC side to the DC measurement side. Outputs a DC measurement voltage that one could read with an arduino analog input pin. This one reads +/- 0 to 5 amps, but there are higher current models available.