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Does anyone know how to build a circuit which would sense that a motor is turned on by "sensing" the inductance on the power line going into the motor ?

I want to use my arduino to monitor and collect the activity on this particular household circuit. So a simple hi/lo 0-5 volts is all I need as output from the circuit.

The normal way is to use a current clamp on one of the conductors. (Wikipedia current clamp.) That would give you an AC signal that you can amplify, rectify and feed to your Arduino.

An easier way might be to wrap a few turns of the one conductor around a reed switch (yeah, wikipedia that, too) and that might get enough of a magnetic field to close the switch. Depends on how much current and how many turns you wind.

Hope that helps,

-Vince

The simplest way would be to use an optoisolator across the power feed to the motor. If it's an AC motor, limit the current to a fwew milliamps with a resistor, rectify the voltage with a diode, filter it with a small capacitor and feed that to the optoisolator. The other side of the optoisolator will be a nice switch closure which will nicely go into an aurduino input. Be sure to put like a 10K resistor to bleed off the open-circuit voltage.