Can an LED run by harvesting energy from mains hum?
Curiosity got the better of me, so I had a look at how much power you can capture from power line hum.

I built the following circuit:







simulate this circuit &ndash; Schematic created using CircuitLab

I get about 16 millivolts RMS across the capacitor.  Since a 10nF capacitor has about 318 kiloohms of impedance, it's pretty easy to calculate the received power and the current.

$$P=EI$$
$$E=IR$$
$$I=\frac{E}{R}$$
$$P=\frac{E^2}{R}$$

In this case, we can use the impedance of the capacitor as R.

$$I=\frac{16mV}{318000}= 0.056 microamperes$$

$$P=\frac{16mV^2}{318000}=0.0008 microwatts$$

That's not much.

If I cheat, and do this:







simulate this circuit

Where the ground symbol means "connected to household ground from an outlet," I get 41mV RMS.

That's still only 0.13 microamperes and 0.005 microwatts.

There are LEDs that light visibly using 0.1 milliamperes of current.  That's 100 microamperes.  That's  1700 times the current I figured for no ground connection, and the LED will need a couple of volts besides.

You could consider a tuned inductor and capacitor circuit, but then you'd need some pretty big parts.  I figured it up, and you'd need a 3180 microhenry inductor and a 3180 microfarad capacitor at 50Hz.  Both are physically large parts, and making one smaller (in value, which also means smaller physically) makes the other larger (both in value and physically.)

Conclusion:

You can't "harvest" enough power in a typical home to light an LED from just the power line hum.

I think it's a safe bet that the LED "throwie" you found is just running from its battery.



I found a 3mH inductor that is 8mmX7mmX5mm, and a 3000µF capacitor that is 18mm in diameter, and 22mm high.  Those are the smallest ones I ran into on a quick check at digikey.