I will put the obvious stuff first with wordy technical explanations after
First take a look at this
video (second one) The part of interest is that he has 10 LED lamps, but they do not take 10 times as much power as one lamp... in fact they only take about double...
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Yes you got that right, one 9 watt lamp took 9 watts, but 10 9 watt LED lamps only took about 20 watts. What gives? Ok, try this at home: plug a LED lamp into an outlet and turn it on. Plug a hand drill (angle grinder, whatever) into the same outlet and turn it on. The LED (and some CFLs) gets brighter. (this may not work with all of them especially the dim-ables)
OK, what is happening? To understand this we need to understand how LED lamps work. In days gone by when LEDs were used mostly for power on indicators, the standard circuit was a simple dropping resister in series with the LED to drop the voltage to what the LED would handle. Because the LED is a diode and has a drop voltage, it acts as it's own voltage regulator and the resistor acts as a current regulator. Cheap and easy and a great way to start a child learning about voltage dividers and current through easy calculations. But! very wasteful. The dropping resistor was the main power grab at between 10 to 100 times the power draw of the LED itself. LED lamps do not work this way. LED lamps have a capacitor to act as a battery for the LED, this capacitor is kept charged by short little spikes of power at full voltage. This kind of power supply has become cheap and is even used to charge your cell phone these days. We have known for some time how to detect the AC zero crossing and time from there and this is how most dimmers work, they shorten the AC wave so that the incandescent lamp will get less power. This does not work with a switching power supply that just grabs a pulse of power near the beginning of the AC cycle. So an LEDs power saving is determined time rather than constant draw. The drill motor that is making power spikes every time the brushes make and break was making the lamp brighter because those spikes where high enough and at the right time to over charge the capacitor in the lamp.
So back the the joule ringer. The first thing to note is that the frequency is much higher than 60 Hz. The frequency is determined by the inductance of the coil and the capacitance of wire placement and whatever capacitance the load sends back up the line. I have an old inverter (12v dc to 120 ac) that works the same way, but has a capacitor that was chosen to work with the transformer to give close to 60 Hz. Modern inverters use switching technology instead to be lighter, smaller, and cheaper. (more efficient too) The frequency of the joule ringer sounds to me to be 10kHz or higher (digital sampling may take a frequency higher than 20kHz and fold it back down into audible range). Anyway, the power use of the LED lamps is being measured by knowing the peak AC voltage, multiplying by .703 for RMS voltage, then taking the peak current use and multiplying that by the same .703 for RMS current. Power is voltage times current. All of this is done inside the meter.... but it is not accurate. The the peak current draw is for a very short time and each lamp takes those peaks at different times depending on the charge state of the internal capacitor. So each lamp may be taking the same peak only occasionally... it seems to turn out only 10% of the time. The idea that this joule ringer saves energy because 10 lamps only takes twice the power as 1 lamp seems to be in error. The current needs to be measured with a true RMS meter... perhaps one of the old mechanical meter models.
This begs the question of how accurate the new "smart meters" are that the power companies are using. Though I am pretty sure they measure true RMS to make sure they can charge you for
all the power used.
Anyway, the moral of the story is to understand the tools you use to measure things...