Okay, I wanted a cup of tea, and this sounded fun. :)

And the winner is...Induction by a head!
Full Results, 1 cup cool tap water measured in same measuring cup to level:
HEAT SOURCE VESSEL TIME TO ROLLING BOIL/WHISTLE

Induction Le Creuset kettle 1:00, with rolling boil
Gaggenau, 21 cm enamelled steel a second ahead of whistle
2.2kW, level 9 -- heavy bottom
boosted to 3.3kW removable whistle
____________________________________________________________
1960's Farberware Self 1:15 - 1:20
compact percolator I would call it rolling at
generally used for 1:15 but then it got rollinger
boiling water while while I was trying to pull the
car camping plug
____________________________________________________________
1991 Black & Decker Self 1:30 to heavy steam
electric teakettle 1:40 to whistle
____________________________________________________________
Gas Le Creuset kettle 2:30 to whistle
Wolf Same as above
12K BTU on high
closed burner
____________________________________________________________
Microwave Corelle cereal bowl 2:30-2:45*
Advantium Pro 240
Microwave Express (high)
____________________________________________________________

*Notes on microwaving: Advantium is an excellent microwave, but it doesn't seem to have a boil sensor, so I had to try time. There isn't a continuous light on on Microwave mode because the light is the same powerful halogen used for the speed cook, so I could only check intermittently. You get a couple seconds per look, and turning the light on too much adds heat. "Tea" setting was 1:30 but the result, in a ceramic mug, was barely above tepid. I tried 2:00 with a cool mug and having done my best to cool down the interior of the oven, but that was just a bit hotter. I opened to check. Added 30 seconds, no boil apparent on opening door. Added another half minute, and it was boiling. At this point, though, I was getting bored, and didn't want to start up with the ice to cool down the oven. I wiped it with a damp cloth, and it wasn't very warm to the touch, but there was still warmth in the glass tray and some of the other surfaces. Used the bowl to see if I'd have a better view of the boiling, and my mug was very hot from actually having achieved a boil and I was too lazy to go into the other room for another one. Plus I didn't have to worry about the Corelle cracking. I'm not exactly sure when it started to boil. I'm pretty sure I checked at 2:30 and it was still. I know it was boiling at 2:45 and for sure it wasn't at 2:00, but my mind was wandering (that pesky boredom before the experiment is finished). The Advantium is powerful, however, and it couldn't touch the kettles, only competitive with the gas.

That was fun. Those of you who want to try that should be careful with the microwave. Sometimes the water will superheat, but not boil until it is removed, or the surface of the water is touched. Then it explodes boiling water.

More likely with very clean glass ware. Here's a link that talks about nucleation sites etc.

Here is a link that might be useful: Superheated water- Snopes

Yep, that glass measuring cup needs a bamboo skewer in it for safety. I had to do that in my mother's old 1980 MW. The mug was fine. I was a little unsure about the bowl, being Corelle, but that went all bubbly-wubbly while the MW was running.

Good job plllog!

The other part of the OP's question, efficiency, asks which is fastest given the same amount of power drawn (or equivalent BTUs used). The most efficient would be the electric kettle which puts almost all of its heat into the water.

Next would be induction, which is as efficient as its power supply and coil losses. I don't know any particular value for any particular device, but believe from the state of power supply technology and exhausted waste heat from my cooktop that induction efficiency lies in the 90 - 95% region.

Electric coil type cooktops and gas burners partly radiate and convect elsewhere than the pan, so they would trail in the competition.

I would use an electric kettle for water heating for tea if I found one that was at least 2 quarts and more powerful than my induction cooktop. (Brewing is performed in a 2 qt Corning Ware tea pot.) Failing to have found one, I use a Demeyere induction-compatible kettle instead. It is relatively inexpensive, for a Demeyere; I suspect it is a part of a bistro cookware line.

kas

Wow, you guys are amazing. Where would the microwave fall in terms of efficiency??
I may win this bet yet!

Microwave ovens are rumored to be about 65% efficient.

kas

The inefficiency of a microwave oven is lost in the power supply and magnetron, not in the oven itself. But the specified power rating of a microwave oven is delivered power, not drawn power, I believe.

I am unclear about which is used to characterize induction hobs, drawn or delivered power.

In any case, it may be seen in plllog's results that the induction hob running at perhaps 2.5x the microwave's power output requires around 2.5x less time.

kas

Thanks, Kas! I wasn't touching the efficiency part. :) FWIW, the electric kettle says it's 1500W (forgot to put that in, above). The Advantium is rated at 950W.

Nice work Pillog, buttt~~~~~~I'm just soooooo used to neuking my coffee in the AM, and I am only semi-conscious when I do that, that I just can't be "Inducted" into doing my coffee that way, even after all your hard work---What A bummer

Gary

Take that same "cup of water" put it in a very thin aluminum or stainless pan with a large bottom like 12" over a 15K+ Gas burner and it would be close to the Induction.

But for one cup of water the reigning champ of which nothing will ever come even close to is my Keurig which will deliver 192 degree water in under 10 seconds.

Yeah, but Nunyabiz, no one who owns a saucepan, let alone a kettle, is going to boil water for tea in a big skillet. On induction the same pan will boil in seconds.

true, just saying the "method" is almost as important as the heat source.
and none beat a Keurig.

Agreed, but I used the same kettle on the gas and induction, which is like to like, and the bowl vs. mug in the microwave weren't wildly divergent, even if they accounted for the entirety of the time different (rather than the door opening, etc.) Comparing a thin skillet to a thick kettle doesn't make any sense.

Just for grins I tried something like it. The only pots I have that are that big are my cast iron braiser and my stockpot. Just for you, I made three trials:

The same one cup of water measure level in the same measuring cup:

HEAT SOURCE VESSEL TIME TO ROLLING BOIL

Induction De Buyer 35 seconds
Gaggenau, 21 cm carbon steel
2.2kW, level 9 -- very thin
boosted to 3.3kW 8" diameter bottom

Induction Demeyere 35 seconds
Gaggenau, 21 cm 7-ply
2.2kW, level 9 -- thick and heavy
boosted to 3.3kW 7"-ish diameter bottom

Induction Le Creuset 20 qt. 40 seconds
Gaggenau, 28 cm enamelled steel Made a lot of
3.6kW, level 9 -- very thin noise. Obviously
boosted to 4.4kW 11" diameter bottom didn't like it.
From the bubble
pattern, I don't
think the outer
ring was engaged,
which makes sense
that it would be
the same time as
the others.

The number of seconds is approximate as it's hard to judge exactly when the field goes on, and how rolling the boil is when one stops. As far as I could tell they were all pretty much the same. The boil in the stock pot started earliest but took a bit longer to really get going.