Todd, you forgot one formula that helps figure out the wattage (a lot of vapers look at the watts to judge how warm their vapor is going to be) which is wattage (w) = v^2/r or given the above parameters: (3.7 * 3.7)/1.7 = 8.052 watts. The reason this is important is when people look at either raising their voltage and raising their resistance or vice versa. In essense, for me 7-9 watts is my "sweet spot", meaning thats gives me the amount of vapor and warmth that I like.
Your right, the formula you posted above volts squared divided by resistance does give Watts. Watts is the end product of the combination of voltage, amperes and resistance. Watts is power. I just tried to answer the question being asked which was what kills batteries or actually switches in batteries. Amperage is what will destroy a switch. A battery is rated in MAH (miliiamp hours) If you take a 450 MAH battery and connect it to a atomizer say at 3.7 volts with a 1.7 ohm resister you would be pulling 2.18 amp or 2180 Milliamps per hour. If your battery is rated at 3000 MAH and you still were at 3.7 volts and a 1.7 ohm resistor you still would be pulling the same or 2.18 amps or 2180 milliamps per hour.
The 450 MAH battery could maintain a continuous output for 450/2180=..21 hours x 60 miinutes=12.8 minutes. The 3000 MAH battery would maintain a continuous output for 3000/2180=1.38 hours x 60 minutes=82.8 minutes.
I used a standard 3.7 volt battery and a low resistance 1.7 atomizer to give Amiles an idea of how long one could vape with the two different batteries and a 1.7 atty with a standard kit. A 450 MAH would only last 12.8 minutes; that would be about 2 hours actual time for me as I vape about 6 or 7 minutes per hour.
Back to the switches, most switches are rated at 12 volts for the most part. the amperage rating is what you need to look at. If a 12 volt switch rated at 2 amps were pushed to 3 amps at 3 volts it would still fry. Amps or current is what destroys them. Although you never want to exceed the volt rating either.
Little technical, but hey it works when you need to size your battery for your vaping requirements, By the way my sweet spot depends on what I'm looking at as far as watts go. If I want to taste the fullness of the flavor 4.7 watts is perfect. If I am after a better throat hit 6.4 watts is right where I like to be. The hotter or more watts you use the less the flavor comes out; that's what I have found anyway.
Rather than trying to figure out ohms law on paper or a calculator this is a good application that even includes a DIY recipe software program. Just click on tools; pv tuning and enter any two known variable and enter 0 for the other two and hit calculate and wholla you have einstein.
http://ejuice.breaktru.com/