Originally Posted by opus
In that order?
Well, you sure don't want to be at the bottom of a hill when you discover the thing about electricity! Better to learn #1 first!
It's easy enough to figure wattage and temperature rise. Specific heat of water is around 1 Btu per pound per degree F (it varies with temperature), so if we have a mug holding 8 fluid ounces of water at 50 F and we want to raise it to 120 F, that's 0.52 pounds times 70 degree rise so 36 Btu needed (ignoring heat lost to the mug, ambient, etc). That's 0.0106 kw-hr, 10.6 watt-hours, so at 120 watts input it'll take 5.3 minutes (longer in the real world, where the heater doesn't achieve its rated output and heat is lost to the mug etc).