V = IR. With 9v across a resistor of 100ohm, V = 9, R = 100, so I = V/R = 9/100 = 90mA
Yep.
Power dissipation is P = I^2*R. Or, P = V^2/R. P = 9*9 / 100 = 81/100 = 0.81A = 810mA.
Yep.
Well, I too often wonder how a resistor can dissipate as much power as claimed by its rating, when they get super hot at much lower power. The answer is, temperature gradients. The more power a resistor dissipates, the more heat, so the hotter it gets. But the ambient temperature generaly stays the same, so the
difference temperature increases. The greater this difference, the faster heat is transfered from high to low, so eventually things will settle at a temperature where the heat generated in watts, is equal to the heat dissiapated, in watts. Larger resistors have a bigger surface area, as well as larger volume, and so can conduct heat better to the surface, and the surface is larger so it can transfer heat better to air (OR a heat sink for bigger resistors..).
This is also why a very hot object, once placed in ambient temperature will cool down very quickly at first, but the change in temperature will slow down. Say for example something thats 150C. It will quickly drop to 100C in say, 30seconds, thats a 50C drop in temp. But in the next 30 seconds, it will drop from 100, to 66 - a 33C drop. Next 30 seconds? 44C
Therefore, if we assume we have two perfect resistors of the same value, that are indestructable and hold their resistance perfectly regardless of temperature. One is rated at 0.5W, the other at 3W. Apply the same votlage across eah one in turn, same current will flow through either, and they will both dissipate the same amount of power (P= V^2 / R). However, the 3W will run much cooler, because it naturally has a better ability to transfer heat to the air than the smaller 0.5W resistor. So it settles at a lower temperature. Also note that resistors can handle quite a bit of heat. 150C isn't unheard off, and touching something thats 70C feels very hot. So a 5W rated resistor would need roughly 5W of dissipation to get to 150C, where-as, given 1W, it might only get to 60 - which still feels too toasty.
Ratings are often the 'absolute max' assuming good air flow, and ambient temp of 20-25C. I'm unsure of the official specs
I usually use 2W resistors for anything over 0.5W, 3W for anything over 1W and then 5W. Most would say that above half the rating is pushing it, I'm just overly cautious beause heat can transfer to other parts of the circuit, which can change how the circuit operates. For transistors, google 'thermal runaway'. I recently repaired something that failed, and thermal runaway and the cause - but it was started because a pwoer resistor was too close to a transistor, so they both 'cooked' eachother.
Too much detail?
Blueteeth