A lot of resistors, like This one, are rated both for breakdown voltage and for maximum power. Well, this is probably a stupid question, but if a 10MOhm resistor is rated for 10kV, 1Watt, certainly at 10KV it will dissipate 10W and will be destroyed (which is the most evident breakdown failure). Similarly, considering a usual 1/4 Watt film resistor of 10MOhm, rated at 500V breakdown voltage, if 500V is applied to it, surely it will dissipate less than 1/4 Watt. At least one of these ratings is redundant and even contradictory with the other. What is the logic here ?
if a 10MOhm resistor is rated for 10kV, 1Watt, certainly at 10KV it will dissipate 10W and will be destroyed
Apply 10kV to the resistor for 0.1 second...
It is rated for 10kV, so it does not arc over and explode (this failure mode would be pretty much instant death).
Now, it dissipates 10x its rated free-air power, but most resistors can do that (and a lot more) easily for a short time, this is the pulse power rating which should appear somewhere in the datasheet.
This is to highlight the difference between:
constant (or average power) which depends mostly on how much watts the resistor can shed into the surrounding air (a fan blowing on your resistor will increase its power rating, btw)
pulse power, which depends mostly on thermal inertia of the part of the resistor which actually heats (ie, carbon composition spreads the heat through the entire mass and tends to have enormous pulse power ratings)... A small SMD resistor can take 100W or more for a short time.
Voltage rating, which governs the "zap-poof-smoke" failure mode.
0.25 Watt film resistor of 10MOhm, rated at 500V breakdown voltage, if 500V is applied to it, surely it will dissipate less than 1/4 Watt.
Agreed. But you don't get one datasheet per resistor value, so the 0.25W rating will be for the entire component series, over all values, and no one will bother publishing a datasheet without power rating just for your 10Mohm resistor.
However if the air temperature inside your enclosure reaches uncomfortable levels and you design for that, then you might perhaps also want to check the dissipation rating on these.
So it depends.