Resistors wattage

[POTL]

Hello.
The question is quite simple about the power of the resistors.
Ohm's Law says that when directly connected to 9 volt batteries (power adapters), the minimum resistor resistance at 1 / 4W = 324Ω and 648Ω at 1 / 8W.
At a voltage of 18V, these values ​​are 1.296kΩ for 1 / 4W and 2.592kΩ for 1 / 8W.
It seems that everything is simple and clear, but often in power schemes I see resistors with a value of 10 Ohm-100 Ohm with a power of 1/4 watt.
There are such resistors in
1) Power filtering (many projects Madbean 1N4001 + 10ohm resistor).
2) In "amplifier in a box" projects, when they put an RC filter between the stages and use 100 Ohm resistors (Dr Boogie).
3) Separation of the power section, between the analog part and the BBD, for example, in the BOSS(CE-2 & DM-2) pedals there are 22Ohm-33Ohm resistors.
All these resistors are 1/4 watt, they are much lower than the minimum value calculated according to Ohm's law and they are connected directly to the voltage. Why do they work and do not burn out and how to calculate their power correctly?

[bluebunny]

These low-value resistors might get into trouble if they are connect between both power rails, but they're not.  The power-filter one may indeed have 9V (or 18V) at one end, but it's not connected to 0V at the other.

Try it.  Measure the voltage at the other end of such a resistor to calculate the voltage across it.  Lift one end of the resistor so that you can measure the current flowing through your circuit.  Now plug these numbers into P=VA and discover the tiny power being dissipated.

[ElectricDruid]

+1 what Bunny said.

In the case of the power input RC smoothing filter resistor, you *definitely* don't want 9V across it, because if you did you'd have no volts for your circuit! Instead, you want the volt-drop across that resistor to be as low as possible so that it doesn't eat into your potential headroom. This is one reason you see such small values in that position. If the rest of the circuit draws a reasonable current, a larger value would cause an unacceptable voltage drop. If the current needed by the circuit is very small, it makes sense to make that resistor larger because you can have better smoothing with a small cap. So (as usual) there's a trade-off - RC filter cap size requirement against voltage drop across the R.

[WormBoy]

Just to add to the good replies, this link might help, especially Example 2: https://www.electronics-tutorials.ws/resistor/res_7.html. You can calculate the maximum current through a given resistor, given its power rating. So, a 10 ohm, 0.25 Watt series resistor for power filtering (as in your example 1) would be safe up to a current draw by the circuit of 158 mA (although you really would like to have some safety margin, of course, this would be plenty for most stomp boxes).

[bluebunny]

That's a good article.  If I were being picky, I would take exception to the use of the word "absorb".  There is no "absorb", there is only "dissipate".  (Sound like Yoda I do...)  Nothing can magically absorb energy to make it go away^*; you can only move it somewhere else.  Anything that has a current flowing through it will heat up.  It's not just resistors.  You just have to win the battle between dissipate and heat up.

___
^* Yes, you can store it - but only up to a point.  Then you have to dissipate, or else stop supplying energy.

[POTL]

Shyly looks away.
Indeed, I feel stupid, I was not thinking about the difference in potentials, but in all the tension as a whole.
Okay, I was only interested in the power supply circuit and interstage filtration, in both cases it will be ok.
Thank)