In a circuit I designed, there is a moment when a capacitor should be discharged through a resistor.
The power dissipated in the resistor has the format of the screenshot in the LTspice.
Should I select the average as a power rating and thus choosing a 1/4 watt resistor or should I select a bigger value?
As it can be observed, the power will reach 4 watts at the starting of the discharge phase.
The power rating of a resistor is not the peak power (though that's in the datasheet too!) but the average power. So what you need to do is not only figure out the max power in a pulse, but also the duty cycle/ frequency of pulses.
In your case, as an overestimate of the energy dissipated in a pulse, lets say that your pulse dissipates 4W for 4ms, so your total energy would be \$4W*.004s= .016J\$ (you can get a better estimate by having LTSpice integrate your power trace). Lets also say that these pulses occur 20 times/s, so you would need a resistor with at least \$0.16J*20Hz=0.32W\$, so a \$½W\$ resistor would probably be fine.
Using all the resistor rating results in a 100’C rise so consider derating all resistors 50%.
The time constant may be less than the thermal so average power is a reasonable choice for some types. But review the product limits to be sure and have ambient air flow in mind or else derate further.
Resistor power specification is for average power, but the actual lifetime might be shortened because of thermal stress. You should select a resistor designed to withstand energy pulses that cause thermal stress, they usually go by name "surge resistor" or "pulse resistor".
If your average power is below 1/4 W, then a pulse resistor specified for 1/4 W is a good selection, even if peak power exceeds 1/4 W.
