Inrush current limiter resistor power dissipation calculation
Decades ago I was tasked with analyzing the power dissipation of switch-cap circuits.

As part of that, I wrote the integrals of energy in the switch and in the capacitor.

Turns out the SWITCH(RESISTOR) energy dissipation is exactly the energy stored in the capacitor.

Thus if you have a large audio amplifier with 100,000 uF capacitors on +50v and -50v rails, the energy stored in each will be

Energy = 1/2 * C * V^2 = 0.5 * 0.1Farad * 50 * 50 = 2500 * 0.1 * 0.5 = 125 joules

Assume your surge-limited resistor dissipates that energy in 1/120 second.