Your theory is 100% correct.

So lets apply the theory into practice:
Discharge and charge time of a RC filter is 5*R*C.
R is very small, ideally zero, as its a short wire with a descent cross section.
To make a worst case scenario, lets say you got a 1 meter ESC wire, with a 12mm² cross section.

R = ρL/A
ρ[Cu] = 17.2 nΩ/m

17.2*10⁻⁶*1/0.012² = 0.12Ω

So 0.12Ω is the resistance of a 1 meter long ESC wire.

My 200A Suppo ESC has 5x270µF capacitors, thats 1.37mF.

The time constant for a 200A Suppo ESC with a 1 meter long wire is:
5 * 1.37*10⁻3*0.12 = 8.22 *10⁻4

That is less than a millisecond.
With a 1 meter long wire and a 1.37µF ESC capacitor, you got less than a millisecond of "capacitor boost" before the capacitor is drained, and the voltage drop is the same way as it would be without any capacitor at all.


Lets take another extreme example, a 1 Farad car audio capacitor. they would never ever fit in a RC boat anyway, and their weight can not be justified by its tiny advandage, but lets just calculate it to see...

5*R*C

C=1
R=0.12

5*1*0.12 = 0.6

With a 1 Farad capacitor, which is larger than the boat its supposed to fit inside, you will have roughly half second of capacitor boost before voltage drop is as it would been before.
And mind you, the capacitor discharge curve is exponential, already after 1*R*C time, you will have discharged down to 63% of the full potential.

I maintain my statement, a capacitor is not a energy storage device.


Laplace was nice, as as long as we could answer in S form. Converting back and forth from time plane to S plane was teedious.
I agreed that fourier analysis was worse. I never got the hang of that, and I hope I will never ever see it again
Integration, derivation and differential equations in time plane wasn't as bad as its hyped up to be