Power supply design, Pi filter
I use R = sqrt(L / C), thus 1uh and 1,000uF need sqrt(0.001) or about 0.03 ohms.

Your circuit, with 1uH and 1uF, needs sqrt(1/1) = 1 ohm, connected across Inductor.

You can derive this, using any resonant circuit formula with dampening resistor, and setting the Q to be 1, then solving for L/C or similar.

Consider 1 Henry and 1 Farad. The Fresonance is 0.16 Hz. Xl = Xc =   +-J1 ohm.
Using 1 ohm for the dampening resistor, the Q must be one.

Is Q of 1 what you wish?