This is my personal problem not any acadamic or homework.

Given this circuit We will charge the capacitor with V1 until it fully charge then switch to RLC circuit at, t = 0


simulate this circuit – Schematic created using CircuitLab

For constant C and L, what is optimal R value for quickest dissipate energy?

  1. If R = 0, the system will oscilator forever
  2. If R = inf, current will not pass through resistor there for no loss, no energy dissipate.

So the optimal value should exist between 0 to inf.

  • 1
    \$\begingroup\$ Useful search term : "critical damping". \$\endgroup\$
    – user16324
    Dec 14, 2021 at 22:17
  • \$\begingroup\$ The discharge NEVER ends, and the energy is always dissipated if a wire is used. So, you should define a tolerance (%) used for "total" discharge ... \$\endgroup\$
    – Antonio51
    Dec 15, 2021 at 9:57
  • \$\begingroup\$ I have tried to simulate this exercise. Power integration on Resistance. i.stack.imgur.com/lLVBZ.png ? Unless I am wrong. \$\endgroup\$
    – Antonio51
    Dec 15, 2021 at 14:41
  • \$\begingroup\$ @Antonio51 if it decay faster It might faster at all tolerance. but if you let me specify I think 1% should be good \$\endgroup\$
    – M lab
    Dec 15, 2021 at 16:08
  • \$\begingroup\$ Here is what I simulated (unless error) Gray Curve (R1=~1.4 Ohm) seems the fastest, but not as complete as "orange" nearest, because of the behavior within the limits (?). i.stack.imgur.com/tuC5n.png \$\endgroup\$
    – Antonio51
    Dec 15, 2021 at 20:21

1 Answer 1


The optimal resistance value can be calculated by analyzing the damping factor of the RLC circuit.

When resistance is too large, i.e. the circuit is overdamped, there is no oscillation and the voltage just decays.

When resistance is too low, i.e. the circuit is underdamped, there is a decaying oscillation.

When resistance is just right, the circuit is said to be critically damped, and the voltage decays the fastest without going to oscillation.

The RLC circuit is critically damped when damping factor is 1, i.e. DF = (R/2)*sqrt(C/L) = 1.

For further info refer to this Wikipedia article on RLC circuits

  • \$\begingroup\$ From my understanding, critically damped is "fastest decay without oscilation" How to be sure that it decay faster than oscilation case? \$\endgroup\$
    – M lab
    Dec 15, 2021 at 16:11
  • \$\begingroup\$ @Mlab You just said quickest to dissipate energy. I interpreted it as dissipate all the energy. Now you updated the specs and allow to dissipate below 1%, so fastest way will of course now be to allow oscillations but so that they are within 1%. \$\endgroup\$
    – Justme
    Dec 15, 2021 at 18:14
  • \$\begingroup\$ For ideal case is "dissipate all the energy" as your understanding. if your approach can prove that without tolerant would be great! \$\endgroup\$
    – M lab
    Dec 15, 2021 at 18:55

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