For a damped RLC circuit, why must R be small?

[Taulant Sholla]

Homework Statement

I'm reading the textbook section covering damped series RLC circuits (provided below). I'm wondering why the author stipulates "When R is small..."

Homework Equations

Given above.

The Attempt at a Solution

Given above.
Any gentle and courteous comments are welcome!

 

[gneill]

There are three cases for damping in mechanical or electrical systems. What are they?

Hint: The solution of the differential equation describing the motion has different forms depending upon the level of damping.

 

[Taulant Sholla]

There are three cases for damping in mechanical or electrical systems. What are they?

Hint: The solution of the differential equation describing the motion has different forms depending upon the level of damping.

Ah - very helpful, thank you!

 

[Delta2]

Wikipedia has a very good entry (I believe so) in this subject https://en.wikipedia.org/wiki/RLC_circuit#Series_RLC_circuit

Notice the general form of the solution and how it changes in the three cases;
Underdamped, Overdamped, Critically Damped. Oscillations (to be accurate decaying oscillations) happen only in the underdamped case . That's because the characteristic equation has complex roots at this case so the exponentials of the generic solution have an oscillation term $e^{-j\omega t}$. In the other two cases we just have exponential decay of the current.