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

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Homework Help Overview

The discussion revolves around the behavior of damped series RLC circuits, specifically focusing on the implications of having a small resistance (R). Participants are exploring the conditions under which different damping scenarios occur in such circuits.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are questioning the significance of small resistance in relation to damping effects and are discussing the different cases of damping (underdamped, overdamped, critically damped) as described in the context of the differential equations governing the system.

Discussion Status

Some participants have provided hints regarding the forms of solutions to the differential equations based on the level of damping, while others have referenced external resources for further clarification. The conversation is exploring various interpretations of damping without reaching a consensus.

Contextual Notes

There is an emphasis on understanding the conditions under which oscillations occur in damped systems, with specific reference to the characteristics of the solutions based on resistance values. The original poster has indicated a desire for gentle feedback and clarification on these concepts.

Taulant Sholla
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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..."
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Homework Equations


Given above.

The Attempt at a Solution


Given above.
Any gentle and courteous comments are welcome!
 

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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.
 
gneill said:
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!
 
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.
 
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