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

AI Thread Summary
In a damped RLC circuit, a small resistance (R) is crucial for achieving underdamped behavior, which allows for oscillations in the system. The discussion highlights that the differential equation governing the circuit's motion has different solutions based on the damping level, categorized into underdamped, overdamped, and critically damped cases. Only the underdamped case exhibits oscillations due to the presence of complex roots in the characteristic equation, leading to decaying oscillations. In contrast, overdamped and critically damped cases result in purely exponential decay without oscillations. Understanding these damping scenarios is essential for analyzing circuit behavior effectively.
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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