Understanding RLC Circuits: Critical Damping & Homework Equations

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SUMMARY

This discussion focuses on understanding RLC circuits, specifically the concept of critical damping and the associated equations. The critical damping equation, diL/dt = -vc(0) - Ri(0), is highlighted as essential for solving circuit problems. Participants express confusion regarding whether to solve for the voltage across the capacitor (vc) or the current through the inductor (iL) after determining the damping condition. Clarifications are provided regarding the correct interpretation of circuit diagrams and calculations, emphasizing the importance of accurately identifying circuit components.

PREREQUISITES
  • Understanding of RLC circuit components (resistors, inductors, capacitors)
  • Familiarity with differential equations in circuit analysis
  • Knowledge of damping conditions (overdamped, underdamped, critically damped)
  • Ability to interpret circuit diagrams accurately
NEXT STEPS
  • Study the derivation and application of the critical damping equation in RLC circuits
  • Learn how to analyze circuit responses using the Laplace transform
  • Explore textbooks or resources that provide detailed examples of RLC circuit problems
  • Investigate simulation tools like LTspice for visualizing RLC circuit behavior
USEFUL FOR

Electrical engineering students, educators teaching circuit analysis, and anyone seeking to deepen their understanding of RLC circuits and damping behavior.

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Homework Statement



Image

Homework Equations



Critical Damping

* related to '*' on image : diL/dt = -vc(0) - Ri(0)
When do we use this to solve for the other constant? In the text, an example problem is never fully explained in mathematical terms.

The Attempt at a Solution



I am looking for someone to kind of explain what to keep an eye out for when analyzing RLC circuits, or provide a source. I have looked through a couple different textbooks and certain things vary and its leading to confusion. One particular concern is after we calculate whether a circuit is over/under damped or critical (I know the characteristic equations for each), are we solving vc or iL. Now I'm sure it depends on what the question asks, but sometimes it includes both instances. Can someone please sort this out for me?**EDIT**
The voltage for capacitor should be 12/5 = 2.4 Correct?
 

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dwn said:


**EDIT**
The voltage for capacitor should be 12/5 = 2.4 Correct?


Incorrect. What is the total resistance in series with L?

Also, your t(0+) diagram is wrong. The 1 ohm resistor has mysteriously migrated away from C!
 

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