24. Undriven RLC Circuits

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• Syllabus
• Electric Fields

  • 1. Introduction to Electric Fields
  • 2. Math Review, Fields
  • 3. Electric Fields and Discrete Charge Distributions
  • 4. Electric Fields and Continuous Charge Distributions
  • 5. Gauss's Law
• Electric Potential

  • 6. Discrete and Continuous Distributions of Charge
  • 7. Equipotential Lines and Electric Fields
  • 8. Gauss's Law and Configuration Energy
• Capacitors

  • 9. Conductors and Insulators, Conductors as Shields
  • 10. Capacitance and Capacitors, Energy Stored in Capacitors
  • 11. Capacitors and Dielectrics
• Circuits

  • 12. Current, Current Density, Resistance, and Ohm's Law
  • 13. Batteries and Circuit Elements
  • 14. DC Circuits
  • 15. DC Circuits with Capacitors
• Magnetic Fields and Forces

  • 16. Magnetic Field
  • 17. Magnetic Forces
  • 18. Magnetic Dipoles
• Creating Magnetic Fields

  • 19. Biot-Savart Law
  • 20. Ampere's Law
• Faraday's Law

  • 21. Faraday's Law
  • 22. Inductance and Magnetic Energy
  • 23. RL Circuits
• Oscillating Circuits

  • 24. Undriven RLC Circuits
  • 25. Driven RLC Circuits
• Maxwell's Equations

  • 26. The Displacement Current and Maxwell's Equations
  • 27. Poynting Vector and Energy Flow in a Capacitor
• Electromagnetic Waves

  • 28. Maxwell's Equations and Electromagnetic Waves
  • 29. Energy and Momentum in Electromagnetic Waves
  • 30. Generating EM Waves, Dipole Radiation and Polarization
• Nature of Light

  • 31. Interference
  • 32. Diffraction
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Learning Objectives

• To comprehend the analogy between the mass on a spring problem and the behavior of undriven RLC circuits.
• To comprehend the mathematics governing the LC circuit with no resistance.
• To comprehend the mathematics governing the LC circuit with light damping (small resistance).

Preparation

Course Notes

Read through the course notes before watching the video. The course note files may also contain links to associated animations or interactive simulations.

Read sections 11.4 through 11.13:
Inductance and Magnetic Energy (PDF - 1MB)

Lecture Video

Video Excerpts

Learning Activities

Guided Activities

Read through the class slides. They explain all of the concepts from the module.

Slides (PDF - 1.7MB)

Self-Assessment

Do the Concept Questions first to make sure you understand the main concepts from this module. Then, when you are ready, try the Challenge Problems.

Concept Questions

Concept Questions (PDF)

Solutions (PDF)

Challenge Problems

Challenge Problems (PDF)

Solutions (PDF)

Problem Solving Help

Watch the Problem Solving Help videos for insights on how to approach and solve problems related to the concepts in this module.

Problem 1: Lightly Damped Undriven RLC Circuits

A circuit consists of a battery, a resistor with resistance R, a capacitor with capacitance C, and an inductor with an inductance L. Apply Faraday’s Law to this circuit and deduce the equation that governs the way that the current in this circuit changes with time. Discuss the solution to this equation when the battery emf is zero and we have “light damping”, that is when the resistance R is smaller than 2√(L/C)

Problem 2: An LC Circuit

A capacitor with capacitance C of 6 x 10^-4 F is initially charged to a voltage of 24 V. At t = 0, it is connected to an inductor of inductance L = 3 H. Describe the subsequent behavior of the system.

Related Visualizations

The visualizations linked below are related to the concepts covered in this module.

• Creating a Magnetic Field
• Destroying a Magnetic Field
• The Levitating Ring
• The Falling Ring with Finite Resistance
• The Force on a Moving Charge in a Time-Changing Field

 

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