# 24. Undriven RLC Circuits

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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.

Inductance and Magnetic Energy (PDF - 1MB)

## Lecture Video

### Video Excerpts

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## 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)

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» iTunes U (MP4 - 31MB)
» Internet Archive (MP4 - 31MB)

### 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.

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