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23. RL Circuits

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Learning Objectives

  • To comprehend how the presence of an inductor in a circuit modifies the behavior of the circuit.
  • To explore the meaning of exponential decay and the L/R time constant.
  • To be able to solve L/R circuits with various initial conditions.

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 11.1 through 11.4:
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)

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: Faraday's Law Applied to Circuits

How does a circuit containing a solenoid work, from the point of view of Faraday's Law? Consider a circuit carrying current I, consisting of a battery, a resistor, and a solenoid with N turns and height l. What is the magnetic field inside the solenoid? Use Ampere's Law without the displacement term to calculate this field. Now apply Faraday's Law to this circuit, choosing a closed loop for Faraday's Law carefully. You will find that choosing an open surface whose boundary is this closed loop is difficult, so think carefully about this. You will in this process derive an equation for the self-inductance of the solenoid.

Now consider a circuit consisting of a battery and a resistor and a solenoid which has been in place for a long time. At t = 0, we close a switch that cuts the battery of the circuit, so that we have left only a closed circuit containing the resistor and the solenoid. Use Faraday's Law to find the current in this closed circuit as a function of time.

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Download this video:
» iTunes U (MP4 - 36MB)
» Internet Archive (MP4 - 36MB)

 

Problem 2: A Step-Up Transformer

An ideal transformer is connected to a 120 V (root mean square) power supply. We want this transformer to supply 15,600 V (rms) to a light fixture. We have a fuse in the primary circuit that for safety we want to blow when the rms current in the secondary circuit exceeds 10 milliamps. What is the ratio of the number of turns in the secondary to the number of turns in the primary? What power must be supplied to the transformer to get a 10 milliamp current in the secondary circuit. What rms current rating should the fuse in the primary circuit have?

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Download this video:
» iTunes U (MP4 - 17MB)
» Internet Archive (MP4 - 17MB)

 

Related Visualizations

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

 

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