ODEs and Electric Circuits

• Preface & Acknowledgements

• Instructions

• Introduction: Modeling Electric Circuits

I. Exploring R-L and R-C Circuits

DC Circuits

• Example 1 ( R=12, L=4, EMF=60 )
  
• Example 2 ( R=5, C=0.05, EMF=60 )
  
• Practice Problem 1 ( R=6, L=2, EMF=100 )
  
• Practice Problem 2 ( R=5 kΩ, C=1 µF, EMF=2 V )

AC Circuits

• Example 1 ( R=2, C=1/6, EMF=100cos(4t) )
  
• Example 2 ( R=6, L=2, EMF=100sin(4t) )
  
• Practice Problem 1 ( R=5, C=0.05, EMF=60cos(4t) )
  
• Practice Problem 2 ( R=12, L=4, EMF=60sin(4t))

II. Solving First Order Linear Differential Equations

Method of Separation of Variables

• Example 1
  
• General Method
  
• Example 2 ( R=6, L=2, EMF=100 )

Method of Integrating Factors

• Example 1
  
• General Method
  
• Example 2 ( R=5, C=0.05, EMF=60cos(4t) )

III. Analyzing R-L and R-C Circuits

DC Circuits

• Example 1 ( R=12, L=4, EMF=60 )
  
• Example 2 ( R=5, C=0.05, EMF=60 )
  
• Practice Problem 1 (R=2, C=1/6, EMF=100 )
  
• Practice Problem 2 ( R=50, L=0.1, EMF=100 )

AC Circuits

• Example 1 ( R=5 kΩ, C=1 µF, EMF=2sin(200t) )
  
• Example 2 ( R=6, L=2, EMF=100sin(4t) )
  
• Practice Problem 1 ( R=2, C=1/6, EMF=100cos(4t) )
  
• Practice Problem 2 ( R=1.2, L=0.4, EMF=60sin(50t) )

Other Examples

• Example 1 ( R=6, L=2, EMF=100exp(-t) )
  
• Example 2 ( R=12, L=4, EMF=E(t) )

IV. Technology

TI calculator (TI-92 or TI-89)

• R-L text variable
  
• R-C text variable

Maple software

• R-L worksheet
  
• R-C worksheet

V. Exercises

• Setting Up Electric Circuit ODE and Verifying Solution
  
• Solving Electric Circuit ODE