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Solving Circuits Using Differential Equations

Circuits are a basic application of second order differential equations. Their math is identical to the math of spring mass systems and so are their solution methods. In this video, I setup the circuit problem using resistance, inductance, capacitance and a basic electromagnetic force. I also turn the circuit into phase mode form, discuss damping of the circuit and transient vs. steady state solutions. I provide two problems to show the setup, derive damping and give a basic outline of solution methods. I use constant coefficients and undetermined coefficients (the method of annihilators) to solve for the charge. If you need a review of constant coefficients, here is a video:    • Differential Equations- Homogeneous D.E.'s...   If you need a review of the method of annihilators:    • The Method of Undetermined Coefficients or...   You can also use Laplace Transforms to solve these and here is a tutorial for solving differential equations using Laplace transforms:    • Solving Initial Value Problems using Lapla...   There is also a playlist on the channel. 00:00 Introduction 00:24 Introduction, variables and setup 02:55 Basic Equations 04:09 Phase Mode Form 07:03 Damping 12:31 Example 1: No EMF- Homogeneous 17:17 Example 2-With EMF 22:46 Transient and Steady State Solutions 25:17 Conclusion