Laplace Transform Solved Problems: Circuits with Initial Conditions (Part 2)

In this video, we solve two circuit problems using the Laplace Transform, both involving initial conditions in capacitors and inductors. The end goal is to help you become comfortable with: • Modeling initial energy in the s-domain • Correctly setting up source terms • Solving for circuit responses using algebra instead of differential equations • Interpreting the final time-domain response physically This video builds directly on the earlier Laplace introduction and derivation videos in this playlist. ⏱️ Chapters Question 1 00:21 – Pre-Solve Analysis 02:32 – Drawing the Circuit in s-Domain 07:02 – Evaluating Vo(s) 14:44 – Simplifying with Partial Fractions for Vo(s) 15:58 – Inverse Laplace to solve for Vo(t) Question 2 18:04 – Pre-Solve Analysis 19:08 – Drawing the Circuit in s-Domain 22:19 – Evaluating Vo(s) 25:28 – Simplifying with Partial Fractions 27:21 – Inverse Laplace to solve for Vo(t) 📌 Prerequisites: • Basic Laplace Transform definitions • s-domain modeling of R, L, and C • Derivative property of the Laplace Transform