Circuit Theory/Transients Summary and Study guide

This cover the basics of transients, the analysis of circuit response that goes away after a long time. RC or LC Circuits General solution steps for RL and LC circuits with a voltage source (with out voltage source Vc=0): Use KVL and KCL, get 1st order differential equation Find particular solution (Forcing Function) (Table is at bottom of page) The complete solution is the particular + the complementary. Substitute solution into differential equation to find and s. (Or find by solving in steady state.) Use the given initial conditions to find Write final solution RLC Circuits DC circuits -> constant forcing functions AC circuits -> sinusoidal forcing functions Particular solution for VDc =>L-> SC, C-> OC Concept Formula notes Damping Coefficiant (series LC) Damping Coefficiant (parallel LC) Undamped resonant frequency General Form Characteristic equation Roots Characteristic eqn Damping ratio Overdamped roots real and distinct Critically damped roots real and equal Natural Frequency Underdamped roots complex Table of Forcing functions Value Approximation Cons. A sin(t)/cos(t)