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):


 * 1) Use KVL and KCL, get 1st order differential equation
 * 2) Find particular solution (Forcing Function) $$Y_p$$ (Table is at bottom of page)
 * 3) The complete solution is the particular + the complementary.

$$ y(x)=Y_p+ y_c $$

$$y_c(x)=K_1+K_2e^{sx} $$


 * 1) Substitute solution into differential equation to find $$K_1$$ and s. (Or find $$K_1$$ by solving in steady state.)
 * 2) Use the given initial conditions to find $$K_2$$
 * 3) Write final solution

RLC Circuits

 * DC circuits -> constant forcing functions
 * AC circuits -> sinusoidal forcing functions
 * Particular solution for VDc =>L-> SC, C-> OC