Circuit Theory/Transients Summary and Study guide
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This cover the basics of transients, the analysis of circuit response that goes away after a long time.
RC or LC Circuits[edit]
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[edit]
 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[edit]
Value  Approximation 

Cons.  A 
sin(t)/cos(t)  