# 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 CircuitsEdit

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 CircuitsEdit

- 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 functionsEdit

Value | Approximation |
---|---|

Cons. | A |

sin(t)/cos(t) | |