ELECTRIC CIRCUIT ANALYSIS

“The Laplace transform can be applied to solve the switching transient phenomenon in the series or parallel RL,RC or RLC circuits ”

Laplace transform saves us the hassle of solving ODEs by converting such equations into algebraic ones so they may be solved more easily.

Fundamentals of analyzing RLC/RL/RC circuits:

“1. Develop the differential equation in the time-domain using Kirchhoff’s laws (KVL, KCL) and element equations.

2. Apply the Laplace transformation of the differential equation to put the equation in the s-domain.”

3. Algebraically solve for the solution, or response transform.

4. Apply the inverse Laplace transformation to produce the solution to the original differential equation described in the time-domain. “

It transforms a typical KVL equation such as,

into this,

which, by isolating our target variable I is:

which is a function involving only the variable s and some other constants (V0, I0, L, R, C).

Reference:

Continuing the example above with actual values of R, L,and C:http://www.dummies.com/education/science/science-electronics/analyze-an-rlc-circuit-using-laplace-methods/