Matthew's Asgn

I decided that I would attempt to perform a simple analysis of a series RL circuit, which could then be used to do a more complex analysis on a basic transformer. I have always had interest in electronics, and transformers are key to basic electronics.

I decided that i would do the analysis of a RL circuit with the variables instead of given values.

Given:

V(t)=$\cos w*t$

V(s)=$s/(s^2+w^2)$

I(0)=i

The Laplace transform for an inductor:

${ℒ}\{f(t)\}$ = $Ls+Li$

The Laplace transform for a resistor:

${ℒ}\{f(t)\}$ = $R$

Therefore the Resulting Equation for the system after applying the Laplace Transform:

$0=-s/(s^2+w^2)+RI(s)+LsI(s)-Li$

A series of algebraic manipulations follows to come up with I(s):

$s/(s^2+w^2)=(R+Ls)I(s)+Li$

$I(s)=s/((s^2+w^2)(R+Ls))-Li/(R+Ls)$