PX157 - E4b - LRC circuits 2

{\tilde{Z}}_{e q} = R + j ω L

\tilde{I} = \frac{{\tilde{V}}_{i n}}{{\tilde{Z}}_{e q}} = \frac{{\tilde{V}}_{i n}}{R + j ω L}

{\tilde{V}}_{o u t} = {\tilde{Z}}_{L} \tilde{I} = j ω L \frac{{\tilde{V}}_{i n}}{R + j ω L}

\frac{| {\tilde{V}}_{o u t} |}{| {\tilde{V}}_{i n} |} = \frac{ω L}{\sqrt{R^{2} + ω^{2} L^{2}}}

ϕ = \arctan (\frac{ω L}{R})

- ${\tilde{V}}_{i n}$ leads $\tilde{I}$ by $ϕ$