AC Steady-State Analysis
  • Reactance

$S=wL-\frac{1}{wC}$

  • Impedance

$\sqrt{R^2+S^2}$

  • RLC-circuit
(1)
\begin{align} LI'+RI+\frac{1}{C}\int Idt=E(t)=E_0sinwt \end{align}
(2)
\begin{align} LI''+RI'+\frac{1}{C}I=E'(t)=E_0wcoswt \end{align}
(3)
\begin{align} I_p(t)=I_0sin(wt-\theta) \end{align}

$I_0=\frac{E_0}{\sqrt{R^2+S^2}}$, $tan\theta=\frac{S}{R}$

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