Practical Electronics/Series LC

Summary

Circuit	Series LC
LC
Impedance	$Z=j\omega L+{\frac {1}{j\omega C}}={\frac {j\omega ^{2}LC+1}{j\omega C}}$
Differential Equation	$L{\frac {dI}{dt}}+{\frac {1}{C}}\int Idt=0$
Root of the Equation	$I=ASin\omega t$
$\omega$	$\omega ={\sqrt {\frac {1}{LC}}}$
Resonance $Z_{L}-Z_{C}=0.V_{L}+V_{C}=0$	$Z_{L}-Z_{C}=0$ $\omega L={\frac {1}{\omega C}}$ $\omega ={\sqrt {\frac {1}{LC}}}$ . $V_{L}=-V_{C}$ At Resonance, the response of the circuit is Standing Wave

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