# Practical Electronics/Standing Wave Oscillator

With an LC series when ${\displaystyle Z_{L}-Z_{C}=0V_{C}+V_{L}=0}$ circuit is said to be in resonance

${\displaystyle Z_{L}=Z_{C}}$
${\displaystyle j\omega L={\frac {1}{j\omega C}}}$
${\displaystyle \omega _{o}=\pm j{\sqrt {{\frac {1}{L}}{C}}}}$
${\displaystyle V_{C}=-V_{L}}$
${\displaystyle V(\theta )=A\sin(\omega _{o}t+2\pi )-A\sin(\omega _{o}t-2\pi )}$

Circuit is capable of producing a Standing Wave Oscillation Therefore , LC can be used as Standing Wave Oscillator with fruency of oscillation equals to resonance frequency

${\displaystyle f={\frac {1}{2\pi }}{\sqrt {\frac {1}{LC}}}}$