LC circuit

A circuit of 2 component a capacitor and an inductor connected in series

Circuit	Configuration	Formula
Series LC		At equilibrium ${\displaystyle V_{L}+V_{C}=0}$ ${\displaystyle L{\frac {d^{2}i}{dt^{2}}}+{\frac {1}{C}}\int idt=0}$ ${\displaystyle {\frac {d^{2}i}{dt^{2}}}+{\frac {1}{LC}}i=0}$ ${\displaystyle {\frac {d^{2}i}{dt^{2}}}=-{\frac {1}{T}}i}$ ${\displaystyle i=A\sin \omega t}$ ${\displaystyle \omega ={\sqrt {\frac {1}{T}}}}$ ${\displaystyle T=LC}$ At resonance ${\displaystyle Z_{L}=-Z_{C}}$ ${\displaystyle \omega _{o}={\sqrt {\frac {1}{T}}}}$ ${\displaystyle T=LC}$ ${\displaystyle V_{L}=-V_{C}}$ ${\displaystyle v(\theta )=A\sin(\omega _{o}t+2\pi )-A\sin(\omega _{o}t-2\pi )}$