Resonant series RLC response
= Resonant series RLC response
{title2=$I_0(t)=V_M\sin(\omega_0t)/R$}
For a <series RLC circuit> driven by $V(t)=V_M\sin(\omega_0t)$ with $R>0$ and $\omega_0^2=1/(LC)$, substitution shows that $I_0=V_M\sin(\omega_0t)/R$ solves the current equation. The inductive and capacitive terms cancel at this <resonance>. Every homogeneous contribution decays, so every solution approaches this periodic response. Its <Q factor> is $L\omega_0/R$.