= Solution
With <phasors> proportional to $e^{i\omega t}$, the series <RLC circuit> has
$$
Z=R+i\left(\omega L-\frac1{\omega C}\right),\qquad I_0=\frac{V_0}{\sqrt{R^2+(\omega L-1/(\omega C))^2}}.
$$
For fixed $V_0$ and frequency-independent positive $R$, the maximum occurs when the reactances cancel. Thus
$$
\boxed{\omega_0=\frac1{\sqrt{LC}},\qquad I_{0,\max}=\frac{V_0}{R}.}
$$
This is the driven current <resonance>; a damped free-oscillation frequency is a different quantity.
Back to article page
