Medium
Write the formula of resonant frequency.
(N/A) In an $LCR$ series circuit,resonance occurs when the inductive reactance $(X_L)$ equals the capacitive reactance $(X_C)$.
Given $X_L = X_C$,we have $\omega L = \frac{1}{\omega C}$.
Rearranging for angular frequency $\omega$,we get $\omega^2 = \frac{1}{LC}$,which implies $\omega = \frac{1}{\sqrt{LC}}$.
Since $\omega = 2\pi f$,the resonant frequency $f_r$ is given by $f_r = \frac{1}{2\pi \sqrt{LC}}$.
Given $X_L = X_C$,we have $\omega L = \frac{1}{\omega C}$.
Rearranging for angular frequency $\omega$,we get $\omega^2 = \frac{1}{LC}$,which implies $\omega = \frac{1}{\sqrt{LC}}$.
Since $\omega = 2\pi f$,the resonant frequency $f_r$ is given by $f_r = \frac{1}{2\pi \sqrt{LC}}$.
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