All Problems Electric Oscillations
Problem 4.131
A series circuit consisting of a capacitor and a coil with active resistance is connected to a source of harmonic voltage whose frequency can be varied, keeping the voltage amplitude constant. At frequencies \(\omega_{1}\) and \(\omega_{2}\) the current amplitudes are \(n\) times less than the resonance amplitude. Find: (a) the resonance frequency; (b) the quality factor of the circuit.
(a) \(\omega_{0}=\sqrt{\omega_{1} \omega_{2}}\) (b) \(Q=\sqrt{\frac{\omega_{1} \omega_{2}\left(n^{2}-1\right)}{\left(\omega_{2}-\omega_{1}\right)^{2}}-\frac{1}{4}}\).