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 ω1\omega_{1} and ω2\omega_{2} the current amplitudes are nn times less than the resonance amplitude. Find: (a) the resonance frequency; (b) the quality factor of the circuit.

Reveal Answer
(a) ω0=ω1ω2\omega_{0}=\sqrt{\omega_{1} \omega_{2}} (b) Q=ω1ω2(n21)(ω2ω1)214Q=\sqrt{\frac{\omega_{1} \omega_{2}\left(n^{2}-1\right)}{\left(\omega_{2}-\omega_{1}\right)^{2}}-\frac{1}{4}}.