Physics

Physics

Problem

Which one of the following gives the angular resonant frequency ω0\omega_0 of an ideal series LC circuit? a) 12πLC\dfrac{1}{2\pi\sqrt{LC}} b) 2πLC\dfrac{2\pi}{\sqrt{LC}} c) 1LC\dfrac{1}{\sqrt{LC}} d) 12LC\dfrac{1}{\sqrt{2LC}}
Intuitive explanation

In a series LC circuit, energy oscillates back and forth between the magnetic field in the inductor and the electric field in the capacitor. The resonant frequency is the natural rate at which this energy exchange happens—determined entirely by how quickly the inductor can store/release energy and how readily the capacitor can charge/discharge. You'll find ω0\omega_0 by setting the inductive and capacitive reactances equal, or equivalently, by recognizing that at resonance the impedance is purely resistive (or minimal).

Intuitive explanation

In a series LC circuit, energy oscillates back and forth between the magnetic field in the inductor and the electric field in the capacitor. The resonant frequency is the natural rate at which this energy exchange happens—determined entirely by how quickly the inductor can store/release energy and how readily the capacitor can charge/discharge. You'll find ω0\omega_0 by setting the inductive and capacitive reactances equal, or equivalently, by recognizing that at resonance the impedance is purely resistive (or minimal).

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