Physics

Problem

Which of the following gives the resonant angular frequency

\omega_0

of a series LCR circuit having inductance

L

and capacitance

C

? a)

\displaystyle \frac{1}{2\pi\sqrt{LC}}

\displaystyle \frac{2\pi}{\sqrt{LC}}

\displaystyle \frac{1}{\sqrt{LC}}

\displaystyle \frac{1}{\sqrt{2LC}}

Intuitive explanation

At resonance, the circuit's inductive and capacitive reactances cancel each other out, leaving only resistance to oppose the current. This happens at a special frequency where the energy sloshes back and forth between the magnetic field in $L$ and the electric field in $C$ with maximum efficiency. The key is setting $X_L = X_C$ (or equivalently, the imaginary part of impedance to zero) and solving for $\omega_0$ .

Intuitive explanation

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