Resonant frequency of LCR circuit – Rankers Physics
Topic: Alternating Current
Subtopic: LR, RC and LCR Circuits

Resonant frequency of LCR circuit

A series LCR circuit contains a capacitor of capacitance \(10^{-6}\text{ F}\) and an inductor of inductance \(10^{-4}\text{ H}\). The resonant frequency of the circuit will be
\(10^5\text{ Hz}\)
\(10\text{ Hz}\)
\(\frac{10^5}{2\pi}\text{ Hz}\)
\(\frac{10}{2\pi}\text{ Hz}\)

Solution:

The resonant frequency of a series LCR circuit is given by \(f_0 = \frac{1}{2\pi\sqrt{LC}}\). Substituting values: \(f_0 = \frac{1}{2\pi\sqrt{10^{-4} \times 10^{-6}}} = \frac{10^5}{2\pi}\text{ Hz}\).

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