Resonant Frequency of LCR Circuit – Rankers Physics

LR, RC and LCR Circuits: Practice Problem & Solution

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
\[10^5\text{ Hz}\]
\[10\text{ Hz}\]
\[\frac{10^5}{2\pi}\text{ Hz}\]
\[\frac{10}{2\pi}\text{ Hz}\]

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of LR, RC and LCR Circuits. Understanding the underlying formula is key to arriving at the correct answer below:

The resonant frequency is \[f = \frac{1}{2\pi\sqrt{LC}} = \frac{1}{2\pi\sqrt{10^{-4} \times 10^{-6}}} = \frac{10^5}{2\pi}\text{ Hz}\].

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