(D) The angular frequency of free oscillations for an $LC$ circuit is given by the formula $\omega_{0} = \frac{1}{\sqrt{LC}}$.Given values are $L = 16

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(D) The angular frequency of free oscillations for an $LC$ circuit is given by the formula $\omega_{0} = \frac{1}{\sqrt{LC}}$.Given values are $L = 16 \text{ mH} = 16 \times 10^{-3} \text{ H}$ and $C = 10 \mu F = 10 \times 10^{-6} \text{ F}$.Substituting these values into the formula:$\omega_{0} = \frac{1}{\sqrt{16 \times 10^{-3} \times 10 \times 10^{-6}}}$$\omega_{0} = \frac{1}{\sqrt{16 \times 10^{-8}}}$$\omega_{0} = \frac{1}{4 \times 10^{-4}}$$\omega_{0} = \frac{10^{4}}{4} = 2500 \text{ rad s}^{-1}$.

Class 12 Physics Alternating Current LC Oscillations

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$A$ charged $10 \mu F$ capacitor is connected to a $16 \text{ mH}$ inductor. What is the angular frequency of free oscillations of the circuit?

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A
$250 \text{ rad s}^{-1}$
B
$25 \text{ rad s}^{-1}$
C
$1111 \text{ rad s}^{-1}$
D
$2500 \text{ rad s}^{-1}$

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$A$ charged $10 \mu F$ capacitor is connected to a $16 \text{ mH}$ inductor. What is the angular frequency of free oscillations of the circuit?

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