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(A) The resonant frequency $f_r$ of an $LCR$ series circuit is given by the formula: $f_r = \frac{1}{2 \pi \sqrt{LC}}$.Given values are $L = 1 	ext{

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$15.9$

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(A) The resonant frequency $f_r$ of an $LCR$ series circuit is given by the formula: $f_r = \frac{1}{2 \pi \sqrt{LC}}$.Given values are $L = 1 	ext{ mH} = 10^{-3} 	ext{ H}$ and $C = 0.1 \mu	ext{F} = 0.1 	imes 10^{-6} 	ext{ F} = 10^{-7} 	ext{ F}$.Substituting these values into the formula:$\sqrt{LC} = \sqrt{10^{-3} 	imes 10^{-7}} = \sqrt{10^{-10}} = 10^{-5}$.Now, $f_r = \frac{1}{2 \pi 	imes 10^{-5}} = \frac{10^5}{2 	imes 3.14159} \approx \frac{100000}{6.283} \approx 15915.5 	ext{ Hz}$.Converting to kHz, $f_r \approx 15.9 	ext{ kHz}$.Therefore, the correct option is $A$.

An $AC$ circuit contains a resistance of $1 \text{ k}\Omega$, a capacitor of $0.1 \mu\text{F}$, and an inductor of $1 \text{ mH}$ connected in series. The resonance frequency of the circuit is approximately: (in $kHz$)

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