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(B) The impedance of an $LCR$ series circuit is minimum at the resonant frequency, where the inductive reactance equals the capacitive reactance $(X_L

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(B) The impedance of an $LCR$ series circuit is minimum at the resonant frequency, where the inductive reactance equals the capacitive reactance $(X_L = X_C)$.The resonant angular frequency is given by $\omega = \frac{1}{\sqrt{LC}}$.Given: $L = \frac{25}{\pi^2} 	imes 10^{-3} 	ext{ H}$, $C = 0.1 	imes 10^{-6} 	ext{ F}$.Substituting the values:$\omega = \frac{1}{\sqrt{\frac{25}{\pi^2} 	imes 10^{-3} 	imes 0.1 	imes 10^{-6}}} = \frac{1}{\sqrt{\frac{2.5}{\pi^2} 	imes 10^{-9}}} = \frac{1}{\sqrt{\frac{25}{\pi^2} 	imes 10^{-10}}} = \frac{\pi}{5 	imes 10^{-5}} = \frac{\pi}{5} 	imes 10^5 	ext{ rad/s}$.Since $\omega = 2\pi f$, we have $2\pi f = \frac{\pi}{5} 	imes 10^5$.$f = \frac{10^5}{10} = 10^4 	ext{ Hz} = 10 	ext{ kHz}$.

$A$ resistor of $100 \Omega$, an inductor of $\frac{25}{\pi^2} \text{ mH}$ and a capacitor of $0.1 \mu\text{F}$ are connected in series to an $AC$ source. The impedance of the circuit is minimum for a frequency of (in $\text{ kHz}$)

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