Pyq- Electromagnetic Induction & Alternating Currents L-3

Question: In a series LCR circuit, the inductance $L$ is $10 \mathrm{mH}$, capacitance $C$ is $1 \mu \mathrm{F}$ and resistance $R$ is $100 \Omega$. The frequency at which resonance occurs is :- (NEET-2023)#

A) $15.9 \hspace{1 mm} \mathrm{kHz}$

B) $1.59 \hspace{1 mm} \mathrm{rad} / \mathrm{s}$

C) $1.59 \hspace{1 mm} \mathrm{kHz}$

D) $15.9 \hspace{1 mm} \mathrm{rad} / \mathrm{s}$

Answer: $1.59 \hspace{1 mm} \mathrm{kHz}$#

Explanation#

$\mathrm{L}=10 \times 10^{-3} \mathrm{H}$

$\mathrm{C}=1 \times 10^{-6} \mathrm{~F}$

$\mathrm{R}=100 \Omega$

At resonance $X_L=X_c$

$\omega \mathrm{L}=\frac{1}{\omega \mathrm{C}}$

$\mathrm{f}=\frac{1}{2 \pi \sqrt{\mathrm{LC}}}=\frac{1}{2 \pi \sqrt{10 \times 10^{-3} \times 10^{-6}}}=1.59 \mathrm{KHz}$