An LCR series circuit with L=100 mH, C= 100 μF, R=10 Ω is connected to an AC source of emf 220 V. The resonant frequency of the circuit will be nearly
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $50\, Hz$
Given:
$L=100\,\text{mH}=0.1\,\text{H}$
$C=100\,\mu\text{F}=1\times10^{-4}\,\text{F}$
Resonant\ frequency:
$f_0=\frac{1}{2\pi\sqrt{LC}}$
Compute $\sqrt{LC}$:
$LC=0.1\times10^{-4}=10^{-5}$
$\sqrt{LC}=\sqrt{10^{-5}}=3.1623\times10^{-3}$
Therefore:
$f_0=\frac{1}{2\pi\times3.1623\times10^{-3}}\approx50.3\,\text{Hz}$
Answer: $f_0\approx50\,\text{Hz}$