An $L-C$ circuit contains $196 \mathrm{pF}$ capacitor and a $441 \mu \mathrm{H}$ inductor. The frequency of…

An $L-C$ circuit contains $196 \mathrm{pF}$ capacitor and a $441 \mu \mathrm{H}$ inductor. The frequency of electromagnetic radiation emitted by antenna coupled to the $L-C$ circuit is
  1. $7.96 \times 10^5 \mathrm{~Hz}$
  2. $54.1 \times 10^5 \mathrm{~Hz}$
  3. $79.6 \times 10^5 \mathrm{~Hz}$
  4. $5.41 \times 10^5 \mathrm{~Hz}$

Solution

Given, capacitance, $C=196 \mathrm{pF}=196 \times 10^{-12} \mathrm{~F}$ Inductance, $L=441 \mu \mathrm{H}$ $ =441 \times 10^{-6} \mathrm{H} $ Since, frequency, $f=\frac{1}{2 \pi \sqrt{L C}}$ $ \begin{aligned} \therefore \quad f & =\frac{1}{2 \pi \sqrt{441 \times 10^{-6} \times 196 \times 10^{-12}}} \\ & =\frac{1}{2 \pi \times 14 \times 21 \times 10^{-9}} \\ & =5.41 \times 10^5 \mathrm{~Hz} \end{aligned} $

Asked in: AP EAMCET 2021 (23 Aug Shift 1)

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