KCET · Physics · Alternating Current
In the given circuit, the resonant frequency is
- A \(15.92 \mathrm{~Hz}\)
- B \(159.2 \mathrm{~Hz}\)
- C \(1592 \mathrm{~Hz}\)
- D \(15910 \mathrm{~Hz}\)
Answer & Solution
Correct Answer
(C) \(1592 \mathrm{~Hz}\)
Step-by-step Solution
Detailed explanation
Given, \(L=0.5 \mathrm{mH}=0.5 \times 10^{-3} \mathrm{H}\) and \(C=20 \mu \mathrm{F}=20 \times 10^{-6} \mathrm{~F}\)
The resonant frequency of \(L-C\) circuit is
\(\begin{aligned}
f &=\frac{1}{2 \pi \sqrt{L C}}=\frac{1}{2 \pi \sqrt{0.5 \times 10^{-3} \times 20 \times 10^{-6}}} \\
&=\frac{1}{2 \pi \times \sqrt{10 \times 10^{-9}}}=\frac{10^{4}}{2 \pi}=1592.3 \simeq 1592 \mathrm{~Hz}
\end{aligned}\)
The resonant frequency of \(L-C\) circuit is
\(\begin{aligned}
f &=\frac{1}{2 \pi \sqrt{L C}}=\frac{1}{2 \pi \sqrt{0.5 \times 10^{-3} \times 20 \times 10^{-6}}} \\
&=\frac{1}{2 \pi \times \sqrt{10 \times 10^{-9}}}=\frac{10^{4}}{2 \pi}=1592.3 \simeq 1592 \mathrm{~Hz}
\end{aligned}\)
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