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The resonant frequency of an LC circuit with $L = 100\,\text{mH}$ and $C = 1\,\mu\text{F}$ is closest to
A$50\,\text{Hz}$
B$160\,\text{Hz}$
C$503\,\text{Hz}$
D$5\,\text{kHz}$
Answer & Solution
Correct answer: C. $503\,\text{Hz}$
1. Resonance: $f_0 = \dfrac{1}{2\pi\sqrt{LC}}$.
2. $L = 100\,\text{mH} = 0.1\,\text{H}$; $C = 1\,\mu\text{F} = 10^{-6}\,\text{F}$.
3. $LC = 0.1 \times 10^{-6} = 10^{-7}$.
4. $\sqrt{LC} = \sqrt{10^{-7}} = 3.162\times 10^{-4}\,\text{s}$.
5. $f_0 = 1/(2\pi \cdot 3.162\times 10^{-4}) = 1/(1.987\times 10^{-3}) = 503.3\,\text{Hz}$.
6. Other options are off by orders of magnitude or wrong calculations.
_Source: Tony Kuphaldt, "Lessons in Electric Circuits — AC", Vol II, Ch 6 (Resonance numerical)._
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