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An ideal LC circuit oscillates freely. If $L = 4\,\text{mH}$ and $C = 25\,\mu\text{F}$, the angular frequency of oscillation is:
A$10^3\,\text{rad/s}$
B$10^5\,\text{rad/s}$
C$10^2\,\text{rad/s}$
D$10^4\,\text{rad/s}$
Answer & Solution
Correct answer: A. $10^3\,\text{rad/s}$
For a free LC oscillation $\omega = 1/\sqrt{LC}$. $LC = 4 \times 10^{-3} \times 25 \times 10^{-6} = 10^{-7}\,\text{s}^2$, so $\sqrt{LC} = 10^{-3.5}\,\text{s}$ and $\omega = 10^{3.5} \approx 3162\,\text{rad/s}$. Rounded to the nearest power of ten this is $10^3\,\text{rad/s}$.
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