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GUJCET · Physics · Alternating Current
A charged \(10 \mu \mathrm{~F}\) capacitor is connected to a 16 mH inductor. What is the angular frequency of free oscillations of the circuit ?
- A \(250 \mathrm{rad} \mathrm{s}^{-1}\)
- B \(25 \mathrm{rad} \mathrm{s}^{-1}\)
- C \(1111 \mathrm{rad} \mathrm{s}^{-1}\)
- D \(2500 \mathrm{rad} \mathrm{s}^{-1}\)
Answer & Solution
Correct Answer
(D) \(2500 \mathrm{rad} \mathrm{s}^{-1}\)
Step-by-step Solution
Detailed explanation
(D) \(2500 \mathrm{rad} \mathrm{s}^{-1}\)
angular frequency of free oscillations
\(\omega_{0}=\frac{1}{\sqrt{\mathrm{LC}}}\)
\(\omega_{0}=\frac{1}{\sqrt{16 \times 10^{-3} \times 10 \times 10^{-6}}}\)
\(\omega_{0}=\frac{10^{4}}{4}\)
\(\omega_{0}=2500 \mathrm{rad} \mathrm{s}^{-1}\)
angular frequency of free oscillations
\(\omega_{0}=\frac{1}{\sqrt{\mathrm{LC}}}\)
\(\omega_{0}=\frac{1}{\sqrt{16 \times 10^{-3} \times 10 \times 10^{-6}}}\)
\(\omega_{0}=\frac{10^{4}}{4}\)
\(\omega_{0}=2500 \mathrm{rad} \mathrm{s}^{-1}\)
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