JEE Mains · Physics · STD 12 -Alternating current
- JEE Mains 2024
- Hard
- Numerical
For a given series \(LCR\) circuit it is found that maximum current is drawn when value of variable capacitance is \(2.5 \mathrm{nF}\). If resistance of \(200 \Omega\) and \(100 \mathrm{mH}\) inductor is being used in the given circuit. The frequency of ac source is _______ \(\times 10^3 \mathrm{~Hz}\). (given \(\pi^2=10\) )
Pick an option to check your answer.
Answer & Solution
Correct Answer
(B) \(10\)
Step-by-step Solution
Detailed explanation
for maximum current, circuit must be in resonance
\(\mathrm{f}_0=\frac{1}{2 \pi \sqrt{\mathrm{L} \times \mathrm{C}}}\)
\(\mathrm{f}_0=\frac{1}{2 \pi \sqrt{100 \times 10^{-3} \times 2.5 \times 10^{-9}}}\)
\(=\frac{1}{2 \pi \sqrt{25 \times 10^{-11}}}\)
\(=\frac{1}{2 \pi \times 5} \times 10^5 \times \sqrt{10} \mathrm{~Hz}\)
\(=\frac{100}{10} \times 10^3 \mathrm{~Hz}\)
\(\mathrm{f}_0=10 \times 10^3 \mathrm{~Hz}\)
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