Alternating Current

JEE Main level, numerical answer, medium

67 of 190

Question 67 of 190

For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is 25nF25 \mathrm{nF}. If resistance of 200Ω200 \Omega and 100mH100 \mathrm{mH} inductor is being used in the given circuit. The frequency of ac source is ______ ×103 Hz\times 10^3 \mathrm{~Hz}. (given π2=10\pi^2=10 )

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Answer: 10

f0=12πL×Cf0=12π100×10−3×25×10−9=12π25×10−10=12π×5×105×10 Hz=10010×103 Hzf0=10×103 Hz\begin{aligned} & \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 25 \times 10^{-9}}} \\ & =\frac{1}{2 \pi \sqrt{25 \times 10^{-10}}} \\ & =\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}\end{aligned}

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