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  4. An LCR series circuit of capacitance 62.5 nF and resistance of 50 Ω. is connected to an A.C. source of frequency 2.0 kHz. For maximum value of amplitude of current in circuit, the value of inductance is mH. (Take .π2=10)

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Q. An LCR series circuit of capacitance $62.5\, nF$ and resistance of $50\, \Omega$. is connected to an A.C. source of frequency $2.0\,kHz$. For maximum value of amplitude of current in circuit, the value of inductance is ___$mH$.
(Take $\left.\pi^2=10\right)$

JEE MainJEE Main 2023Alternating Current

Solution:

$ f =\frac{1}{2 \pi \sqrt{ LC }} $
$ 2000\, Hz =\frac{1}{2 \pi \sqrt{ L \times 62.5 \times 10^{-9}}}$
$ L =\frac{1}{4 \pi^2 \times 2000^2 \times 62.5 \times 10^{-9}}=0.1 H =100\, mH $