An LCR series circuit of capacitance 62.5 nF and resistance of , 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 )

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Solution

Q.
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 $π^{2} = 10$ ) [2023]

Ans.
(100)

$C = 62.5 nF, R = 50 Ω, f = 2 kHz$

$i_{\max} condition is Z_{\min} (resonance condition)$

$f = \frac{1}{2 π \sqrt{L C}}$

$L = \frac{1}{4 π^{2} f^{2} C} = \frac{1}{4 \times 10 \times 4 \times 10^{6} \times 62.5 \times 10^{- 9}} = 100 mH$

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