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Resonance in Series LCR Circuit
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What is the value of inductance $L$ for which the current is maximum in a series LCR circuit with $C = 10\,\mu F$ and $\omega = 1000$ s$^{-1}$?The current in a series LCR circuit is maximum at resonance, when the inductive reactance equals the capacitive reactance: $\omega L = \dfrac{1}{\omega C}$
The condition is $\omega = \dfrac{1}{\sqrt{LC}}$; it does not involve $R$.
$1000 = \dfrac{1}{\sqrt{L(10 \times 10^{-6})}}$
$L = \dfrac{1}{\omega^2 C} = \dfrac{1}{(1000)^2 \times 10 \times 10^{-6}}$
$L = \dfrac{1}{10} = 0.1$ H
$\Rightarrow L = 100$ mH