What is the value of inductance $L$ for which the current is maximum in a series LCR circuit with $C=10 \mu…

What is the value of inductance $L$ for which the current is maximum in a series LCR circuit with $C=10 \mu \mathrm{F}$ and $\omega=1000$ $\mathrm{s}^{-1}$ ?
  1. $1 \mathrm{mH}$
  2. cannot be calculated unless $R$ is known
  3. $10 \mathrm{mH}$
  4. $100 \mathrm{mH}$.

Solution

According to question current is maximum at resonance $\begin{aligned} \Rightarrow \quad \omega^2 & =\frac{1}{L C} \\ \Rightarrow \quad L & =\frac{1}{\omega^2 C} \\ & =\frac{1}{(1000)^2\left(10 \times 10^{-6}\right)} \\ & =0.1 \mathrm{H}=100 \mathrm{mH} \end{aligned}$

Asked in: NEET 2007

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