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 $\omega=1000$ $\mathrm{s}^{-1}$ ?
$1 \mathrm{mH}$
cannot be calculated unless $R$ is known
$10 \mathrm{mH}$
$100 \mathrm{mH}$.
Solution
According to question current is maximum at resonance
$\begin{aligned}
\Rightarrow \quad \omega^2 & =\frac{1}{L C} \\
\Rightarrow \quad L & =\frac{1}{\omega^2 C} \\
& =\frac{1}{(1000)^2\left(10 \times 10^{-6}\right)} \\
& =0.1 \mathrm{H}=100 \mathrm{mH}
\end{aligned}$