Find the peak current and resonant frequency of the following circuit (as shown in figure).

\(x _{ L }=\omega_{ L }=100 \times 100 \times 10^{-3}=10 \, \Omega\)

\(x _{ C }=\frac{1}{\omega_{ C }}=\frac{1}{100 \times 100 \times 10^{-6}}=10\, \Omega\)

\(z=\sqrt{(10-100)^{2}+R^{2}}=\sqrt{90^{2}+120^{2}}\)

\(=30 \times 5=150\, \Omega\)

\(i _{ peal }=\frac{\Delta v }{ z }=\frac{30}{150}=\frac{1}{5} amp =0.2\,amp\)

And For resonant frequency

\(\Rightarrow \omega L =\frac{1}{\omega C } \Rightarrow \omega^{2}=\frac{1}{ LC } \Rightarrow \omega=\frac{1}{\sqrt{ LC }}\)

And \(f=\frac{1}{2 \pi \sqrt{L C}} \Rightarrow \frac{1}{2 \pi \sqrt{100 \times 10^{-3} \times 100 \times 10^{-6}}}\)

\(=\frac{100 \sqrt{10}}{2 \pi}=\frac{100 \pi}{2 \pi}=50\, Hz\)

as \(\sqrt{10} \approx \pi\)