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

$$X_L = \omega L = 100 \times 0.1 = 10\ \Omega$$

$$X_C = \frac{1}{\omega C} = \frac{1}{100 \times 10^{-4}} = 100\ \Omega$$

$$Z = \sqrt{120^2 + (10 - 100)^2} = \sqrt{120^2 + (-90)^2} = 150\ \Omega$$

$$I_0 = \frac{V_0}{Z} \implies I_0 = \frac{30}{150} = 0.2\text{ A}$$

$$f_r = \frac{1}{2\pi\sqrt{LC}} \implies f_r = \frac{1}{2\pi\sqrt{0.1 \times 10^{-4}}} = \frac{1}{2\pi\sqrt{10^{-5}}} = \frac{100\sqrt{10}}{2\pi} \approx 50.3\text{ Hz} \approx 50\text{ Hz}$$