A capacitor is charged to a potential of V₀. It is connected with an inductor through a switch S. The switch is closed at time t = 0. Which of the following statement(s) is/are correct?

LC circuit, $\mathrm{q}={\mathrm{q}}_0\cos \mathrm{\omega t}\text{ and }\mathrm{V}={\mathrm{V}}_0\cos \mathrm{\omega t}$

Where $\mathrm{\omega }=\frac{1}{\sqrt{\mathrm{LC}}},\mathrm{i}=\frac{\mathrm{dq}}{\mathrm{dt}}=-{\mathrm{q}}_0\mathrm{\omega sin}\mathrm{\omega t}$

a) ${\mathrm{i}}_{max}={\mathrm{q}}_0\mathrm{\omega }={\mathrm{V}}_0\sqrt{\frac{\mathrm{C}}{\mathrm{L}}}$

b) V in C is zero first time after  $\mathrm{t}=\frac{\mathrm{T}}{4}=\frac{\mathrm{\pi }}{2}\sqrt{\mathrm{LC}}$.

c) at time $\mathrm{t}=\frac{\mathrm{\pi }}{2}\sqrt{\mathrm{LC}}=\frac{\mathrm{T}}{4}$ energy in C is zero and ${\mathrm{U}}_{\mathrm{i}}=\frac{1}{2}{\mathrm{CV}}_0^2$ stored in the inductor.

d) ${\mathrm{U}}_{max}=\frac{1}{2}{\mathrm{CV}}_0^2\text{ in }\mathrm{L}$.