Physics - Capacitor Question with Solution | TestHub

In$LC$oscillation, energy is transferred$C \mathrm{t}\mathrm{o} L \mathrm{o}\mathrm{r} L \mathrm{t}\mathrm{o} C$, maximum energy in$L \mathrm{i}\mathrm{s}\frac{1}{2}L{I}_{max}^2$

Maximum energy in$C \mathrm{i}\mathrm{s}\frac{q_{max}^2}{2C}$

Energy will be equal when,

$\frac{1}{2}L{I}^2=\frac{1}{2}\frac{1}{2}L{I}_{max}^2\Rightarrow I=\frac{I_{max}}{\sqrt{2}}$

$I=I_{max}\sin \omega t=\frac{1}{\sqrt{2}}{I}_{max}$

$\omega t=\frac{\pi }{4}\Rightarrow \frac{2\pi }{T} t=\frac{\pi }{4}\Rightarrow t=\frac{T}{8}$

$t=\frac{1}{8}2\pi \sqrt{LC}=\frac{\pi }{4}\sqrt{LC}$

$\Rightarrow t=\frac{\pi }{4}\sqrt{LC}$