Problem 4.117

A circuit consists of a capacitor with capacitance $C$ and a coil of inductance $L$ connected in series, as well as a switch and a resistance equal to the critical value for this circuit. With the switch disconnected, the capacitor was charged to a voltage $V_{0},$ and at the moment $t=0$ the switch was closed. Find the current $I$ in the circuit as a function of time $t .$ What is $I_{\max }$ equal to?

\begin{aligned} &\text { 4.117. } I=\frac{V_{0}}{L} t \mathrm{e}^{-t / \sqrt{L C} ;} I=I_{\max }=\frac{V_{0}}{\mathrm{e}} \sqrt{\frac{C}{L}} \text { at the moment }\\ &t_{m}=\sqrt{L C} \end{aligned}

Electric Oscillations