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Electric Oscillations

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?

Reveal Answer
 4.117. I=V0Lte−t/LC;I=Imax⁡=V0eCL at the moment tm=LC\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}
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