All Problems Electric Oscillations
Problem 4.96
An oscillating circuit consists of a capacitor with capacitance \(C,\) a coil of inductance \(L\) with negligible resistance, and a switch. With the switch disconnected, the capacitor was charged to a voltage \(V_{m}\) and then at the moment \(t=0\) the switch was closed. Find: (a) the current \(I\) (t) in the circuit as a function of time; (b) the emf of self-inductance in the coil at the moments when the electric energy of the capacitor is equal to that of the current in the coil.
4.96. (a) \(I=I_{m} \sin \omega_{0} t,\) where \(I_{m}=V_{m} \sqrt{C / L}, \quad \omega_{0}=1 / V \overline{L C} ;\) (b) \(\mathscr{E}_{S}=V_{m} / \sqrt{2}\)