All Problems

Electric Oscillations

Problem 4.96

An oscillating circuit consists of a capacitor with capacitance C,C, a coil of inductance LL with negligible resistance, and a switch. With the switch disconnected, the capacitor was charged to a voltage VmV_{m} and then at the moment t=0t=0 the switch was closed. Find: (a) the current II (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.

Reveal Answer
4.96. (a) I=Imsin⁡ω0t,I=I_{m} \sin \omega_{0} t, where Im=VmC/L,ω0=1/VLC‾;I_{m}=V_{m} \sqrt{C / L}, \quad \omega_{0}=1 / V \overline{L C} ; (b) ES=Vm/2\mathscr{E}_{S}=V_{m} / \sqrt{2}
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