14.5 Oscillations in an LC Circuit

The angular frequency of the oscillations in an LC circuit is $2.0 \times 10^{3}$ rad/s. (a) If $L = 0.10 \text{H}$, what is C? (b) Suppose that at $t = 0 ,$ all the energy is stored in the inductor. What is the value of $\phi ?$ (c) A second identical capacitor is connected in parallel with the original capacitor. What is the angular frequency of this circuit?

Do Kirchhoff’s rules apply to circuits that contain inductors and capacitors?

In an LC circuit, what determines the frequency and the amplitude of the energy oscillations in either the inductor or capacitor?

The self-inductance and capacitance of an LC circuit are 0.20 mH and 5.0 pF. What is the angular frequency at which the circuit oscillates?

In an oscillating LC circuit, the maximum charge on the capacitor is $2.0 \times 10^{−6} \text{C}$ and the maximum current through the inductor is 8.0 mA. (a) What is the period of the oscillations? (b) How much time elapses between an instant when the capacitor is uncharged and the next instant when it is fully charged?

In an oscillating LC circuit, the maximum charge on the capacitor is $q_{m}$. Determine the charge on the capacitor and the current through the inductor when energy is shared equally between the electric and magnetic fields. Express your answer in terms of $q_{m}$, L, and C.

An LC circuit in an AM tuner (in a car stereo) uses a coil with an inductance of 2.5 mH and a variable capacitor. If the natural frequency of the circuit is to be adjustable over the range 540 to 1600 kHz (the AM broadcast band), what range of capacitance is required?