What energy forms are exchanged in an ideal LC circuit?

State the natural angular frequency of an ideal LC circuit.

State the period of an ideal LC circuit.

An LC circuit has \(L=0.20\,\mathrm{H}\) and \(C=50\,\mu\mathrm{F}\). Find \(\omega_0\).

For the LC circuit with \(L=0.20\,\mathrm{H}\) and \(C=50\,\mu\mathrm{F}\), find the period.

State the total energy in an ideal LC circuit in terms of \(q\), \(C\), \(L\), and \(I\).

At the instant capacitor charge is maximum in an ideal LC circuit, what is the current?

At the instant capacitor charge is zero in an ideal LC circuit, what is true about the current?

A capacitor with \(C=10\,\mu\mathrm{F}\) is initially charged to \(12\,\mathrm{V}\) and connected to an ideal inductor. Find the initial energy.

Using the energy from the previous question with \(L=0.20\,\mathrm{H}\), find the maximum current.

Derive the LC oscillator equation for charge.

Why does an ideal LC circuit oscillate rather than settle?

How does \(\omega_0\) change if the capacitance is quadrupled while \(L\) is fixed?

How does the period change if both \(L\) and \(C\) are doubled?

An LC circuit has maximum capacitor charge \(Q=4.0\,\mu\mathrm{C}\), \(L=0.50\,\mathrm{H}\), and \(C=20\,\mu\mathrm{F}\). Find \(I_{\max}\).

If \(q(t)=Q\cos\omega_0t\), write the current \(I(t)\).

Why are charge and current out of phase in an LC oscillator?

An LC circuit has \(L=0.10\,\mathrm{H}\). What capacitance gives \(f=1.0\,\mathrm{kHz}\)?

At some instant in an ideal LC circuit, \(q=Q/2\). What fraction of the total energy is magnetic?

Explain why the LC circuit is mathematically analogous to a mass-spring oscillator.