In an ideal lossless LC oscillator (no resistance), what is the qualitative behavior of energy exchange between electric and magnetic forms, and what is the period?

In an ideal lossless LC oscillator (no resistance), what is the qualitative behavior of energy exchange between electric and magnetic forms, and what is the period?

• A. Energy oscillates between capacitor (electric) and inductor (magnetic) with total energy constant; T = 2π √(L C)
• B. Energy remains entirely in the capacitor; period undefined
• C. Energy decays exponentially; T = 2π √(L C)
• D. Energy oscillates but total energy increases with time; T = π √(L C)

Answer: (A)

In an ideal lossless LC oscillator, energy shuttles back and forth between the electric field of the capacitor and the magnetic field of the inductor, while the total energy stays constant. As the capacitor discharges, energy moves into the inductor; when the current reaches its peak, all energy is magnetic, then it flows back to recharge the capacitor in the opposite sense, and the cycle repeats. This motion follows a simple harmonic equation for the charge q: q'' + (1/LC) q = 0, which gives an angular frequency ω = 1/√(LC). The period is then T = 2π/ω = 2π√(LC). This describes why the energy is exchanged rather than confined to just one element, and why the period depends only on the inductance and capacitance. The other views either imply energy remaining entirely in one component, energy decaying due to loss, or energy increasing without a source—none of which happen in an ideal LC circuit.

In an ideal lossless LC oscillator, energy shuttles back and forth between the electric field of the capacitor and the magnetic field of the inductor, while the total energy stays constant. As the capacitor discharges, energy moves into the inductor; when the current reaches its peak, all energy is magnetic, then it flows back to recharge the capacitor in the opposite sense, and the cycle repeats. This motion follows a simple harmonic equation for the charge q: q'' + (1/LC) q = 0, which gives an angular frequency ω = 1/√(LC). The period is then T = 2π/ω = 2π√(LC).

This describes why the energy is exchanged rather than confined to just one element, and why the period depends only on the inductance and capacitance. The other views either imply energy remaining entirely in one component, energy decaying due to loss, or energy increasing without a source—none of which happen in an ideal LC circuit.