LC Circuit Energy Conservation
This simulation demonstrates how the sum of energies stored in the capacitor and inductor remains constant in a free LC oscillation circuit, as shown in Example 7.11.
Capacitor Energy (UE)
0.00 J
UE = ½ q²/C
Inductor Energy (UM)
0.00 J
UM = ½ L i²
Total Energy
0.00 J
UE + UM = constant
Explanation (from Example 7.11):
In an LC circuit, energy oscillates between the capacitor and inductor. The capacitor energy is maximum when the inductor energy is zero, and vice versa. However, their sum remains constant over time, equal to the initial energy stored in the capacitor.
Mathematically: UE + UM = (q₀²/2C)[cos²(ωt) + sin²(ωt)] = q₀²/2C (since cos² + sin² = 1)
