Why Does An LC Circuit Stop Oscillating When The Capacitor Is Totally Discharged?

In an LC circuit, consisting of an inductor (L) and a capacitor (C), oscillations occur due to the exchange of energy between the electric field of the capacitor and the magnetic field of the inductor. This article delves into the detailed reasons why oscillations stop when the capacitor is fully discharged.

Energy Transfer

In the initial stages, the capacitor, charged with electrical energy in the form of an electric field, begins to transfer this energy to the inductor. This creates a magnetic field around the inductor. The oscillation is a result of the continuous transfer of energy between the capacitor and the inductor, back and forth.

Capacitor Discharge

As the capacitor discharges, the voltage across it decreases, and the current through the inductor increases. This process continues until the capacitor is fully discharged, meaning it has no voltage and, consequently, no stored energy.

Maximum Current

At the point of full discharge, the current in the circuit reaches its maximum value. Since the capacitor has no charge left, it cannot store any more energy. The inductor, which has stored magnetic energy due to the current, then releases this energy back into the circuit.

Energy Loss

In a real LC circuit, resistive losses due to resistance in the wires, the inductor, or other components always exist. Once the capacitor is fully discharged, there is no longer any energy to sustain the oscillations. The energy stored in the inductor is gradually dissipated as heat in the resistive components, ultimately stopping the oscillations.

Damping

In the presence of resistance, damping occurs, and the oscillations decay exponentially over time. The resistance in the circuit absorbs the energy, causing the oscillations to stop completely.

Energy Exchange in Ideal Lossless LC Circuits

Contrary to the real-world scenarios, in an ideal lossless LC circuit, there are no resistive losses. The inductor and capacitor alternate in transferring their stored energy, theoretically sustaining indefinitely.

The stored charge in the capacitor discharges into the inductor, which stores this charge in the magnetic field induced by the current. When the magnetic field of the inductor collapses, the current induced in the inductor's windings recharges the capacitor. This cycle continues, ensuring that all the stored energy in one component is completely transferred to the other.

For example, when the capacitor is fully discharged, meaning the voltage across the capacitor and the current flowing out of the capacitor are zero, the inductor's magnetic field is at its maximum, indicating that the inductor is fully charged.

In a lossless LC circuit, neither the inductor nor the capacitor has any resistance that would dissipate energy as heat and damp out the oscillation. Therefore, the alternating exchange of reactive energy between the two components continues indefinitely. The initial oscillations require external supplies of reactive energy, but no additional energy is needed after that.

Understanding the behavior of LC circuits is crucial for engineers and scientists working in fields such as electronics, radio engineering, and physics.