In the realm of electrical circuits, LC oscillations play a significant role. These oscillations occur when a charged capacitor is linked with an inductor, causing the electric current and the capacitor's charge to oscillate. The initial charge, also known as q m , stored in the capacitor , provides the electrical energy.
This can be expressed as,
At the beginning, the inductor holds no energy. The charge fluctuates sinusoidally with time.
When the circuit is activated, the current begins to rise while the capacitor's charge starts to decrease. This current flow induces a magnetic field within the inductor. When the current reaches its peak, denoted as I m , the magnetic energy in the circuit can be represented as:
As the magnetic field begins to diminish over time due to no further change in the inductor's current, it induces a current in the circuit. With reversed polarity , the current starts recharging the capacitor. This cycle repeats once the capacitor is fully charged as per its previous state. As a result, the energy in the system oscillates between the capacitor and the inductor.
After applying Kirchhoff’s law to the circuit, we find that the charge oscillates at a natural frequency.
However, it is important to note that this entire process is theoretical and cannot be achieved in reality. This discrepancy arises due to energy loss caused by resistance in the circuit and radiation in the form of electromagnetic waves.