Explanation of the Electrical Oscillation

When a capacitor is discharge through an inductance, electrical oscillations of constant amplitude q0 (the initial charge on the capacitor) are produced in the circuit. The production of oscillations can be explained in the following way:
In the beginning when the capacitor is fully charged, an amount of energy 1/2 q20/C is stored in the electric field between its plates. When the circuit is closed, the capacitor begins to discharge through the inductance L, causing a current is closed, the capacitor begins to discharge through the inductance L, causing a current to flow. As the current rises from zero, it builds up a magnetic field around the inductance.


When the current has reached its maximum value i0, the energy stored in the magnetic field is 1/2 Li20. At the same, time, the capacitor has completely discharged and the p.d. between its plates has reduced to zero. Thus the energy of the electric field between the capacitor plates in transferred to the magnetic field. The current, however does not stop instantaneously but continuous to flow for some time while the magnetic field dies down. By Lenz’s law, the duying magnetic field induces an emf in the inductance an emf in the inductance in the same direction as the current. The current therefore persists, and now charges the capacitor in the opposite sense until the magnetic field has disappeared. Thus the energy is once again stored as 1/2 q20/C in the electric field between the capacitor plates. The process now repeats itself in the reverse direction and the charger on the capacitor surges back and for the indefinitely. In other word, electric oscillations take place indefinitely.

The electrical oscillations in an LC circuit can be very well compared with the oscillations of a mass of a spring.

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