Why Do Capacitors Discharge In Oscillator Circuits

In LC oscillations, after the discharge of the capacitor is complete, the magnetic flux linked with the inductor decreases. Why?

If an inductor is connected across a charged capacitor, current will start to flow through the inductor, building up a magnetic field around it and reducing the voltage on the capacitor. Eventually all the charge on the capacitor will be gone and the voltage across it will reach zero. However, the current will continue, because inductors resist changes in current. The current will begin to charge the capacitor with a voltage of opposite polarity to its original charge. Due to Faradays Law, the EMF which drives the current is caused by a decrease in the magnetic field, thus the energy required to charge the capacitor is extracted from the magnetic field. When the magnetic field is completely dissipated the current will stop and the charge will again be stored in the capacitor, with the opposite polarity as before. Then the cycle will begin again, with the current flowing in the opposite direction through the inductor.

Why in a L-C tank circuit, once the capacitor is fully charged, the charge on it doesn't remain stable?

An inductor draws current when a voltage is applied to it. When the capacitor is fully charged, the inductor current momentarily becomes zero, only to be subjected to a voltage in the opposite direction, which causes current flow in the direction opposite to the initial current flow. This process keeps repeating if the capacitor and the inductor are ideal.The charge cannot stabilise as long as there is an element that draws current. In a tank circuit, the energy keeps flowing from inductor to capacitor and capacitor to inductor in alternate half cycles. It can never be dissipated, so it stays in the circuit.

Why does an LC circuit stop the oscillation when the capacitor is totally discharged?

In an ideal (lossless) LC circuit, the inductor and capacitor alternately exchange their stored energy with each other, alternately charging and discharging, theoretically indefinitely.The stored charge in the capacitor discharges into the inductor, which stores that charge in the magnetic field that is induced by the current that flows out of the capacitor during he discharge process. As the inductor’s magnetic field collapses, the current which is induced in the inductor’s windings then (re)charges the capacitor, and so on.In either case, all of the stored energy in one component, is completely transferred to the other component. For example, when the capacitor is completely discharged (i.e., the voltage across the capacitor, and the current flowing out of the capacitor, is zero), the inductor’s magnetic field is at a maximum (i.e., the inductor is fully charged).In a lossless LC circuit, neither the inductor or the capacitor has any resistance that would otherwise dissipate energy as heat, and eventually damp out the oscillation. Thus the alternating exchange of reactive energy between the two, goes on indefinitely. Obviously the reactive energy to initiate the oscillation must be supplied initially, but (again, in an ideal, lossless LC circuit) no additional (external) energy is required after that.

How does a capacitor discharge when disconnected from a circuit?

Capacitors that can carry considerable charge - that are dangerous to touch - are equipped with a resistor across their terminals to allow them to discharge within a few seconds, when disconnected from their load. Smaller values of capacitors are allowed to leak down using their own leakage resistance.

Why is a capacitor used in an RC circuit?

An oscillator bounces energy back and forth between two energy storage means. For example, a pendulum bounces energy back and forth between kinetic energy (when the pendulum is moving fastest at the low point of its swing) and potential energy (when it comes to a stop at either end of its swing). Similarly, an RC circuit is an oscillator that bounces energy back and forth between the magnetic field of an induction coil (when maximum current is flowing) and the electric field between capacitor plates (when the voltage across the capacitor is maximum).

What does “if a charged capacitor C is short circuited through an inductor” mean?

If a charged capacitor is connected across inductor, capacitor discharge through inductor and current begins through inductor.As current begins to flow through inductor, magnetic field set up across inductor. This field get cut by inductor itself and emf induce in inductor. Such emf is called back emf.When capacitor completely discharge, energy stored in inductor releases and charges capacitor with opposite polarity ( because of back emf)Capacitor now charges with opposite polarity. Again capacitor discharge through inductor and cycle repeat.From this it is clear that voltage across capacitor periodically becomes positive and negative. This gives rise to oscillation across capacitor.Frequency of oscillation is given byF = 1/{(2×pi)(L × C)^1/2}As water can be stored in tank, energy can be stored in this circuit, therefore circuit is also called as tank circuit.Amplitude of oscillations in tank circuit decreases with time( because of resistance in practical circuit) therefore oscillations are called as damped oscillations.To obtain oscillations with constant amplitude called sustained oscillations, tank circuit is connected in feedback path of amplifier. Such oscillator is called as LC oscillator.In ideal circuit ( with zero resistance), energy is not radiated to surrounding and sustained oscillations are obtained.Hope this will clear concept of LC Oscillations.