Question

Why is an LC circuit a harmonic oscillator?

Answer 1

An electric circuit that is made up of an inductor and the capacitor is called the LC circuit. We can also call an LC circuit a tank circuit or resonant circuit or tuned circuit. Since this circuit does not contain a resistance there will be no loss in energy. However, this case is ideal because practically there will be some energy loss because of the non-zero resistance of the components and connecting wires.

Complete answer:
As we already said the LC circuit contains both inductor and capacitor. Capacitors and inductors store energy in the form of electric and magnetic fields respectively. A circuit containing capacitors and inductors can oscillate without a source of emf. This process happens because the circuit shifts the energy stored in the circuit between the electric and magnetic fields.
At first, all the energy of the circuit is stored in the capacitor. And then the capacitor will begin to discharge producing a current in the circuit. Since the current is flowing through the circuit a magnetic field will be created in the inductor. This will result in the diminishing of energy in the capacitor and increasing the magnetic field in the inductor.
After this, the current will transport charges between the capacitor and thereby recharges the capacitor. We know that the inductor resists a change in current. Therefore current continues to flow, even though the capacitor is discharged fully. This will cause the capacitor to charge with opposite polarity. Now the magnetic field in the inductor will be slowly diminished while the electric field in the capacitor increases steadily in the opposite direction. This cycle continues and in the last part the energy flows back to the capacitor. These electromagnetic oscillations are said to be analogous to the mechanical oscillations of a mass at the end of the spring and that is why we call the LC circuit a harmonic oscillator.

Note:
In the frictionless mass-spring system the mechanical oscillations would continue indefinitely. Similarly in the ideal case of the LC circuit that is with the absence of the resistance in the LC circuit, the electromagnetic oscillations would continue indefinitely if it is undisturbed. However, it is practically not possible to have zero resistance in a circuit.