Q.Explain briefly how the oscillations are produced in a tank circuit.

A tank circuit is an inductor L and a capacitor C in parallel; oscillations arise from the repeated interchange of energy between the electrostatic field of the capacitor and the magnetic field of the coil.

[!ANSWER]

When the charged capacitor discharges through the coil its electrostatic energy is converted into magnetic energy in L; the collapsing magnetic field then recharges the capacitor with reversed polarity, and this charge–discharge cycle repeats to give an alternating (oscillating) current of frequency $f = \dfrac{1}{2\pi\sqrt{LC}}$.

[!TLDR]

In an LC tank circuit energy shuttles back and forth between the capacitor's electric field and the coil's magnetic field, producing an oscillating current at $f = \dfrac{1}{2\pi\sqrt{LC}}$.

A tank (oscillatory) circuit is a capacitor C connected in parallel with an inductor L. Suppose the capacitor is first charged from a source so that its upper plate is positive and its lower plate negative; it now stores electrostatic energy.

When the capacitor is allowed to discharge through the coil, the changing current induces an emf in L (Lenz's law) that opposes the growth of current, so the capacitor does not discharge instantly. The current builds up gradually and sets up a magnetic field around the coil. When the current is maximum the capacitor is fully discharged — the electrostatic energy has been completely converted into magnetic energy stored in L.

The magnetic field now begins to collapse and, by Lenz's law, the induced emf keeps the current flowing in the same direction, recharging the capacitor with the opposite polarity (upper plate negative, lower plate positive). The capacitor then discharges again, driving current in the reverse direction. This continuous interchange of energy between L and C produces the electrical oscillations.

The frequency of these oscillations depends only on the tank elements and is given by $f = \dfrac{1}{2\pi\sqrt{LC}}$. In a practical tank there are resistive and radiation losses in the coil and dielectric losses in the capacitor, so a little energy is lost each cycle and the oscillations are damped; connecting an amplifier that supplies the lost energy makes the oscillations sustained.

[!ANSWER]

The capacitor and inductor exchange energy repeatedly — the electrostatic energy of C converts to the magnetic energy of L and back again — producing an oscillating current of frequency $f = \dfrac{1}{2\pi\sqrt{LC}}$; circuit losses make it damped unless an amplifier replaces the lost energy for sustained oscillations.