Lc Oscillations

NCERT Class 12, Chapter 7 (Alternating Current) describes how a charged capacitor connected to an inductor produces electrical oscillations in which energy shuttles between the capacitor's electric field and the inductor's magnetic field, at frequency $f=\frac{1}{2\pi \sqrt{LC}}$. Substituting $L=8\times 10^{-3}\text{H}$ and $C=2\times 10^{-6}\text{F}$: $LC=16\times 10^{-9}$, so $\sqrt{LC}=4\times 10^{-4.5}=1.265\times 10^{-4}\text{s}$. Then $f=\frac{1}{2\pi \times 1.265\times 10^{-4}}=\frac{1}{7.95\times 10^{-4}}\approx 1258\text{Hz}\approx 1.26\text{kHz}$. The option 2.52 kHz doubles the correct frequency. The option 0.63 kHz halves it. The option 7.96 kHz forgets the factor of $2\pi$, giving angular rather than ordinary frequency divided incorrectly. A plausibility check confirms the analogy with a mechanical oscillator, where the LC circuit behaves like a mass-spring system and its natural frequency depends only on $L$ and $C$, giving a physically reasonable kilohertz-scale oscillation. In this analogy the inductance plays the role of the mass, representing electrical inertia that resists changes in current, while the reciprocal of the capacitance behaves like the spring stiffness. At the moment the capacitor is fully charged, all the energy resides in its electric field and the current is momentarily zero; a quarter-period later the capacitor is fully discharged, the current is maximum, and all the energy has transferred to the inductor's magnetic field. In a truly ideal loop with zero resistance these oscillations would persist forever, but any real resistance would gradually dissipate the energy as heat, damping the oscillation exactly as friction damps a mechanical oscillator.