Physics · Alternating Current · NEET
They use the SAME frequency formula but are different situations. LC oscillation is a FREE oscillation: a charged capacitor and an inductor exchange energy on their own, with no external source. Resonance is a DRIVEN case: an ac source pushes an LCR circuit, and current becomes maximum when the source frequency matches the natural frequency 1/(2 pi root(LC)). So the LC natural frequency f = 1/(2 pi root(LC)) is the bridge between the two topics.
Energy sits in two places. In the capacitor as electric energy = q^2 / (2C), and in the inductor as magnetic energy = (1/2) L i^2. When the capacitor is fully charged, all energy is electric and current is zero. A quarter cycle later the capacitor is empty, current is maximum, and all energy is magnetic. The sum q^2/(2C) + (1/2)L i^2 stays constant in the ideal case.
Because of the inductor. An inductor opposes any change in current (its back emf). When the capacitor becomes empty, the current is at maximum, and the inductor keeps that current flowing for a moment. This flowing current then charges the capacitor the OTHER way. That is why the circuit does not stop at zero charge but keeps oscillating, like a pendulum that does not stop at the bottom.
Both exist, do not mix them. Angular frequency omega = 1/root(LC) (units rad/s). Ordinary frequency f = omega / (2 pi) = 1/(2 pi root(LC)) (units Hz). NEET options are usually in Hz or kHz, so you almost always need f = 1/(2 pi root(LC)). If the option is in rad/s, use omega = 1/root(LC).
You first give the capacitor a charge (connect it briefly to a source, then remove the source). That stored electric energy is the starting push. Once the capacitor is charged and the switch connects it to the inductor, the energy exchange begins by itself. No continuous source is needed for an ideal LC circuit to keep oscillating.
In a series LCR circuit, the inductance L is 10 mH, capacitance C is 1 uF and resistance R is 100 ohm. The frequency at which resonance occurs is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
The angular natural frequency is omega = 1/root(LC) rad/s, and the ordinary frequency is f = 1/(2 pi root(LC)) Hz. This is the rate at which energy swings between the capacitor and the inductor.
In an ideal LC circuit (no resistance) yes, total energy q^2/(2C) + (1/2)L i^2 is constant. In a real circuit some resistance is always present, so energy slowly leaks as heat and the oscillations die down (damped). NEET usually assumes the ideal case.
A mass on a spring, or a pendulum. The capacitor is like the spring (stores potential/electric energy), the inductor is like the mass (stores kinetic/magnetic energy). Charge q is like position, and current i is like velocity.
When the capacitor is fully discharged (q = 0). At that moment all the energy is magnetic, stored in the inductor, so (1/2)L i^2 is maximum and i is at its peak value.
No. The frequency f = 1/(2 pi root(LC)) depends only on L and C, not on how much charge you start with. More starting charge only makes the swings bigger (larger amplitude), not faster.
