Topic 14 of 18 • Chapter: Electromagnetic Induction • Physics

LC-Oscillation – Complete Notes, Revision, Important Questions & Downloads

LC-Oscillation is the chapter's zero-resistance energy-exchange model, and in this topic the textbook keeps the scope tightly on Oscillation in LC Circuit. A charged capacitor discharges through an inductor, the charge and current execute simple harmonic variation, and the total energy keeps moving between the capacitor's electric field and the inductor's magnetic field. NEET tests this topic through direct frequency substitution, identification of the instant of maximum current or maximum charge, and recognition that total energy stays constant in the ideal circuit. The standard formulas are omega = 1 by root LC and nu = 1 by 2 pi root LC, so the real scoring skill is reading the physical state before substituting values.

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Qualitative NEETEnergy ExchangeAC Bridge

Expected QuestionsQ

0-1

usually appears as a concept check on frequency or on electric-energy versus magnetic-energy stages in the oscillation

Time Required⏱

1 Hour

enough to lock the qualitative cycle, the two frequency formulae, and one or two direct substitution numericals

Difficulty⚡

Low

the algebra is short, but students lose easy marks if they forget which quantity is maximum when the capacitor is fully charged or fully discharged

NRI USA Curriculum GapUS

Moderate

many school circuit courses stop at RC and RL behavior, whereas NEET expects immediate transfer of SHM ideas to charge-current oscillation in an ideal LC loop

1Subtopics

18Practice Questions

4Free Downloads

1 hrPrep Time

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NEET Weightage & Exam Pattern

Electromagnetic Induction

NEET Year	Questions from this Topic	Bar	Marks
2024	0	0 Q	0
2023	0	0 Q	0
2022	0	0 Q	0
2021	1	1 Q	4
2020	0	0 Q	0
Topic Weightage	1		4

LC-Oscillation is usually not treated as a long derivation in NEET; it is tested as a direct recognition of frequency and energy swapping between L and C.
The chapter keeps this topic ideal, so resistance and damping are outside the local page scope unless the question explicitly asks why real oscillations die out.
Questions become easiest when the student first decides whether the capacitor is fully charged, fully discharged, or in an intermediate state before writing any formula.

📊

0.2

Avg Questions / Year

🎯

Total Marks (6 yrs)

📈

Irregular

Pattern

⚠️

Low

Difficulty

Preparation Strategy

Memorise The Two Frequency Relations Together Keep omega = 1 by root LC and nu = 1 by 2 pi root LC as a pair. The trap is to remember only one form and then lose time converting between angular frequency and ordinary frequency in the exam hall.

Track Which Energy Form Is Maximum When the capacitor has charge q0, electric energy is maximum and current is zero; when charge becomes zero, magnetic energy is maximum and current is maximum. Most LC-Oscillation mistakes come from reversing these two endpoints.

Treat The Circuit As SHM In Charge Recognise that the oscillation is simple harmonic in the ideal limit. That lets you identify phase-type statements quickly instead of thinking the circuit is a one-way discharge process like an RC circuit.

Separate Ideal LC From Real Damped Circuits The local page assumes zero resistance and no radiation loss. If a question mentions energy loss or decaying amplitude, first note that it has moved beyond the ideal textbook assumption before you reason further.

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PDF · Cheat Sheet · MCQ Set · PYQ

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Full Topic Notes

Focused notes on Oscillation in LC Circuit, frequency relations, and electric-energy to magnetic-energy transfer in one ideal loop.

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Formula Sheet

One-page sheet for omega = 1 by root LC, nu = 1 by 2 pi root LC, and the endpoint conditions for charge, current, and stored energy.

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MCQ Practice

Practice set on LC frequency calculation, energy distribution at special instants, and comparison with RC or RL behavior.

PDF18 Questions

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⏳

Previous Year Questions

Selected NEET-style and board-style questions on qualitative LC oscillation, frequency reading, and state-variable interpretation.

PDF6 Questions

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Topic Coverage

2-Column Table

Column A	Column B
Oscillation in LC Circuit↗

Quick Revision

Concept → Trap → Example

1) Oscillation in LC Circuit

Charge Current Energy

When a charged capacitor C having an initial charge q0 is discharged through an inductor L, the charge and current in the circuit starts oscillating simple harmonically. Frequency of oscillation is given by omega = 1 by root LC and nu = 1 by 2 pi root LC.

The capacitor stores electric energy when charge is maximum, while the inductor stores magnetic energy when current is maximum.
The textbook page assumes zero resistance and no radiation loss, so the total energy associated with the circuit is constant.
Trap: treating LC-Oscillation like a simple discharge problem and forgetting that the capacitor recharges with opposite polarity after the current reaches its maximum.

Example (NEET-style)If L = 2 mH and C = 8 microfarad, then root LC = root(16 x 10^-9) = 4 x 10^-4. So omega = 1/(4 x 10^-4) = 2500 rad/s and nu is about 398 Hz. The question is direct only after the unit conversion is kept clean.

US Curriculum Gaps

Note for NRI/OCI students studying abroad.

AP Physics C Often Reaches Forced AC Faster Than Ideal LC Energy Swapping

Many students learn reactance and resonance formulae but do not spend enough time on the ideal LC picture where charge, current, and stored energy exchange roles cyclically inside one isolated loop.

lock the two endpoint states: q maximum means i zero
treat LC as SHM in charge before moving to LCR resonance

General High-School Circuit Units Rarely Stress Qualitative State Reading

NEET asks conceptual statements such as when magnetic energy is maximum or whether frequency changes with initial charge. Those are easy only if the student has practised reading the oscillation cycle, not just plugging values into a calculator.

frequency depends on L and C, not on q0
energy swaps form even when total energy stays constant

Concept IQ Check

Exam-style checks

1In an ideal LC circuit, the capacitor is initially charged and then connected to the inductor. At the instant when the charge on the capacitor becomes zero for the first time, which statement is correct?Energy state

Current is zero and electric energy is maximum

Current is maximum and magnetic energy is maximum

Current is maximum and total energy is zero

Current is zero and magnetic energy is maximum

In an ideal LC loop, total energy remains constant but changes form. When the capacitor momentarily has zero charge, its electric-field energy is zero because Uc = q squared by 2C. At that same instant the current is maximum, so the inductor stores maximum magnetic energy as one-half L i squared. Option B is therefore correct. Option A reverses the endpoint states, option C violates conservation of energy, and option D incorrectly sets current to zero when magnetic energy is supposed to be largest.

2Two ideal LC circuits have the same capacitor C, but the first has inductance L and the second has inductance 4L. If the frequency of the first is f, the frequency of the second is:Frequency scaling

f/2

f/4

The frequency of an ideal LC circuit is nu = 1 by 2 pi root LC. If inductance becomes 4L while C stays unchanged, the denominator becomes 2 pi root 4LC = 2 multiplied by 2 pi root LC. That doubles the denominator and halves the frequency, so the new value is f by 2. Option C matches the proportionality nu proportional to 1 by root L. The other options come from treating frequency as directly proportional to L or from over-squaring the dependence.

Practice Questions

Click "Reveal Answer" after attempting

1An ideal LC circuit has L = 5 mH and C = 20 microfarad. Find the angular frequency of oscillation.

1000 rad/s

2000 rad/s

3162 rad/s

5000 rad/s

👁 Reveal Answer

Correct option: C. Use omega = 1 by root LC. Here LC = 5 x 10^-3 x 20 x 10^-6 = 10^-7. Therefore root LC = 10^-3.5 about 3.162 x 10^-4. Hence omega about 1/(3.162 x 10^-4) = 3162 rad/s. The main check is unit conversion from milli and micro before taking the square root.

2In an ideal LC oscillation, the capacitor is fully charged at t = 0. Which quantity is zero at that instant?

Charge on capacitor

Electric energy

Current in circuit

Total energy

👁 Reveal Answer

Correct option: C. When the capacitor is fully charged, charge and electric-field energy are maximum. Since the current has not yet built up, the magnetic field in the inductor is absent at that endpoint, so current is zero. Total energy is not zero because it is fully stored in the capacitor.

3If both L and C of an ideal LC circuit are doubled, how does the frequency change?

It becomes four times

It becomes two times

It becomes half

It remains unchanged

👁 Reveal Answer

Correct option: C. Frequency is nu = 1 by 2 pi root LC. If both L and C are doubled, the product LC becomes 4LC. The square root therefore becomes 2 root LC, so the denominator doubles and frequency becomes half. Students often choose one-fourth by forgetting that the square root reduces the factor 4 to 2.

4A question states that the initial charge on the capacitor in an ideal LC circuit is made three times larger while L and C stay fixed. Which statement is correct?

Frequency becomes three times

Frequency becomes one-third

Frequency remains unchanged

Oscillation stops

👁 Reveal Answer

Correct option: C. The frequency relation contains only L and C, so changing the initial charge alters the energy amplitude but not the natural frequency. A larger q0 means larger stored energy and a larger maximum current, but the time scale of oscillation still comes from the same 1 by root LC dependence.

Physics Revision Checklist

Check off chapters as you revise

Use this section for quick chapter tracking before mocks, part tests, and final NEET revision.

Oscillation in LC Circuit: derive the frequency relation from the page formulasWrite omega = 1 by root LC and nu = 1 by 2 pi root LC from memory and verify you can convert between them without re-deriving the whole motion.

Oscillation in LC Circuit: mark the two endpoint statesState clearly what happens when capacitor charge is maximum and when it becomes zero, including current, electric energy, and magnetic energy in each case.

Oscillation in LC Circuit: solve one numerical with milli and micro unitsPick one pair of L and C values, convert units to SI, and compute omega and nu without calculator slips in powers of ten.

Oscillation in LC Circuit: compare it with RC dischargeWrite one line explaining why LC motion oscillates while an RC circuit only decays, so the exam does not trap you into treating both as the same process.

Oscillation in LC Circuit: test the constant-energy statementExplain in words why the total energy stays constant in the ideal page model and identify the two assumptions that make this statement valid.

LC-Oscillation FAQs

Notes · Downloads · Revision · Important Questions

Why is LC-Oscillation described as simple harmonic in the textbook?

The local model says that a charged capacitor discharges through an inductor and the charge and current start oscillating simply harmonically. The restoring tendency comes from the capacitor-inductor combination itself: when charge decreases, current grows; when current reaches maximum, the capacitor becomes uncharged and then charges again with opposite polarity. That cyclic reversal makes the motion analogous to SHM in the variable q.

Why does the total energy stay constant in the page's LC model?

The page explicitly assumes zero circuit resistance and also assumes that energy is not radiated away from the circuit. Under those two ideal conditions, no heat loss and no radiation loss occur, so the stored energy merely shifts between electric form in the capacitor and magnetic form in the inductor. That is why the total energy associated with the circuit is constant in the textbook treatment.

Does increasing the initial charge q0 change the frequency of LC-Oscillation?

No. The natural frequency depends only on L and C through omega = 1 by root LC or nu = 1 by 2 pi root LC. A larger initial charge only raises the total stored energy and therefore changes the maximum current and charge amplitude. It does not alter the basic time scale fixed by the inductance-capacitance combination.

At which instant is the current maximum in an ideal LC circuit?

The current is maximum when the capacitor momentarily becomes uncharged. At that instant electric energy in the capacitor is zero, while magnetic energy in the inductor is maximum. This is the standard state that NEET uses to test whether the student can connect charge, current, and energy correctly rather than memorising the formula in isolation.

Why is LC-Oscillation placed under electromagnetic induction when it looks like an AC topic?

The circuit oscillates because the inductor resists change in current through induced emf, so the underlying mechanism is still electromagnetic induction. The topic also acts as a bridge to alternating current because the charge and current vary periodically, but the physical reason the loop keeps exchanging energy lies in the inductor's induced back emf and the capacitor's stored electric energy.

What is the most common exam mistake in LC-Oscillation?

The most common mistake is reversing the endpoint states. Students often say that current is maximum when the capacitor is fully charged or that electric energy remains maximum throughout the cycle. The safe method is to check the two limiting states first: q maximum implies i zero, and q zero implies i maximum. Once those endpoints are fixed, the rest of the cycle becomes consistent.

Why do real LC circuits not oscillate forever even though the textbook says the energy is constant?

The textbook statement belongs to an idealised model. Real inductors have some resistance, and real circuits lose energy through heat and electromagnetic radiation. Those non-ideal effects gradually reduce amplitude, so the oscillation becomes damped instead of perfectly sustained. For the assigned page, however, the exam expectation is to reason inside the ideal assumption unless the question explicitly introduces losses.

How should an NRI student revise LC-Oscillation quickly before NEET?

Start with the two frequency formulae, then memorise the two endpoint states of the cycle, and finally solve one clean substitution problem with milli- and micro-unit values. That short sequence covers almost every direct LC-Oscillation question asked at NEET level. If time remains, compare the topic once with RC discharge and once with LCR resonance so the qualitative differences stay sharp.

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LC-Oscillation

LC-Oscillation – Complete Notes, Revision, Important Questions & Downloads

1) Oscillation in LC Circuit

AP Physics C Often Reaches Forced AC Faster Than Ideal LC Energy Swapping

General High-School Circuit Units Rarely Stress Qualitative State Reading

Physics Revision Checklist

NEET NRI Counseling & Admission eBook Download

Schedule Trial Session For NEET Prep

Oscillation in LC Circuit

Subtopics

Oscillation in LC Circuit

NEET > Physics > Electromagnetic Induction and Alternating Currents Chapters

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LC-Oscillation

Overview content

LC-Oscillation – Complete Notes, Revision, Important Questions & Downloads

1) Oscillation in LC Circuit

AP Physics C Often Reaches Forced AC Faster Than Ideal LC Energy Swapping

General High-School Circuit Units Rarely Stress Qualitative State Reading

Physics Revision Checklist

NEET NRI Counseling & Admission eBook Download

Schedule Trial Session For NEET Prep

Oscillation in LC Circuit

Subtopics

Oscillation in LC Circuit

NEET > Physics > Electromagnetic Induction and Alternating Currents Chapters

Comments

Leave a comment

Comments (0)