---
title: "LC oscillation qualitative description"
subject: "Engineering Physics"
chapter: 1
key: "semester_1/engineering_physics:lc-oscillation-qualitative-graph"
source: https://www.bctengineer.com/q/semester_1/engineering_physics/lc-oscillation-qualitative-graph
site: BCT Engineering
---

# LC oscillation qualitative description

Engineering Physics · Chapter 1: Oscillation

- Asked in: 2074 Chaitra, 5 marks
- Video: [LC Oscillator Qualitative Analysis](https://www.youtube.com/watch?v=b8hTgJQsfFg) — Jordan Edmunds Chetty
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/engineering_physics/lc-oscillation-qualitative-graph
- Whole chapter: https://www.bctengineer.com/md/semester_1/engineering_physics/chapter-1

## Question

Describe L.C oscillation qualitatively by using necessary circuits and graph.

## Short answer

Initially capacitor fully charged, all energy electric. Discharge causes current to grow, energy transfers to magnetic field; at T/4, q=0, i max. Inductor keeps current, recharges capacitor with opposite polarity at T/2. Cycle repeats. Graphs: q = q₀ cos ω₀t, i = -ω₀q₀ sin ω₀t; current leads charge by a quarter period. Total energy remains constant.

## Answer

An ideal LC circuit has an inductor L and a capacitor C. Energy shuttles between the electric field of C (energy q²/2C) and the magnetic field of L (energy ½Li²).

#### Four stages in one period T
```text
(a) t=0       (b) t=T/4     (c) t=T/2     (d) t=3T/4
 +|-|          | |          -|-|+         | |
 C   L        C   L         C   L         C   L
 q=+q0, i=0   q=0, i=max    q=-q0, i=0    q=0, i=max (reverse)
 all energy   all energy    all energy    all energy
 electric     magnetic      electric      magnetic
```
1. **t = 0**: capacitor fully charged (charge q0), no current. All energy is electric, q0²/2C.
2. **0 to T/4**: capacitor discharges through L. Current grows, but the inductor opposes the rise (back emf). At T/4: q = 0, i is maximum, energy is all magnetic, ½L i0².
3. **T/4 to T/2**: current continues in the same direction because of the inductor, charging the capacitor with opposite polarity. At T/2: q = −q0, i = 0, energy is all electric again.
4. **T/2 to T**: the process repeats in reverse; at 3T/4 current is maximum in the opposite direction; at T the original state returns.

#### Graphs
```text
 q  q0 |   .--.        .--.
       |  /    \      /    \
       |-/------\----/------\-- t
       |         \  /
       |          '--'
 i      current is a sine wave, T/4 ahead of q
```
- q = q0 cos ω0t and i = −ω0q0 sin ω0t, with ω0 = 1/√(LC) and period T = 2π√(LC).
- Electric energy U_E = (q0²/2C) cos²ω0t, magnetic energy U_B = (q0²/2C) sin²ω0t. They are out of phase, and U_E + U_B = q0²/2C is constant.
- In a real circuit resistance converts energy to heat, so the oscillations die out (damped).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. At t = 0 (capacitor fully charged), the state is?
   A. q = 0, i max
   B. q = q0, i max
   C. q = q0, i = 0, all energy electric
   D. All energy magnetic
   Answer: C. Nothing flows yet. (Key point: Start)

2. At t = T/4?
   A. q = q0, i = 0
   B. q = -q0, i = 0
   C. Energy is zero
   D. q = 0, i maximum, all energy magnetic
   Answer: D. Capacitor fully discharged. (Key point: Quarter period)

3. At t = T/2?
   A. Capacitor charged with opposite polarity, i = 0
   B. q = 0, i max
   C. Same polarity as start
   D. All energy magnetic
   Answer: A. Inductor keeps current flowing and recharges C. (Key point: Half period)

4. How do U_E and U_B relate?
   A. In phase
   B. Out of phase; sum constant
   C. U_E constant
   D. Both zero at the same time
   Answer: B. cos^2 and sin^2 sum to 1. (Key point: Energies)

## Related in Engineering Physics

- [LC oscillation differential equation](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Alc-oscillation-differential-equation) — Engineering Physics, chapter 1
- [Maximum current in LC circuit](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Alc-maximum-current-numerical) — Engineering Physics, chapter 1

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