LC Oscillations
In an ideal LC circuit total electromagnetic energy is constant and the oscillation frequency is 1/(2 pi sqrt(LC)).
Why this shows up in the exam
Radio oscillators · Tuned circuits · Wireless communication
Learn the idea
Energy repeatedly swaps between a capacitor's electric field and an inductor's magnetic field. A charged capacitor begins to discharge through the inductor. Current builds magnetic energy; then the inductor keeps current flowing and charges the capacitor with opposite polarity.
🧠 Memory hook: C holds voltage; L holds current; energy swings between them.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- omega₀ = 1/sqrt(LC) — LC angular frequency
- f₀ = 1/(2 pi sqrt(LC)) — LC frequency
- (1/2) C V_max² = (1/2) L I_max² — energy exchange at extreme states
How to approach it
- 1Use energy conservation for maxima
- 2Use omega0 for timing
- 3Track the quarter-cycle sequence
Common slip-ups that cost marks
- •Assuming charge and current maxima occur together
- •Ignoring resistance in a real circuit
- •Equating CV squared with LI squared without the common one-half only when both are maxima
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A conducting rod of length 2 m moves at 3 m/s perpendicular to a 4 T magnetic field. Find the motional emf.
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Motional EMF
Motional EMF is the voltage induced in a conductor moving through a magnetic field, depending on the speed, length, and orientation of the conductor.