Energy in Inductors and AC Circuits
Inductors store energy in their magnetic field, and energy considerations in AC circuits involve power dissipation and conservation.
Why this shows up in the exam
You may be asked to calculate stored energy or power loss in NEET problems.
How NEET tests this
Learn the idea
An inductor stores magnetic energy equal to half the product of its inductance and the square of the current flowing through it; in AC circuits the only real power loss at resonance comes from the resistance, because the inductive and capacitive reactances cancel each other.
🧠 Memory hook: Think of the inductor as a half‑filled magnetic bucket: only half of L I² actually stays inside as energy.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- Magnetic energy in an inductor: U = ½ L I²
- Resonant angular frequency: ω₀ = 1/√(LC)
- At resonance the impedance of a series LCR circuit is purely resistive (Z = R)
- Average power in an AC circuit: P̅ = V_rms I_rms cos φ
- For a pure inductor φ = 90° so average power is zero
How to approach it
- 1Read the question and note the given L and I (or V, I, R at resonance)
- 2Convert micro‑henry to henry and micro‑joule to joule before substituting
- 3Apply U = ½ L I² for stored energy or P̅ = I_rms² R for power loss at resonance
- 4Check units and use the factor ½ correctly
Worked example — watch it click
The magnetic energy stored in an inductor of inductance 4 µH carrying a current of 2 A is
- A)4 mJ
- B)8 mJ
- ✅8 µJ
- D)4 µJ
The concept behind this problem
The worked example asks directly for the magnetic energy stored, so the student must recognise and apply the U = ½ L I² relation.
Step by step
- 1Magnetic energy stored in an inductor: U = (1/2)LI².
- 2Given: L = 4 µH = 4×10⁻⁶ H, I = 2 A.
- 3U = (1/2) × 4×10⁻⁶ × (2)² = (1/2) × 4×10⁻⁶ × 4 = 8×10⁻⁶ J = 8 µJ.
Watch out
Students often forget the ½ factor and would obtain 16 µJ instead of the correct 8 µJ.
Common slip-ups that cost marks
- •Mixing peak current with rms current – NCERT formulas use rms values for power
- •Using L I instead of ½ L I² – the ½ is easy to miss
- •Assuming the inductor itself dissipates power; only the resistance does
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Practise it
These are real questions from past NEET papers that test this exact idea.
For a series LCR circuit, the power loss at resonance is:
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