Energy Stored In An Inductor
An ideal inductor of inductance 0.4 H carries a steady current of 5 A supplied by a battery. How much magnetic energy is stored in the inductor under these steady-state conditions?
Select the correct option:
Solution
5 J
An inductor carrying current stores energy in the magnetic field built up within and around its windings, and this stored energy equals the work the source did against the back-EMF while the current grew. The expression is (U = \tfrac{1}{2}LI^2), which holds in steady state once the current is constant and no further EMF opposes it. Substituting (L = 0.4) H and (I = 5) A gives (U = 0.5 \times 0.4 \times 25 = 5) J. The option 2 J results from forgetting to square the current. The option 10 J omits the factor of one-half. The option 1 J both omits the square and mishandles the constant. This is the energy relation derived in NCERT by integrating the instantaneous power (Li,di/dt) delivered to the coil. A plausibility check confirms the units H·A^2 reduce to joules, and a few joules is a sensible store for a modest inductor at several amperes; importantly, this energy returns to the circuit when the current is switched off.
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About This Question
- Subject
- physics
- Chapter
- electromagnetic induction and alternating currents
- Topic
- energy stored in an inductor
- Difficulty
- Easy
- Year
- 2025
Solution
Correct Answer:
5 J
An inductor carrying current stores energy in the magnetic field built up within and around its windings, and this stored energy equals the work the source did against the back-EMF while the current grew. The expression is (U = \tfrac{1}{2}LI^2), which holds in steady state once the current is constant and no further EMF opposes it. Substituting (L = 0.4) H and (I = 5) A gives (U = 0.5 \times 0.4 \times 25 = 5) J. The option 2 J results from forgetting to square the current. The option 10 J omits the factor of one-half. The option 1 J both omits the square and mishandles the constant. This is the energy relation derived in NCERT by integrating the instantaneous power (Li,di/dt) delivered to the coil. A plausibility check confirms the units H·A^2 reduce to joules, and a few joules is a sensible store for a modest inductor at several amperes; importantly, this energy returns to the circuit when the current is switched off.
This easy difficulty physics question is from the chapter electromagnetic induction and alternating currents, covering the topic of energy stored in an inductor. It appeared in the 2025 exam.
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