Self Inductance, Mutual Inductance, and Energy Stored
Self inductance is the property of a coil by which a changing current in it induces an emf in the same coil. Mutual inductance is the property by which a changing current in one coil induces an emf in a nearby coil.
In one line: Inductance reacts to change in current; no change means no induced back emf.
Concept Practice Coming SoonUnderstand it
In self induction, the coil's own changing current changes magnetic flux linked with it, producing back emf epsilon = -L dI/dt. In mutual induction, changing current in the primary coil changes flux linked with the secondary coil, producing induced emf epsilon = -M dI/dt. An inductor stores magnetic energy U = 1/2 L I2.
Example
Formula and rule
Self induction: epsilon = -L dI/dt, where L is self inductance in henry, I is current in ampere, t is time in second, and epsilon is volt.
Mutual induction: epsilon2 = -M dI1/dt, where M is mutual inductance in henry.
Energy stored in an inductor: U = 1/2 L I2 in joule.
Use these when current changes with time, not for steady DC after transients settle.
See it worked out
Follow the example line by line, then use the same method on new questions.
Worked example
An inductor of 0.80 H carries current increasing uniformly from 1.0 A to 3.0 A in 0.20 s.
- 1Magnitude of induced emf = L Delta I/Delta t = 0.80 × (2.0/0.20) = 8.0 V.
- 2Energy stored at 3.0 A is U = 1/2 L I2 = 0.5 × 0.80 × 9.0 = 3.6 J.
- 3The induced emf opposes the increase of current.
Method you can reuse
- 1Identify whether one coil or two coils are involved.
- 2Check whether current changes with time.
- 3Use L for same-coil induction and M for coupled coils.
- 4Calculate rate of change of current, then apply the emf formula with units.
- 5Use Lenz's law for sign or direction.
Visual tip
For self induction, show one coil with changing current and back emf. For mutual induction, show two nearby coils labelled primary and secondary, with changing current in the primary and induced emf in the secondary.
Check yourself
Answer the question in your head before opening the answer.
Try it yourself
Why does an inductor oppose a sudden change in current?
Think first, then show answerHide answer
Common wrong answer
Applying epsilon = -L dI/dt when current is constant, or writing energy as LI2 instead of 1/2 LI2.
Don't mix this up
Exam tip
Write it in the exam
Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.
How CBSE asks it
- 1
Enough for 1 mark
Self inductance is the property of a coil by which a changing current in it induces an emf in the same coil. Mutual inductance is the property by which a changing current in one coil induces an emf in a nearby coil.
- 2
Add for 2 marks
Example: When current through an inductor is increased suddenly, the inductor opposes the rise of current by producing back emf. In a transformer-like pair of coils, changing current in one coil can induce emf in the other due to mutual inductance.
- 3
Add for 3 marks
In self induction, the coil's own changing current changes magnetic flux linked with it, producing back emf epsilon = -L dI/dt.
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