Combination of Inductances – Complete Notes, Revision, Important Questions & Downloads
Combination of Inductances converts self and mutual inductance ideas into circuit-level equivalent inductance, and this topic is organised through Series Combination and Parallel Combination. The controlling formulas are LS = L1 + L2 for uncoupled series coils, LS = L1 + L2 plus or minus 2M for coupled series coils, LP = L1L2/(L1 + L2) for uncoupled parallel coils, and LP = (L1L2 - M^2)/(L1 + L2 plus or minus 2M) when mutual inductance matters. NEET tests this topic through sign choice in aiding versus opposing flux cases, direct equivalent-inductance numericals, and recognition of when mutual inductance can be neglected. The main trap is algebraic only on the surface; the real error is physical, because students forget to decide first whether the magnetic coupling strengthens or cancels the total flux linkage.
NEET Weightage & Exam Pattern
Electromagnetic Induction| NEET Year | Questions from this Topic | Bar | Marks |
|---|---|---|---|
| 2024 | 1 | 4 | |
| 2023 | 0 | 0 | |
| 2022 | 1 | 4 | |
| 2021 | 1 | 4 | |
| 2020 | 1 | 4 | |
| Topic Weightage | 4 | 16 |
The plus or minus 2M term in series combination is the most common discriminator because it encodes aiding versus opposing flux linkage rather than mere arithmetic choice.
Parallel combination becomes tricky because students often remember the uncoupled reciprocal form but forget the coupled denominator and numerator structure.
Preparation Strategy
Decide First Whether M Matters Before writing any formula, check whether the coils are far apart or magnetically coupled. That single decision tells you whether the mutual-inductance term enters at all.
Attach the Sign to the Flux Relation Use plus when the magnetic effects aid each other and minus when they oppose. Memorising signs without this physical picture creates avoidable errors in both series and parallel cases.
Keep Series and Parallel Forms Separate Series questions usually stay additive in structure, but parallel questions require more care because the equivalent inductance depends on a fraction. Mixing the two forms is one of the fastest ways to lose the mark.
Use Limiting Checks After Solving If M = 0, the coupled formula should reduce to the uncoupled case. This reduction is a quick consistency check and often catches algebra mistakes immediately.
Download Topic Notes
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Quick Revision
Concept → Trap → Example1) Series Combination
Additive FormFor two coils in series, the equivalent inductance is LS = L1 + L2 when mutual inductance is negligible. If the coils are magnetically coupled, the equivalent inductance becomes LS = L1 + L2 plus or minus 2M, with the sign determined by whether the fluxes aid or oppose.
- Far-apart coils behave like uncoupled inductors, so only self-inductance terms survive.
- Aiding flux increases total flux linkage and therefore increases equivalent inductance.
- Trap: choosing the sign from memory without checking whether the coupling helps or cancels the linked flux.
2) Parallel Combination
Fraction FormFor uncoupled parallel inductors, 1/LP = 1/L1 + 1/L2, so LP = L1L2/(L1 + L2). When mutual inductance matters, the textbook expression becomes LP = (L1L2 - M^2)/(L1 + L2 plus or minus 2M), and the same aided or opposing sign logic remains active in the denominator.
- The uncoupled form always gives an equivalent inductance smaller than either individual inductor.
- Mutual coupling changes both the numerator and denominator, so the M = 0 limit is the quickest self-check.
- Trap: carrying the series formula into a parallel question because both contain the same L1, L2, and M symbols.
US Curriculum Gaps
Note for NRI/OCI students studying abroad.Mutual-Coupling Cases Are Often Skipped
Students may practise only uncoupled inductors and then face difficulty when the equivalent inductance depends on magnetic aiding or opposition through M.
- know when M is negligible
- use aiding or opposing logic
Parallel Inductor Form Is Less Familiar
Parallel combinations are usually remembered for resistors and capacitors, so inductors with mutual coupling feel less intuitive unless the formula structure is revised deliberately.
- check the M = 0 limit
- do not copy resistor intuition blindly
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Frequently Asked Questions
Notes · Downloads · Revision · Important QuestionsWhat does Combination of Inductances study?
Why is the uncoupled series formula simply L1 + L2?
What decides whether the series formula uses plus 2M or minus 2M?
Why is parallel combination harder than series combination here?
How do I know mutual inductance can be ignored?
What is the quickest self-check in a coupled-inductor numerical?
Can parallel equivalent inductance be larger than both inductors in the uncoupled case?
How does NEET usually ask this topic?
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