Definition
Mutual inductance
M = Φ_secondary / I_primary. Induced emf in secondary: ε₂ = -M dI₁/dt. Symmetric: M_12 = M_21.
-- NCERT Class 12 Physics, Ch. 6, p. 167Mutual Inductance
8 MCQs4 revision cards9-step worked example
Source: NCERT Electromagnetic Induction and Alternating CurrentsOfficial key: NTA-verifiedLast updated: 27 Sep 2026
Mutual Inductance, explained for NEET
The confusion that costs marks here is treating mutual inductance as a property of one coil. It is not. M is a property of the pair — two coils, fixed in position relative to each other, with a fixed medium between them. Move one coil, or slide an iron rod into the gap, and M changes. Change the current, and M does not.
NCERT Class 12 Physics Chapter 6 (printed page 167) defines it this way: when current I₁ in coil 1 produces flux linkage N₂Φ₂ in coil 2, that linkage is proportional to I₁, and the constant of proportionality is M₂₁:
N₂Φ₂ = M₂₁ I₁
Differentiate and you get the EMF form, which is what questions actually use:
ε₂ = −M (dI₁/dt)
Two things follow that students routinely get wrong.
First, M₁₂ = M₂₁ always. The reciprocity holds regardless of the coils' shapes, sizes, or turn counts. A 10-turn coil and a 1000-turn coil have one mutual inductance between them, not two different ones. So you may compute M whichever way is easier — usually by putting current in the coil whose field you can write down — and use the answer in the other direction.
Second, M depends on geometry and medium, not on current. The variables that change M are: number of turns in each coil, their areas, their separation, their relative orientation, and the permeability of the core. If a question changes the current and asks what happens to M, the answer is nothing.
The unit is the henry, the same unit as self-inductance L. One henry of mutual inductance means a current changing at 1 A s⁻¹ in one coil drives 1 V in the other.
Watch out: when the coils' axes are perpendicular, flux from one links essentially none of the other, so M → 0 even though both coils are perfectly good inductors. Orientation is a variable, not a given.
Can you answer these Mutual Inductance MCQs?
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
MCQ 1Easy RecallPractice
The SI unit of mutual inductance is the
Show answer and why every option is right or wrong
Answer: C. C is correct. Mutual inductance is measured in henry, the same unit as self-inductance, as stated in NCERT Class 12 Physics Chapter 6 (printed page 167).
Why A is wrong: A is wrong because the weber is the unit of magnetic flux, not of the constant relating flux linkage to current.
Why B is wrong: B is wrong because the tesla measures magnetic field strength, not inductance.
Why D is wrong: D is wrong because volt-second per ampere-second reduces to volt per ampere, which is the ohm — the seconds cancel. One henry is volt-second per ampere (V s A⁻¹).
MCQ 2Easy RecallPractice
Mutual inductance between two coils is a property of
Show answer and why every option is right or wrong
Answer: A. A is correct. NCERT Class 12 Physics Chapter 6 (printed page 167) defines M for a system of two coils; it is fixed once geometry, orientation and medium are fixed.
Why B is wrong: B is wrong because a single coil on its own has self-inductance, not mutual inductance — mutual inductance requires a second circuit to link the flux.
Why C is wrong: C is wrong for the same reason as B: naming either coil alone misses that M describes the coupling between them.
Why D is wrong: D is wrong because current is the variable that M multiplies, not a factor that determines M. Doubling the current doubles the flux linkage and leaves M unchanged.
MCQ 3Easy RecallPractice
For two coils labelled 1 and 2, the mutual inductances M₁₂ and M₂₁ satisfy
Show answer and why every option is right or wrong
Answer: D. D is correct. The reciprocity relation M₁₂ = M₂₁ is general and is stated without restriction in NCERT Class 12 Physics Chapter 6 (printed page 167).
Why A is wrong: A is wrong because reciprocity carries no condition on turn counts. A 10-turn and a 1000-turn coil still share a single value of M.
Why B is wrong: B is wrong for the same reason — equal areas are not required. The equality is a general result, not a special case.
Why C is wrong: C is wrong because it invents a turns-ratio correction. No such factor appears; the two mutual inductances are numerically identical.
MCQ 4Direct ApplicationPractice
A current in coil P changes at a steady rate of 2.0 A s⁻¹ and induces an EMF of magnitude 0.60 V in a nearby coil Q. The mutual inductance of the pair is
Show answer and why every option is right or wrong
Answer: B. B is correct. From |ε| = M |dI/dt|, M = 0.60 V ÷ 2.0 A s⁻¹ = 0.30 H, applying the EMF form of the definition in NCERT Class 12 Physics Chapter 6 (printed page 167).
Why A is wrong: A is wrong because it multiplies EMF by the rate of change instead of dividing. Check the unit: V × A s⁻¹ is not the henry.
Why C is wrong: C is wrong because it inverts the division, computing 2.0 ÷ 0.60. That gives the current rate per unit EMF, which is 1/M, not M.
Why D is wrong: D is wrong because it divides by 5.0 rather than 2.0 — arithmetic slip, not a conceptual one. Re-read the given rate.
MCQ 5Direct ApplicationPractice
Two coils have a mutual inductance of 1.5 × 10⁻² H. The current in the first coil is increased uniformly from 0 A to 4.0 A in 0.20 s. The magnitude of the EMF induced in the second coil during this interval is
Show answer and why every option is right or wrong
Answer: D. D is correct. dI/dt = 4.0 A ÷ 0.20 s = 2.0 × 10¹ A s⁻¹, so |ε| = M |dI/dt| = 1.5 × 10⁻² H × 2.0 × 10¹ A s⁻¹ = 0.30 V, using the definition in NCERT Class 12 Physics Chapter 6 (printed page 167).
Why A is wrong: A is wrong because it uses dI/dt = 0.80 A s⁻¹, multiplying 4.0 by 0.20 instead of dividing 4.0 by 0.20.
Why B is wrong: B is wrong because it multiplies M by the current change 4.0 A and then divides by 2.0 × 10¹ rather than by the interval; it also confuses a flux linkage (M I, in weber) with an EMF.
Why C is wrong: C is wrong because it multiplies M by 5.0 A s⁻¹, treating the interval as 0.80 s. Read the interval as 0.20 s.
MCQ 6Concept TrapPractice
Two fixed coaxial coils are coupled by mutual inductance M. The steady current in the primary is doubled and then held constant at the new value. Once the current is steady again, the mutual inductance and the EMF in the secondary are respectively
Show answer and why every option is right or wrong
Answer: A. A is correct. M depends on geometry, orientation and medium — not on current — and with dI/dt = 0 the induced EMF vanishes, per the EMF form given in NCERT Class 12 Physics Chapter 6 (printed page 167).
Why B is wrong: B is wrong on the first half: it treats M as proportional to current. M is a constant of the pair, so doubling I doubles the flux linkage M I but leaves M itself alone.
Why C is wrong: C is wrong because it attaches an EMF to a steady current. Induction responds to dI/dt, which is zero once the new current is held constant.
Why D is wrong: D is wrong on both counts — it scales M with current and also asserts an EMF while nothing is changing.
MCQ 7Direct ApplicationPractice
Two identical coils sit side by side with a common axis and a measurable mutual inductance. One coil is then rotated about a vertical diameter until its axis is perpendicular to the other's, with the separation between centres unchanged. The mutual inductance of the pair
Show answer and why every option is right or wrong
Answer: C. C is correct. Relative orientation is one of the geometric factors M depends on; with the axes perpendicular, the flux of one coil threads essentially no net area of the other, so the linkage — and hence M — collapses. This follows directly from the flux-linkage definition in NCERT Class 12 Physics Chapter 6 (printed page 167).
Why A is wrong: A is wrong because it lists only two of the geometric factors. Relative orientation belongs on that list, and it is exactly what changed here.
Why B is wrong: B is wrong because it invents a path-length argument and gets the direction backwards — turning the axes perpendicular reduces the linkage, it does not enhance it.
Why D is wrong: D is wrong because a sign flip describes reversing a winding direction, not a 90° rotation. A perpendicular orientation removes the linkage rather than inverting it.
MCQ 8CalculationPractice
Two coils P and Q have mutual inductance M. With P as primary, a current changing at 5.0 A s⁻¹ in P induces 0.25 V in Q. The roles are now swapped: Q becomes the primary and carries a current changing at 2.0 A s⁻¹. The EMF induced in P is
Show answer and why every option is right or wrong
Answer: D. D is correct. First find M = 0.25 V ÷ 5.0 A s⁻¹ = 5.0 × 10⁻² H; reciprocity (NCERT Class 12 Physics Chapter 6, printed page 167) lets the same M be used in the reverse direction, giving |ε| = 5.0 × 10⁻² H × 2.0 A s⁻¹ = 0.10 V.
Why A is wrong: A is wrong because it denies reciprocity. There is one M for the pair; swapping which coil carries the changing current does not require a new value.
Why B is wrong: B is wrong because it treats the EMF, rather than M, as the fixed property of the pair. M is fixed; the EMF tracks whatever dI/dt is applied, so a different rate gives a different EMF.
Why C is wrong: C is wrong because it reaches the right number by a wrong route — reciprocity says M₁₂ equals M₂₁, not its reciprocal. Taking 1/M here would give 2.0 × 10¹ H and an EMF of 4.0 × 10¹ V; the quoted 0.10 V does not follow from the stated reasoning.
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Mutual Inductance: quick recall before you leave
How do you solve a Mutual Inductance question? A worked example
- 1
Given
Mutual inductance of a pair of coils, M = 2.0 × 10⁻² H.
Current in the primary falls steadily from 6.0 A to 2.0 A.
Time taken, Δt = 0.10 s. - 2
Required
The magnitude of the EMF induced in the secondary coil, and the value of M if the secondary instead carried a current changing at the same rate.
- 3
Concept
Mutual inductance links the two coils: a changing current in either one induces an EMF in the other. The magnitude of that EMF is set by M and by the rate at which the current changes — not by the current's own value. M itself is fixed by the coils' turns, areas, separation, orientation and core (NCERT Class 12 Physics Chapter 6, printed page 167).
- 4
Formula
|ε₂| = M |dI₁/dt|, with M in henry, dI/dt in A s⁻¹, ε in volt.
- 5
Substitution
dI₁/dt = (2.0 A − 6.0 A) / 0.10 s = −4.0 A / 0.10 s = −4.0 × 10¹ A s⁻¹
|ε₂| = (2.0 × 10⁻² H) × (4.0 × 10¹ A s⁻¹) - 6
Calculation
|ε₂| = 2.0 × 4.0 × 10⁻²⁺¹ = 8.0 × 10⁻¹ V = 0.80 V
Both given quantities carry two significant figures, so the answer is quoted to two. No exact constants enter this calculation — every number here is a measured quantity, so all of them constrain the significant-figure count.
For the second part: reciprocity gives M₁₂ = M₂₁ = 2.0 × 10⁻² H. Swapping which coil is driven does not change M at all, so no recalculation is needed. - 7
Final answer
|ε₂| = 0.80 V. Mutual inductance with the roles reversed: 2.0 × 10⁻² H — unchanged.
- 8
Common trap
The current falls here, from 6.0 A to 2.0 A. Two slips follow. The first is using the current values themselves — writing M × 6.0 or M × 2.0 — instead of their rate of change; that produces a flux linkage in weber, not an EMF in volt, so a unit check catches it. The second is treating the decrease as though it should give a smaller answer than an increase would: the magnitude of the EMF depends on |dI/dt| alone, so a fall of 4.0 A in 0.10 s induces exactly the same magnitude as a rise of 4.0 A in 0.10 s. Only the direction of the induced current differs.
- 9
Similar NEET-style question
Two coils have M = 5.0 × 10⁻³ H. The current in one is reversed from +3.0 A to −3.0 A uniformly in 0.050 s. Find the magnitude of the EMF induced in the other. *(Watch the total change: the current swings through 6.0 A, not 3.0 A.)*
What to remember before solving Mutual Inductance questions
More in Electromagnetic Induction and Alternating Currents: 4 exam traps and mistakes · 11 formulas · 6 question patterns from its other lessons.
Mutual Inductance questions from past NEET papers
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Sources
Page numbers are the ones printed in the current NCERT textbook (2023 rationalised edition), unless marked pre-2023. The books are free at ncert.nic.in.
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