If number of turns in primary and secondary coils – Class 12 Physics | ConceptFirst

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Q. If number of turns in primary and secondary coils is increased to two times each, the mutual inductance

(1) becomes 4 times

(2) becomes 2 times

(3) becomes 1/4 time

(4) remains unchanged

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Concept understanding — Mutual Inductance

Mutual Inductance: From Intuition to Definition

Imagine you have two separate coils of wire placed close to each other, but not electrically connected. You connect the first coil to a battery through a switch. The moment you close the switch, current begins to flow in coil 1. That current doesn't just stay in coil 1 — it creates a magnetic field around it. Some of that magnetic field spreads out and passes through the loops of coil 2.

Now, here is the key physical fact: a changing magnetic field through a coil induces an emf (electromotive force) in that coil. So when you close the switch, the current in coil 1 rises from zero to some steady value. During that brief rise, the magnetic field through coil 2 is also changing — from zero to some steady value. That changing field induces a temporary emf in coil 2. If coil 2 is part of a closed circuit, that induced emf will drive a current for as long as the field is changing.

The same thing happens in reverse: if you change the current in coil 2, it induces an emf in coil 1. This mutual influence — the ability of a changing current in one circuit to induce an emf in a nearby circuit — is called mutual inductance.

Note

Mutual inductance is a geometric property. It depends only on the shapes, sizes, number of turns, and relative positions of the two coils, and on the magnetic properties of the medium between them. It does not depend on how much current is actually flowing.

The Precise Definition

Let coil 1 carry a current $I_1$ . This current produces a magnetic flux $\Phi_{21}$ through each turn of coil 2. The total flux linkage through coil 2 is $N_2 \Phi_{21}$ , where $N_2$ is the number of turns in coil 2.

For a given geometry, the flux through coil 2 is directly proportional to the current in coil 1:

N_2 \Phi_{21} = M_{21} I_1

The constant of proportionality $M_{21}$ is called the mutual inductance of the pair of coils. The subscript $21$ means "flux in coil 2 due to current in coil 1."

By Faraday's law, the induced emf in coil 2 is the negative rate of change of flux linkage:

\mathcal{E}_2 = -\frac{d}{dt}(N_2 \Phi_{21}) = -M_{21} \frac{dI_1}{dt}

The negative sign indicates Lenz's law — the induced emf opposes the change that produces it.

\mathcal{E}_2 = -M \frac{dI_1}{dt}

If you reverse the roles — change current in coil 2 and measure the induced emf in coil 1 — you get:

\mathcal{E}_1 = -M_{12} \frac{dI_2}{dt}

A remarkable fact (which follows from energy conservation) is that the two mutual inductances are equal:

M_{12} = M_{21} = M

So we simply call it $M$ , the mutual inductance of the pair.

Units and Typical Values

The SI unit of mutual inductance is the henry (H). From the defining equation:

1\ \text{H} = 1\ \frac{\text{V} \cdot \text{s}}{\text{A}}

One henry means that a current changing at the rate of 1 ampere per second induces an emf of 1 volt in the other coil. In practice, typical values are much smaller — millihenries (mH) for transformers and microhenries ( $\mu$ H) for circuits on a circuit board.

Watch out

Mutual inductance is not a property of either coil alone. It is a property of the pair of coils and their relative arrangement. If you move the coils farther apart, $M$ decreases. If you align them differently, $M$ changes. If you remove one coil, the concept of mutual inductance becomes meaningless.

A Simple Example: Two Coaxial Solenoids …

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Mutual inductance is proportional to the product of the number of turns in the two coils.

…

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Same / Similar Concept — real previous-year questions on the same or a closely similar concept, not this exact question.

CBSE 2026Set ANNUAL1 markMCQ
$Q. Two coils A (primary) and B (secondary) have mutual inductance 2 x 10^-2 henry. If the current in the primary is i = 5 sin(10πt), then the maximum value of e.m.f. induced in coil B is$
(a) π volt
(b) π/2 volt
(c) π/3 volt
(d) π/4 volt
›Reveal solutionSolution

Maximum induced emf = $M\times(di/dt)_{max} = 2\times10^{-2}\times50\pi = \pi$ V.

The emf induced in the secondary coil due to mutual inductance $M$ is

$e = -M\dfrac{di}{dt}$

Given $i = 5\sin(10\pi t)$ , so

$\dfrac{di}{dt} = 5\times10\pi\cos(10\pi t) = 50\pi\cos(10\pi t)$

…

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CBSE 2025Set ANNUAL1 markMCQ
$Q. The unit of mutual inductance is$
(a) weber
(b) ohm
(c) henry
(d) gauss
›Reveal solutionSolution

Mutual inductance M is defined through EMF2 = -M (dI1/dt), and working out the units of this relation gives the henry.

From emf = -M (dI/dt), we get M = emf / (dI/dt), with units volt / (ampere/second) = volt-second/ampere, which is defined as the henry (H).

…

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CBSE 2025Set ANNUAL1 mark
$Q. Name two useful devices based on the phenomenon of mutual induction.$
›Reveal solutionSolution
Mutual induction — a changing current in one coil inducing an emf in a neighbouring coil — is the working principle behind the transformer and the induction coil.

Mutual induction occurs when a changing current in one coil (primary) sets up a changing magnetic flux that links a nearby second coil (secondary), inducing an emf in it.

Two devices that use this principle:

Transformer — used to step up or step down AC voltage, by having primary and secondary windings around a common iron core. …
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CBSE 2024Set A11 mark
$Q.The mutual inductance of a solenoid can be decreased by ———————— the number of turns per unit length either in inner or outer solenoid. Fill in the blank choosing the appropriate answer from the bracket: (decreasing, interference, helium, greater, diffraction, increasing)$
›Reveal solutionSolution

decreasing (reducing the number of turns per unit length decreases the mutual inductance). …

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CBSE 2024Set ANNUAL1 markMCQ
$Q. The device is based on the principle of mutual induction is -$
(a) ac generator
(b) galvanometer
(c) voltmeter
(d) transformer
›Reveal solutionSolution

A transformer transfers electrical energy between two coils purely through the changing magnetic flux linking them — this is mutual induction.

Mutual induction is the phenomenon where a changing current in one coil (primary) induces an emf in a neighbouring coil (secondary) due to the changing magnetic flux linking it, with no direct electrical connection between the coils.

…

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CBSE 2024Set ANNUAL1 mark
$Q. Define one henry.$
›Reveal solutionSolution

$1\,\text{H}$ : $1\,$ A/s rate of current change induces $1\,$ V of self-induced EMF.

The self-inductance $L$ of a coil is defined by $\varepsilon = -L\dfrac{dI}{dt}$ , relating the self-induced EMF to the rate of change of current through the coil. One henry (1 H) is the self-inductance of a coil in which an EMF of 1 volt is induced when the current through it c …

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CBSE 2023Set ANNUAL1 markMCQ
$Q. If number of turns in primary and secondary coils is increased to two times each, the mutual inductance$
(1) becomes 4 times
(2) becomes 2 times
(3) becomes 1/4 time
(4) remains unchanged
›Reveal solutionSolution

Mutual inductance is proportional to the product of the number of turns in the two coils.

…

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CBSE 2023Set ANNUAL1 mark
$Q. What is the phenomenon of generation of induced electromotive force in another coil due to change in current in one coil called?$
›Reveal solutionSolution

This coupling between two coils, where a changing current in one produces an induced emf in the other via the shared changing flux, is called mutual induction.

When the current in one coil (primary) changes, the magnetic flux linked with a nearby second coil (secondary) also changes, inducing an emf in the second coil by Faraday's law — even though there is no direct electrical connection between them. …

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CBSE 2023Set ANNUAL1 mark
$Q. True/False : The SI unit of mutual inductance is Henry.$
›Reveal solutionSolution

True — mutual inductance is measured in henry (H).

Mutual inductance M relates the emf induced in one coil to the rate of change of current in a neighbouring coil: emf = -M (dI/dt). Its SI unit is the henry, where 1 H = 1 volt-second per ampere (1 V s/A). Self-inductance is measured in the same unit. This is …

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CBSE 2020Set ANNUAL1 markMCQ
$Q. Coefficient of mutual inductance of two coils is 1 H. Current in one of the coils is increased from 4 to 5 A in 1 ms. What average emf will be induced in the other coil?$
(a) 1000 V
(b) 2000 V
(c) 100 V
(d) 200 V
›Reveal solutionSolution

Mutually induced emf is $\varepsilon = M\,\dfrac{dI}{dt}$ ; with $M=1\text{ H}$ and the current changing by $1\text{ A}$ in $1\text{ ms}$ , $\varepsilon = 1000\text{ V}$ .

When the current in one coil changes, it induces an emf in a nearby (mutually coupled) coil, given by

$\varepsilon = M\,\frac{dI}{dt}$

where $M$ is the coefficient of mutual inductance.

…

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