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Self and mutual inductance: NEET MCQs with answers

50 questions on this topic of Electromagnetic Induction and Alternating Currents (NEET 2027 syllabus). Here are 12; tap one to see its answer and explanation.

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easy

1. Consider the following two statements regarding self-inductance and mutual inductance: Statement I: The mutual inductance between two concentric coplanar circular coils depends on their orientations and relative positions. Statement II: Self-inductance of a coil resists any change in current through itself by inducing a back emf. In the light of the above statements, choose the correct answer:

  1. Both Statement I and Statement II are correct
  2. Statement I is correct but Statement II is incorrect
  3. Statement I is incorrect but Statement II is correct
  4. Both Statement I and Statement II are incorrect
Show answer and explanation

Answer: (A) Both Statement I and Statement II are correct

Mutual inductance is purely a geometric property depending on distance, relative orientation, and medium between coils (Statement I is correct). Self-inductance opposes both growth and decay of current in the coil via Lenz's law, acting as electrical inertia (Statement II is correct).

medium

2. Given below are two statements regarding mutual inductance: Statement I: The mutual inductance of a pair of coils decreases when the separation between them is increased. Statement II: The mutual inductance of a pair of coils is independent of the magnetic permeability of the medium filling the space inside the coils. In the light of the above statements, choose the most appropriate answer from the options given below:

  1. Both Statement I and Statement II are correct
  2. Statement I is correct but Statement II is incorrect
  3. Statement I is incorrect but Statement II is correct
  4. Both Statement I and Statement II are incorrect
Show answer and explanation

Answer: (B) Statement I is correct but Statement II is incorrect

Statement I is correct because increasing the distance between two coils reduces magnetic flux linkage, thereby decreasing their mutual inductance. Statement II is incorrect because mutual inductance directly depends on the relative permeability of the core material (M = μᵣM₀).

hard

3. A solenoid of length 50 cm and radius 2 cm has 500 turns. A small coil of 100 turns and radius 1 cm is placed coaxially near the centre of this solenoid. Taking π² ≈ 10, the mutual inductance of the arrangement is approximately:

  1. 3.95 × 10⁻⁵ H
  2. 1.58 × 10⁻⁴ H
  3. 7.90 × 10⁻⁵ H
  4. 3.95 × 10⁻⁴ H
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Answer: (A) 3.95 × 10⁻⁵ H

The magnetic field inside the long solenoid carrying current I₁ is B₁ = μ₀ (N₁ / l) I₁. The flux linked through the inner small coil of turns N₂ and area A₂ = π r₂² is Φ₂ = N₂ B₁ A₂ = μ₀ N₁ N₂ π r₂² I₁ / l. Thus, M = μ₀ N₁ N₂ π r₂² / l. Substituting the given values: M = (4π × 10⁻⁷ × 500 × 100 × π × (0.01)²) / 0.5 = (4 × π² × 10⁻⁷ × 5 × 10⁴ × 10⁻⁴) / 0.5 = (4 × 10 × 10⁻⁷ × 5) / 0.5 = 200 × 10⁻⁷ / 0.5 = 400 × 10⁻⁷ = 4.0 × 10⁻⁵ H ≈ 3.95 × 10⁻⁵ H.

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4. If a long air-core solenoid is stretched uniformly such that its length is doubled while its total number of turns and cross-sectional area remain unchanged, its self-inductance:

  1. remains unchanged
  2. doubles
  3. quadruples
  4. halves
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Answer: (D) halves

Self-inductance of a solenoid is given by L = μ₀ N² A / l. Since the total number of turns N and cross-sectional area A remain constant while the length l is doubled, the self-inductance becomes L / 2, meaning it is halved.

easy

5. A magnetic flux of 8 × 10⁻³ Wb is linked with a coil of 200 turns when a current of 4 A flows through it. The self-inductance of the coil is:

  1. 0.16 H
  2. 0.04 H
  3. 0.4 H
  4. 0.02 H
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Answer: (C) 0.4 H

The total flux linkage is N Φ = L I. Substituting the values gives L = (N Φ) / I = (200 × 8 × 10⁻³) / 4 = 1.6 / 4 = 0.4 H.

hard

6. A primary circuit consists of a coil with resistance R and self-inductance L connected to a battery of emf E via a key. A secondary coil is placed nearby. At the instant the switch is closed (t = 0⁺), the rate of increase of magnetic flux linked with the secondary coil:

  1. is zero
  2. is at its maximum possible value
  3. is half of its maximum value
  4. increases linearly with time from zero
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Answer: (B) is at its maximum possible value

The current in the primary grows as I(t) = (E/R)(1 - e^(-Rt/L)). The rate of change of current is dI/dt = (E/L)e^(-Rt/L), which achieves its maximum value (E/L) at t = 0⁺. Because secondary flux is proportional to primary current, dΦ_s/dt = M(dI/dt) is also at its maximum possible value at t = 0⁺.

medium

7. Two concentric circular coils, one of small radius r and another of large radius R (r << R), are placed coplanar. If the mutual inductance of the system is M, and the radius R of the outer coil is tripled while r is doubled, the new mutual inductance becomes:

  1. (2/3) M
  2. (4/3) M
  3. (3/4) M
  4. (4/9) M
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Answer: (B) (4/3) M

The mutual inductance between concentric coplanar coils (r << R) is M = μ₀ π r² / (2R), so M ∝ r² / R. If r is replaced by 2r and R by 3R, the new mutual inductance is M' = M × (2)² / 3 = (4/3) M.

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8. A coil of wire having 400 turns and self-inductance 16 mH is rewound uniformly into a new coil of identical length and radius, but with 600 turns. The self-inductance of the new coil will be:

  1. 24 mH
  2. 64 mH
  3. 48 mH
  4. 36 mH
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Answer: (D) 36 mH

For a coil of fixed geometry (length and cross-sectional area remaining constant), self-inductance L is proportional to N². Thus, L₂/L₁ = (N₂/N₁)² = (600/400)² = (3/2)² = 9/4. Therefore, L₂ = 16 mH × (9/4) = 36 mH.

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9. Self-inductance is called the electrical analogue of:

  1. Mass (inertia) in mechanics
  2. Spring constant
  3. Friction
  4. Velocity
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Answer: (A) Mass (inertia) in mechanics

An inductor opposes changes in current (back emf = -L dI/dt), just as mass opposes changes in velocity. Hence inductance plays the role of electrical inertia.

NCERT Class 12

easy

10. Which of the following physical quantities plays the role of 'inertia' in an electrical circuit, opposing any change in current?

  1. Self-inductance
  2. Electric resistance
  3. Capacitance
  4. Magnetic flux
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Answer: (A) Self-inductance

Self-inductance opposes any increase or decrease of current in a circuit through the production of back emf (Lenz's law). Hence, self-inductance is often termed the electrical inertia of the circuit.

hard

11. A small flat circular loop of radius r and N₁ turns is placed at the centre of a large circular loop of radius R (R >> r) and N₂ turns, such that their planes are mutually perpendicular. The mutual inductance between the two loops is:

  1. zero
  2. μ₀ π N₁ N₂ r² / (2R)
  3. μ₀ N₁ N₂ r² / (2π R)
  4. μ₀ π N₁ N₂ r / (2R²)
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Answer: (A) zero

When the planes of two concentric coils are perpendicular, the magnetic field produced at the centre by one coil lies entirely in the plane of the other coil. Thus, the magnetic field vectors are parallel to the surface area of the second coil, yielding a magnetic flux of zero through the coil. Consequently, their mutual inductance is zero.

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12. A small circular loop of wire of radius r is placed co-planar and concentrically at the centre of a much larger circular loop of wire of radius R (R >> r). The mutual inductance between the two loops is proportional to:

  1. r / R
  2. r / R²
  3. r² / R²
  4. r² / R
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Answer: (D) r² / R

Current I in the outer loop produces a magnetic field at the centre B = μ₀ I / (2R). Since r << R, this field is approximately uniform across the inner loop. The flux linked with the inner loop is Φ = B × (π r²) = (μ₀ I / (2R)) × π r². Therefore, M = Φ / I = μ₀ π r² / (2R), which is proportional to r² / R.

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