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A solenoid coil has 10 turns per cm along its length and a cross sectional area of 10 cm2. 100 turns of another wire are wound round the first solenoid coaxially. The two coils are electrically insulated from each other. The mutual inductance between the two coils is​
  • a)
    0.13 mH
  • b)
    1.30 mH
  • c)
    0.013 mH
  • d)
    13.0 mH
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
A solenoid coil has 10 turns per cm along its length and a cross secti...
n1=10 turns per cm, =1000 turns per metre
n2l=100, A=10 c=0.1 m2, M=μ0n1(n2l) A
=4πx10-7×1000×100×0.1H=0.13mh
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Most Upvoted Answer
A solenoid coil has 10 turns per cm along its length and a cross secti...
Calculation of Mutual Inductance between Two Coils

Given:
- Number of turns per unit length of the first solenoid coil = 10 turns/cm
- Cross-sectional area of the first solenoid coil = 10 cm²
- Number of turns of the second wire wound around the first solenoid coil = 100 turns
- The two coils are electrically insulated from each other.

To find:
- The mutual inductance between the two coils.

Solution:

Step 1: Calculation of the magnetic field produced by the first solenoid coil

The magnetic field produced by the first solenoid coil can be calculated using the formula:

B = μ₀nI

where B is the magnetic field, n is the number of turns per unit length, I is the current passing through the solenoid, and μ₀ is the permeability of free space.

Here, n = 10 turns/cm = 10,000 turns/m
Cross-sectional area of the solenoid coil = 10 cm² = 0.001 m²
Number of turns in the solenoid coil = length of the solenoid x number of turns per unit length
= 0.1 m x 10,000 turns/m
= 1000 turns

Therefore, the current passing through the solenoid coil can be calculated as:

I = B/(μ₀n) x cross-sectional area of the solenoid coil
= 10^(-4) T/(4π x 10^(-7) Tm/A) x 0.001 m²/(10,000 turns/m)
= 7.96 A

Step 2: Calculation of the magnetic flux produced by the first solenoid coil

The magnetic flux produced by the first solenoid coil can be calculated using the formula:

Φ = B x A

where Φ is the magnetic flux, B is the magnetic field, and A is the cross-sectional area of the solenoid coil.

Here, B = 10^(-4) T and A = 0.001 m²

Therefore, the magnetic flux produced by the first solenoid coil can be calculated as:

Φ = 10^(-4) T x 0.001 m²
= 10^(-7) Wb

Step 3: Calculation of the mutual inductance between the two coils

The mutual inductance between the two coils can be calculated using the formula:

M = NΦ₂/I₁

where M is the mutual inductance, N is the number of turns of the second wire wound around the first solenoid coil, Φ₂ is the magnetic flux produced by the second wire, and I₁ is the current passing through the first solenoid coil.

Here, N = 100 turns, Φ₂ = Φ (since the two coils are wound coaxially), and I₁ = 7.96 A

Therefore, the mutual inductance between the two coils can be calculated as:

M = 100 x 10^(-7) Wb/7.96 A
= 1.2566 x 10^(-5) H
= 0.0126 mH

Therefore, the correct option is (
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Community Answer
A solenoid coil has 10 turns per cm along its length and a cross secti...
M= (u0* N1*N2*A)/L......here, N1= 10, N2= 100, A= 10*10^-4 m^2, L= (1/100) m...... now put the value.... and M= 0. 13 mH.
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Read the following text and answer the following questions on the basis of the same:TOROIDA toroid is a coil of insulated or enamelled wire wound on a donut-shaped form made of powdered iron. A toroid is used as an inductor in electronic circuits, especially at low frequencies where comparatively large inductances are necessary. A toroid has more inductance , for a given number of turns, than a solenoid with a core of the same material and similar size. This makes it possible to construct high-inductance coils of reasonable physical size and mass. Toroidal coils of a given inductance can carry more current than solenoidal coils of similar size, because larger-diameter wires can be used, and the total amount of wire is less, reducing the resistance . In a toroid, all the magnetic flux is contained in the core material. This is because the core has no ends from which flux might leak off. The confinement of the flux prevents external magnetic fields from affecting the behaviour of the toroid, and also prevents the magnetic field in the toroid from affecting other components in a circuit. Standard toroidal transformers typically offer a 95% efficiency, while standard laminated transformers typically offer less than a 90% rating. One of the most important differences between a toroidal transformer and a traditional laminated transformer is the absence of gaps. The leakage flux through the gaps contributes to the stray losses in the form of eddy currents (which is also expelled in the form of heat). A toroidal core doesn’t have an air gap. The core is tightly wound . The result is a stable, predictable toroidal core, free from discontinuities and holes. Audible vibration or hum in transformers is caused by vibration of the windings and core layers from the forces between the coil turns and core laminations. The toroidal transformer’s construction helps quiet this noise. In audio, or signal transmitting applications, unwarranted noise will affect sound quality, so a transformer with low audible vibration is ideal. For this reason, many sound system engineers prefer to use a toroidal transformer instead of a traditional laminated transformer.A toroid has _____ inductance, for a given number of turns, than a solenoid with a core of the same material and similar size.

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A solenoid coil has 10 turns per cm along its length and a cross sectional area of 10 cm2. 100 turns of another wire are wound round the first solenoid coaxially. The two coils are electrically insulated from each other. The mutual inductance between the two coils is​a)0.13 mHb)1.30 mHc)0.013 mHd)13.0 mHCorrect answer is option 'A'. Can you explain this answer?
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A solenoid coil has 10 turns per cm along its length and a cross sectional area of 10 cm2. 100 turns of another wire are wound round the first solenoid coaxially. The two coils are electrically insulated from each other. The mutual inductance between the two coils is​a)0.13 mHb)1.30 mHc)0.013 mHd)13.0 mHCorrect answer is option 'A'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about A solenoid coil has 10 turns per cm along its length and a cross sectional area of 10 cm2. 100 turns of another wire are wound round the first solenoid coaxially. The two coils are electrically insulated from each other. The mutual inductance between the two coils is​a)0.13 mHb)1.30 mHc)0.013 mHd)13.0 mHCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A solenoid coil has 10 turns per cm along its length and a cross sectional area of 10 cm2. 100 turns of another wire are wound round the first solenoid coaxially. The two coils are electrically insulated from each other. The mutual inductance between the two coils is​a)0.13 mHb)1.30 mHc)0.013 mHd)13.0 mHCorrect answer is option 'A'. Can you explain this answer?.
Solutions for A solenoid coil has 10 turns per cm along its length and a cross sectional area of 10 cm2. 100 turns of another wire are wound round the first solenoid coaxially. The two coils are electrically insulated from each other. The mutual inductance between the two coils is​a)0.13 mHb)1.30 mHc)0.013 mHd)13.0 mHCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Class 12. Download more important topics, notes, lectures and mock test series for Class 12 Exam by signing up for free.
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