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The mutual inductance between two coils having self inductances 3 henry and 12 henry and coupling coefficient 0.85 is-
- a)12.75 henry
- b)5.1 henry
- c)0.425 henry
- d)1.7 henry
Correct answer is option 'B'. Can you explain this answer?
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The mutual inductance between two coils having self inductances 3 hen...
M = 5.1H
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The mutual inductance between two coils having self inductances 3 hen...
Understanding Mutual Inductance
Mutual inductance arises when the magnetic field generated by one coil induces an electromotive force (EMF) in another coil. The mutual inductance (M) can be calculated using the formula:
M = k * sqrt(L1 * L2)
Where:
- M = Mutual Inductance
- k = Coupling Coefficient (0 ≤ k ≤ 1)
- L1 = Self Inductance of Coil 1
- L2 = Self Inductance of Coil 2
Given Values
- Self Inductance of Coil 1 (L1) = 3 henry
- Self Inductance of Coil 2 (L2) = 12 henry
- Coupling Coefficient (k) = 0.85
Calculating Mutual Inductance
- First, calculate the product of the self-inductances:
- L1 * L2 = 3 * 12 = 36 henry²
- Next, compute the square root:
- sqrt(L1 * L2) = sqrt(36) = 6 henry
- Now, apply the coupling coefficient:
- M = k * sqrt(L1 * L2) = 0.85 * 6 = 5.1 henry
Conclusion
The mutual inductance between the two coils is calculated to be 5.1 henry. Therefore, the correct answer is option 'B'.
This calculation illustrates how the self-inductance of each coil and their coupling coefficient significantly influence the mutual inductance, which plays a crucial role in applications such as transformers and inductive coupling systems.
Mutual inductance arises when the magnetic field generated by one coil induces an electromotive force (EMF) in another coil. The mutual inductance (M) can be calculated using the formula:
M = k * sqrt(L1 * L2)
Where:
- M = Mutual Inductance
- k = Coupling Coefficient (0 ≤ k ≤ 1)
- L1 = Self Inductance of Coil 1
- L2 = Self Inductance of Coil 2
Given Values
- Self Inductance of Coil 1 (L1) = 3 henry
- Self Inductance of Coil 2 (L2) = 12 henry
- Coupling Coefficient (k) = 0.85
Calculating Mutual Inductance
- First, calculate the product of the self-inductances:
- L1 * L2 = 3 * 12 = 36 henry²
- Next, compute the square root:
- sqrt(L1 * L2) = sqrt(36) = 6 henry
- Now, apply the coupling coefficient:
- M = k * sqrt(L1 * L2) = 0.85 * 6 = 5.1 henry
Conclusion
The mutual inductance between the two coils is calculated to be 5.1 henry. Therefore, the correct answer is option 'B'.
This calculation illustrates how the self-inductance of each coil and their coupling coefficient significantly influence the mutual inductance, which plays a crucial role in applications such as transformers and inductive coupling systems.
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The mutual inductance between two coils having self inductances 3 henry and 12 henry and coupling coefficient 0.85 is-a)12.75 henryb)5.1 henryc)0.425 henryd)1.7 henryCorrect answer is option 'B'. Can you explain this answer?
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The mutual inductance between two coils having self inductances 3 henry and 12 henry and coupling coefficient 0.85 is-a)12.75 henryb)5.1 henryc)0.425 henryd)1.7 henryCorrect answer is option 'B'. Can you explain this answer? for SSC 2024 is part of SSC preparation. The Question and answers have been prepared according to the SSC exam syllabus. Information about The mutual inductance between two coils having self inductances 3 henry and 12 henry and coupling coefficient 0.85 is-a)12.75 henryb)5.1 henryc)0.425 henryd)1.7 henryCorrect answer is option 'B'. Can you explain this answer? covers all topics & solutions for SSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The mutual inductance between two coils having self inductances 3 henry and 12 henry and coupling coefficient 0.85 is-a)12.75 henryb)5.1 henryc)0.425 henryd)1.7 henryCorrect answer is option 'B'. Can you explain this answer?.
Solutions for The mutual inductance between two coils having self inductances 3 henry and 12 henry and coupling coefficient 0.85 is-a)12.75 henryb)5.1 henryc)0.425 henryd)1.7 henryCorrect answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for SSC.
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