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Mutual inductance between two closely coupled coils is 2 H. Now, if the number of turns in one coil is reduced by 50 percent and those of the other coil is doubled then, new value of mutual inductance is:
- a)2 H
- b)8 H
- c)1 H
- d)4 H
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
Mutual inductance between two closely coupled coils is 2 H. Now, if th...
Concept:
The inductance of a coil is given by,
The inductance of a coil is given by,
μ0 is magnetic permeability of free space
μr is relative permeability
N is number if turns
A is cross-sectional area
l is length
Calculation:
Given that M = 2 H
If the turns of one coil are decreased to half and the other is doubled.
Now the new value of the mutual inductance would be 2 H.
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Mutual inductance between two closely coupled coils is 2 H. Now, if th...
Given Data:
- Mutual inductance between two closely coupled coils = 2 H
Calculations:
- Let the original number of turns in the first coil be N1 and the original number of turns in the second coil be N2
- Given that mutual inductance M = 2 H
Formula:
- The mutual inductance between two coils is given by the formula:
M = k * sqrt(L1 * L2)
Calculation of original inductances:
- From the given data, M = 2 H
- Let the original inductance of the first coil be L1 and the original inductance of the second coil be L2
- Therefore, 2 = k * sqrt(L1 * L2) ----(1)
Effect of changes in number of turns:
- When the number of turns in the first coil is reduced by 50% and the number of turns in the second coil is doubled, the new inductance values will be:
- New number of turns in the first coil = 0.5N1
- New number of turns in the second coil = 2N2
Calculation of new inductances:
- New inductance of the first coil = L1' = 0.5N1 * L1
- New inductance of the second coil = L2' = 2N2 * L2
Substitute new inductances into formula:
- Substitute L1' and L2' into equation (1) to find the new mutual inductance value:
2 = k * sqrt(0.5N1 * L1 * 2N2 * L2)
2 = k * sqrt(N1 * N2 * L1 * L2)
- Since the mutual inductance M remains the same, the new mutual inductance is equal to the original mutual inductance:
2 = 2
- Therefore, the new value of mutual inductance is 2 H, which is option 'A'.
- Mutual inductance between two closely coupled coils = 2 H
Calculations:
- Let the original number of turns in the first coil be N1 and the original number of turns in the second coil be N2
- Given that mutual inductance M = 2 H
Formula:
- The mutual inductance between two coils is given by the formula:
M = k * sqrt(L1 * L2)
Calculation of original inductances:
- From the given data, M = 2 H
- Let the original inductance of the first coil be L1 and the original inductance of the second coil be L2
- Therefore, 2 = k * sqrt(L1 * L2) ----(1)
Effect of changes in number of turns:
- When the number of turns in the first coil is reduced by 50% and the number of turns in the second coil is doubled, the new inductance values will be:
- New number of turns in the first coil = 0.5N1
- New number of turns in the second coil = 2N2
Calculation of new inductances:
- New inductance of the first coil = L1' = 0.5N1 * L1
- New inductance of the second coil = L2' = 2N2 * L2
Substitute new inductances into formula:
- Substitute L1' and L2' into equation (1) to find the new mutual inductance value:
2 = k * sqrt(0.5N1 * L1 * 2N2 * L2)
2 = k * sqrt(N1 * N2 * L1 * L2)
- Since the mutual inductance M remains the same, the new mutual inductance is equal to the original mutual inductance:
2 = 2
- Therefore, the new value of mutual inductance is 2 H, which is option 'A'.
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Solutions for Mutual inductance between two closely coupled coils is 2 H. Now, if the number of turns in one coil is reduced by 50 percent and those of the other coil is doubled then, new value of mutual inductance is:a)2 Hb)8 Hc)1 Hd)4 HCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
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