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Two coils of self-inductance 2 mH and 8 mH are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils is
- a)10 mH
- b)4 mH
- c)6 mH
- d)16 mH
Correct answer is option 'B'. Can you explain this answer?
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Introduction:
In this problem, we are given two coils with self-inductances of 2 mH and 8 mH. The coils are placed so close together that the effective flux in one coil is completely linked with the other. We need to determine the mutual inductance between these coils.
Explanation:
Mutual Inductance:
Mutual inductance is a measure of how much a change in current in one coil induces a voltage in another coil. It is denoted by the symbol M and is measured in henries (H).
Formula:
The formula for calculating mutual inductance is given by:
M = √(L1 * L2)
Where M is the mutual inductance, L1 is the self-inductance of the first coil, and L2 is the self-inductance of the second coil.
Given:
L1 = 2 mH = 2 x 10^-3 H
L2 = 8 mH = 8 x 10^-3 H
Calculation:
Using the formula for mutual inductance, we can calculate the value as follows:
M = √(2 x 10^-3 * 8 x 10^-3)
= √(16 x 10^-6)
= 4 x 10^-3 H
= 4 mH
Hence, the mutual inductance between the coils is 4 mH, which corresponds to option B.
Conclusion:
The mutual inductance between the two coils is 4 mH. When the effective flux in one coil is completely linked with the other, the mutual inductance is given by the square root of the product of the self-inductances of the two coils.
In this problem, we are given two coils with self-inductances of 2 mH and 8 mH. The coils are placed so close together that the effective flux in one coil is completely linked with the other. We need to determine the mutual inductance between these coils.
Explanation:
Mutual Inductance:
Mutual inductance is a measure of how much a change in current in one coil induces a voltage in another coil. It is denoted by the symbol M and is measured in henries (H).
Formula:
The formula for calculating mutual inductance is given by:
M = √(L1 * L2)
Where M is the mutual inductance, L1 is the self-inductance of the first coil, and L2 is the self-inductance of the second coil.
Given:
L1 = 2 mH = 2 x 10^-3 H
L2 = 8 mH = 8 x 10^-3 H
Calculation:
Using the formula for mutual inductance, we can calculate the value as follows:
M = √(2 x 10^-3 * 8 x 10^-3)
= √(16 x 10^-6)
= 4 x 10^-3 H
= 4 mH
Hence, the mutual inductance between the coils is 4 mH, which corresponds to option B.
Conclusion:
The mutual inductance between the two coils is 4 mH. When the effective flux in one coil is completely linked with the other, the mutual inductance is given by the square root of the product of the self-inductances of the two coils.
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Two coils of self-inductance 2 mH and 8 mH are placed so close together that the effective flux in one coil is completely linked with the other. The mutual inductance between these coils isa)10 mHb)4 mHc)6 mHd)16 mHCorrect answer is option 'B'. Can you explain this answer?
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