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Two coupled coils connected in series have an equivalent inductance of 16 mH or 8 mH depending on its inter connection. Then the mutual inductance M between the coil is
- a)12 mH
- b)8 √2mH
- c)4 mH
- d)2mH
Correct answer is option 'D'. Can you explain this answer?
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Given: Two coupled coils connected in series have an equivalent inductance of 16 mH or 8 mH depending on its interconnection.
To find: Mutual inductance M between the coils.
Formula: The equivalent inductance of two coils connected in series is given by L = L1 + L2 + 2M, where L1 and L2 are the self-inductances of the coils and M is the mutual inductance between them.
Solution:
Let L1 and L2 be the self-inductances of the coils.
When the coils are connected in series aiding, the equivalent inductance is given by
L = L1 + L2 + 2M = 16 mH
When the coils are connected in series opposing, the equivalent inductance is given by
L = L1 + L2 - 2M = 8 mH
Subtracting the two equations, we get
4M = 8 mH - 16 mH = -8 mH
M = -2 mH (Note that the negative sign indicates that the mutual inductance is opposing the self-inductances of the coils)
Therefore, the mutual inductance between the coils is 2 mH.
Answer: Option (D) 2 mH.
To find: Mutual inductance M between the coils.
Formula: The equivalent inductance of two coils connected in series is given by L = L1 + L2 + 2M, where L1 and L2 are the self-inductances of the coils and M is the mutual inductance between them.
Solution:
Let L1 and L2 be the self-inductances of the coils.
When the coils are connected in series aiding, the equivalent inductance is given by
L = L1 + L2 + 2M = 16 mH
When the coils are connected in series opposing, the equivalent inductance is given by
L = L1 + L2 - 2M = 8 mH
Subtracting the two equations, we get
4M = 8 mH - 16 mH = -8 mH
M = -2 mH (Note that the negative sign indicates that the mutual inductance is opposing the self-inductances of the coils)
Therefore, the mutual inductance between the coils is 2 mH.
Answer: Option (D) 2 mH.
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