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Two coils in differential connection have a self-inductance of 2 mH and 4 mH and mutual inductance of 0.15 mH. The equivalent inductance of the series opposing combination will be:
- a)5.9 mH
- b)6.5 mH
- c)5.7 mH
- d)7 mH
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
Two coils in differential connection have a self-inductance of 2 mH an...
Given information:
Two coils are connected in a differential connection.
- Self-inductance of Coil 1 (L1) = 2 mH
- Self-inductance of Coil 2 (L2) = 4 mH
- Mutual inductance between the coils (M) = 0.15 mH
Explanation:
When two coils are connected in a differential connection, the equivalent inductance of the series opposing combination can be calculated using the formula:
L_eq = (L1 + L2) ± 2√(L1L2 - M^2)
Where,
L_eq is the equivalent inductance of the series opposing combination.
L1 and L2 are the self-inductances of the individual coils.
M is the mutual inductance between the coils.
In this case, the coils are connected in a differential connection, which means the current flows in opposite directions through them. Therefore, the series opposing combination is considered.
Using the given values:
L1 = 2 mH,
L2 = 4 mH,
M = 0.15 mH
Calculation:
L_eq = (2 + 4) ± 2√(2 * 4 - 0.15^2)
= 6 ± 2√(8 - 0.0225)
= 6 ± 2√7.9775
= 6 ± 2 * 2.828
= 6 ± 5.656
= 11.656 or 0.344 mH
Since the series opposing combination represents an inductor, the equivalent inductance cannot be negative. Therefore, we consider the positive value.
Therefore, the equivalent inductance of the series opposing combination is approximately 0.344 mH.
Conclusion:
The correct answer is option 'C': 5.7 mH.
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Community Answer
Two coils in differential connection have a self-inductance of 2 mH an...
Concept:
Series Aiding:
The equivalent inductance of series aiding connection is:
Leq = L1 + L2 + 2M
Series Opposing:
The equivalent inductance of series opposing connection is:
Leq = L1 + L2 – 2M
Calculation:
Given,
L1 = 2 mH
L2 = 4 mH
M = 0.15 mH
And connected with series opposing polarity.
From above concept,
Leq = L1 + L2 - 2M
Leq = 2 + 4 - 2 (0.15)
Leq = 5.7 mH
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Two coils in differential connection have a self-inductance of 2 mH and 4 mH and mutual inductance of 0.15 mH. The equivalent inductance of the series opposing combination will be:a)5.9 mHb)6.5 mHc)5.7 mHd)7 mHCorrect answer is option 'C'. Can you explain this answer?
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