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The total inductance of two coupled coils in the series opposing and series aiding connections are 12 mH and 38 mH, respectively. Find the mutual inductance between the coils.
26 mH
6.5 mH
13 mH
10 mH
6.5 mH
The total inductance of two coupled coils depends on the orientation of the magnetic flux. When coils are connected in series aiding, the mutual inductance adds to the self-inductances, whereas in series opposing, it subtracts from them.
The total inductance of two coupled coils depends on the orientation of the magnetic flux. When coils are connected in series aiding, the mutual inductance adds to the self-inductances, whereas in series opposing, it subtracts from them.
LaidingтАЛ=L1тАЛ+L2тАЛ+2M
LopposingтАЛ=L1тАЛ+L2тАЛтИТ2M
M=4LaidingтАЛтИТLopposingтАЛтАЛ
When two coils with inductances L1тАЛ and L2тАЛ are magnetically coupled with mutual inductance M, the series aiding connection results in LaidingтАЛ=L1тАЛ+L2тАЛ+2M. Conversely, the series opposing connection results in LopposingтАЛ=L1тАЛ+L2тАЛтИТ2M. By subtracting the opposing equation from the aiding equation, we isolate M.
Series aiding total inductance is 38┬аmH.
Series opposing total inductance is 12┬аmH.
Mutual inductance M calculation: M=438тИТ12тАЛ=426тАЛ=6.5┬аmH.
Provides a simple method to experimentally determine mutual inductance.
Essential for transformer design and modeling.
Requires precise measurement of total series inductance.
Assumes constant coupling coefficient and linear magnetic behavior.
Inductive coupling analysis in transformers.
Circuit simulation models for coupled inductors.
The calculation follows M=(LaidingтАЛтИТLopposingтАЛ)/4.
Option A (26 mH) is the difference LaidingтАЛтИТLopposingтАЛ which is 4M.
Option C (13 mH) is 2M.
Option D (10 mH) is a distractor value.
B is correct тАФ The mutual inductance is calculated as 438┬аmHтИТ12┬аmHтАЛ=6.5┬аmH.
Always verify if the question asks for M or 2M; competitive exams often provide distractors based on the 2M term found in the standard series inductance formula.
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