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.

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SSC JE Electrical 07 Jun 2024 Shift 3 Official Paper - 1
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  1. 10 mH
  2. 26 mH
  3. 6.5 mH
  4. 13 mH

Answer (Detailed Solution Below)

Option 3 : 6.5 mH
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Detailed Solution

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Concept

The equivalent inductance of the series aiding connection is:

qImage66c586b407031592c8a23458

\(L_{eq}=L_1+L_2+2M\)

 The equivalent inductance of the series opposing connection is:

qImage66c586b407031592c8a23459

\(L_{eq}=L_1+L_2-2M\)

Calculation

Given, \(12=L_1+L_2-2M\) ............ (i)

\(38=L_1+L_2+2M\) ...............(ii)

Subtracting `equation (i) from (ii):

38-12 = 4M

M = 6.5 H

Additional Information 
The equivalent inductance of the parallel aiding connection is:

qImage66c586b307031592c8a23453

\(L_{eq}={L_1L_2-M^2\over L_1+L_2-2M}\)

The equivalent inductance of the parallel opposing connection is:

qImage66c586b407031592c8a23455

\(L_{eq}={L_1L_2-M^2\over L_1+L_2+2M}\)

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