Question
Download Solution PDFFor the three coupled coils in the figure shown below, calculate the total inductance:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept
The total inductance for series connection is given by:
\(L_{eq}=L_1+L_2+L_3+2(\pm M_1 \space \pm M_2\space \pm M_3)\)
where, L = Self inductance
M = Mutual inductance
+ Sign is used in mutual inductance when current either enters or leaves from the dot in both the coils
- Sign is used in mutual inductance when current enters from a dot in one coil and leaves without a dot from another coil
Calculation
Given, L1 = 12 H, L2 = 16 H and L3 = 20 H
M1 = - 8 H, M2 = -10 and M3 = 4 H
\(L_{eq}=12+16+20+2(-8 \space-10\space + 4)\)
Leq = 20 H
Additional Information The total inductance for parallel connection is given by:
\(L_{eq}={L_1L_2\space -\space M^2\over L_1\space + \space L_2 \space \mp \space 2M}\)
- Sign is used in mutual inductance when current either enters or leaves from the dot in both the coils
+ Sign is used in mutual inductance when current enters from a dot in one coil and leaves without a dot from another coil
Last updated on May 29, 2025
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