For the three coupled coils in the figure shown below, calculate the total inductance:

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SSC JE Electrical 14 Nov 2022 Shift 3 Official Paper
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  1. 20 H
  2. 48 H
  3. 70 H
  4. 100 H

Answer (Detailed Solution Below)

Option 1 : 20 H
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Detailed Solution

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Concept

The total inductance for series connection is given by:

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

Leq = 20 H

Additional Information The total inductance for parallel connection is given by:

- 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

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