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Five pure inductors, each of 3 H, are connected as shown in the figure. The equivalent inductance of this connection between points A and B is _______.

Asked in GSEB Board March 2019 · Coil geometry, cores and combinations

• (1) 2 H
• (2) 1 H
• (3) 3 H
• (4) 9 H

Step-by-step solution

Why the other options are wrong

• (1) No single slip gives 2 H for this network. Sanity check: each route from A to B passes through two 3 H inductors in series (6 H), and two 6 H routes in parallel give 3 H.
• (2) Treats the top arm, the bottom arm and the middle inductor as three single 3 H branches in parallel (3/3 = 1 H). Each arm actually holds two inductors in series, and the middle one does not join A to B at all.
• (4) Adds the three inductors met along the zig-zag route A → C → D → B (3+3+3) as if they were one series chain. The current really splits between two 6 H arms, and the middle inductor carries none.

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