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The equivalent inductance of the circuit shown in the figure, between A and B, is ________. (Neglect any mutual inductance between the coils.)

Asked in GSEB Board March 2016 · Coil geometry, cores and combinations

• (1) 1.75 H
• (2) 1.0 H
• (3) 0.75 H
• (4) 0.25 H

Step-by-step solution

Why the other options are wrong

• (1) Adds all three coils as if they were in series: 0.75+0.5+0.5=1.75 H. The two 0.5 H coils are joined to each other at both ends, so they are in parallel.
• (3) Keeps only the 0.75 H coil, as if the parallel pair added nothing. The pair still has an inductance of 0.25 H, and it is in series with the 0.75 H coil.
• (4) Stops at the parallel pair, (0.5×0.5)/(0.5+0.5)=0.25 H, and forgets to add the 0.75 H coil in series with it.

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