Problem 7. Find the equivalent inductance between points a and b. Assume that initial energy stored in the inductors is zero. (a) a b (b) a b 12 H m 24 H 10 H 80 H60 H 21 H 5 H 4 H 44 H Z 1.2 H 15.8 H 15 H 12 H 10 H 6H 314 H 25 H

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**Problem 7.** Find the equivalent inductance between points a and b. Assume that initial energy stored in the inductors is zero.

### Diagram (a)

The circuit in diagram (a) includes the following inductors:

- A series connection of a 12 H inductor between points a and the first node, and a 5 H inductor to the second node.
- A parallel connection beneath this series, consisting of:
  - A 10 H inductor.
  - A loop consisting of an 80 H inductor and a 60 H inductor connected in parallel, leading down to a 15.8 H in series.
- Beyond this configuration, a 6 H inductor is in series leading to node b.
- A 14 H inductor connects in parallel across the rightmost node to node b.
- A 24 H in parallel goes from node a directly to node b.

### Diagram (b)

The circuit in diagram (b) includes the following inductors:

- A series connection of a 21 H inductor between points a and the first node, with a 4 H inductor further in series.
- From the same first node, a separate loop of:
  - A parallel connection containing a 44 H inductor leading to node b.
  - A series pathway of a 1.2 H inductor connecting to a horizontal 12 H in parallel with node b.
  - A 15 H inductor in parallel connecting to the second node.
  - From the second node, a 10 H inductor connects through to a 25 H in parallel, leading directly to node b.

For calculations, you would combine the series and parallel inductors using the appropriate formulas to find the equivalent inductance between points a and b.
Transcribed Image Text:**Problem 7.** Find the equivalent inductance between points a and b. Assume that initial energy stored in the inductors is zero. ### Diagram (a) The circuit in diagram (a) includes the following inductors: - A series connection of a 12 H inductor between points a and the first node, and a 5 H inductor to the second node. - A parallel connection beneath this series, consisting of: - A 10 H inductor. - A loop consisting of an 80 H inductor and a 60 H inductor connected in parallel, leading down to a 15.8 H in series. - Beyond this configuration, a 6 H inductor is in series leading to node b. - A 14 H inductor connects in parallel across the rightmost node to node b. - A 24 H in parallel goes from node a directly to node b. ### Diagram (b) The circuit in diagram (b) includes the following inductors: - A series connection of a 21 H inductor between points a and the first node, with a 4 H inductor further in series. - From the same first node, a separate loop of: - A parallel connection containing a 44 H inductor leading to node b. - A series pathway of a 1.2 H inductor connecting to a horizontal 12 H in parallel with node b. - A 15 H inductor in parallel connecting to the second node. - From the second node, a 10 H inductor connects through to a 25 H in parallel, leading directly to node b. For calculations, you would combine the series and parallel inductors using the appropriate formulas to find the equivalent inductance between points a and b.
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