Total inductance (multiloop circuit)

[stufaro]

Homework Statement

Essentially I have a circuit that looks like this:

         A
-------|--------
|      |        |
L1     |        L3
|      |        |
----------L4-----
|      |        |
L2     |        L5
|      |        |
-------|---------
          B

L1 = 2
L2 = 10
L3 = 4
L4 = 6
L5 = 8

How can one find the total inductance between A and B?

The Attempt at a Solution

I know inductance rules are the same as resistance rules--but if this is so, the total inductance would be zero because there is a direct path from A to B. But something tells me this isn't right.

Any help would be appreciated!

Much obliged,

- Steve.

 

[Jhero]

Hello Steve,

Thank you for sharing your circuit and question. You are correct in thinking that the total inductance would be zero if there is a direct path from A to B. However, in this case, there are multiple paths from A to B and the inductors are connected in series and parallel. To find the total inductance, we can use the following formula:

1/Ltotal = 1/L1 + 1/L2 + 1/L3 + 1/L4 + 1/L5

Plugging in the values given, we get:

1/Ltotal = 1/2 + 1/10 + 1/4 + 1/6 + 1/8

Simplifying, we get:

1/Ltotal = 3/5

Therefore, the total inductance between A and B is:

Ltotal = 5/3 = 1.67

I hope this helps. Let me know if you have any further questions.