# Total inductance (multiloop circuit)

• stufaro
In summary, the total inductance between A and B in the given circuit can be found by using the formula 1/Ltotal = 1/L1 + 1/L2 + 1/L3 + 1/L4 + 1/L5 and plugging in the values given (L1 = 2, L2 = 10, L3 = 4, L4 = 6, L5 = 8). Simplifying the equation gives a total inductance of 1.67. Multiple paths and series and parallel connections must be taken into account when finding the total inductance.
stufaro

## Homework Statement

Essentially I have a circuit that looks like this:

Code:
         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.

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.

## 1. What is total inductance in a multiloop circuit?

Total inductance in a multiloop circuit is the overall measure of the combined inductances of all the individual loops in the circuit. It takes into account the number of loops, the inductance of each loop, and how they are connected.

## 2. How do you calculate total inductance in a multiloop circuit?

To calculate total inductance in a multiloop circuit, you can use the formula Ltotal = L1 + L2 + L3 + ... where L1, L2, L3, etc. represent the inductance of each individual loop in the circuit. Additionally, if the loops are connected in series, you can use the formula Ltotal = L1 + L2 + L3 + ... and if the loops are connected in parallel, you can use the formula Ltotal = 1/(1/L1 + 1/L2 + 1/L3 + ...).

## 3. What factors affect total inductance in a multiloop circuit?

The number of loops, the inductance of each individual loop, and how they are connected (in series or parallel) are the main factors that affect total inductance in a multiloop circuit. Additionally, the material used for the loops and the geometry of the circuit can also have an impact on total inductance.

## 4. Why is total inductance important in a multiloop circuit?

Total inductance is important in a multiloop circuit because it affects the overall behavior of the circuit. Inductance is a measure of how much a circuit resists changes in current, so a higher total inductance can lead to slower changes in current and voltage. It is also important in calculating the total impedance of the circuit, which can help in determining the circuit's resonance frequency and other important characteristics.

## 5. How can you modify total inductance in a multiloop circuit?

Total inductance in a multiloop circuit can be modified by changing the number of loops, the inductance of each individual loop, or how they are connected. For example, adding more loops or increasing the inductance of each loop will result in a higher total inductance. Additionally, changing the configuration of the loops (e.g. from series to parallel) can also modify the total inductance.

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