Inductance of a double circuit line -- struggling with return the path

In summary, the book "In inductance of transmission line" says that the formula for inductance is H = 2 * 10 -7 Loge { [Ds]/[Dm] }. It explains that there are two sides to the inductance equation, the supply side and the return side. It explains that when two wires are in parallel, the current requirements are greater than would be possible with a single wire, so two are used. The book also provides two examples of how to label the two sides of the inductance equation.
  • #1
jaus tail
615
48
So for inductance of transmission line book says formula
H = 2 * 10 -7 Loge { [Ds]/[Dm] }
I'm struggling to understand self and mutual geometric mean distance.
Here is one solved example
upload_2017-12-26_11-3-26.png

and for this they've drawn
upload_2017-12-26_11-3-56.png

And they say that let a a' form one connection and let b b' form other connection.
I'm struggling to understand how are they in parallel.
Current will go from a and return from a' or return from b?
How can b and b' be return path? As per question two upper and two lower conductors are in parallel so it means a and b are in parallel. So current in a and current in b have to be same.

And in three phase there are conductors r - r', y - y', b - b' So does this mean r and r' are in parallel or is it like current goes from r and returns from r' at one instant.
 

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  • #2
This 3-phase double circuit.
upload_2017-12-26_11-9-32.png

I don't understand what does a -a' mean. Are they in parallel or do they carry currents in opposite direction?
And here is double circuit another example.
upload_2017-12-26_11-12-1.png
 

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  • #3
From the text description I get.

In the first image. You are looking at the ends of four wires. They extend into the page. It seems the current requirement is greater than is convenient for a single conductor to carry. To handle the extra current, two conductors are used, wired electrically in parallel. A set of two conductors would be A&B (call that pair the 'supply' side). For the 'return' side the set of two conductors is A'&B'.

That is certainly not the way I would prefer to label them, it makes it too confusing... perhaps that is the 'standard' way of labeling them, but it seems strange.

p.s. If you are graded as 'wrong', you may have to point out the ambiguous description to your instructor. Print this out if needed to show him.
 
  • #4
Thanks. So according to you the top conductors carry current I and bottom conductors carry -I at a given instant of time?
 

Related to Inductance of a double circuit line -- struggling with return the path

1. What is the concept of inductance in a double circuit line?

Inductance is the property of an electrical circuit that causes an opposing voltage to be generated in response to a changing current. In a double circuit line, inductance refers to the magnetic field created by the flow of current in one circuit that affects the flow of current in the other circuit.

2. How is inductance calculated in a double circuit line?

The inductance of a double circuit line can be calculated using the formula L = μ0(μr/2π)ln(D/d), where μ0 is the permeability of free space, μr is the relative permeability of the medium between the circuits, D is the distance between the circuits, and d is the diameter of the circuits.

3. What factors affect the inductance of a double circuit line?

The inductance of a double circuit line is affected by the distance between the circuits, the diameter of the circuits, and the relative permeability of the medium between the circuits. It is also influenced by the frequency of the current, the shape and arrangement of the circuits, and the presence of any nearby conductive materials.

4. How does inductance impact the performance of a double circuit line?

The inductance of a double circuit line can cause voltage drops and signal distortions, especially at high frequencies. It can also lead to crosstalk between the two circuits, where the magnetic field from one circuit interferes with the signal in the other circuit. Therefore, inductance must be carefully considered and controlled in the design of a double circuit line to ensure optimal performance.

5. How can the return path of a double circuit line be optimized to reduce inductance?

The return path of a double circuit line can be optimized by keeping the two circuits as close together as possible, minimizing the distance between them. It is also important to use conductive materials with low resistance for the return path, and to avoid any nearby conductive materials that could interfere with the magnetic field. Additionally, using twisted pair wiring can help reduce the effects of inductance by canceling out the magnetic fields created by the two circuits.

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