Length of wire in a coil of known dimensions?

In summary, to determine the length of wire needed for a coil around a solid cylinder, you can use the formula W = ∏(D+T/2)(L/T) under ideal conditions. However, if multiple layers of wire are needed, a linear combination must be calculated using an integer multiple of the thickness of the wire. It is important to use consistent units for all measurements.
  • #1
carmatic
92
1
suppose that i have a wire with a known thickness ... and i want to wind it around a solid cylinder with known dimensions, and in the end make a coil with the same length as the solid cylinder

how do i relate between the length of wire required and the diameter of this coil?
 
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  • #2
W = Length of Wire
D = Diameter of Pipe
L = Length of Pipe (and wire coil)
T = Thickness of Wire
∏ = pi

W = ∏(D+T/2)(L/T)

This should give you what you need under ideal situations

The length of the wire is equal to the length of one loop of wire around the tube, ∏(D+T/2), times the number of times it is able to go around the tube, (L/T).

Be sure that your units are all the same (use some common measurement like 'cm' for all of these).
 
  • #3
that seems to only apply for a single layer of wire coiled onto the core

in order to account for multiple layers of wire, it looks like it will take calculating a linear combination ( http://en.wikipedia.org/wiki/Linear_combination ) where you have an integer multiple of T?
 
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Related to Length of wire in a coil of known dimensions?

1. How do you calculate the length of wire in a coil of known dimensions?

The length of wire in a coil can be calculated using the formula L = N x (π x D + 2 x h), where L is the length of the wire, N is the number of turns in the coil, D is the diameter of the coil, and h is the height or thickness of the coil. This formula takes into account the number of turns as well as the physical dimensions of the coil.

2. What is the purpose of knowing the length of wire in a coil of known dimensions?

The length of wire in a coil is an important factor in many electrical and engineering applications. It can be used to determine the resistance, inductance, and capacitance of the coil, which are essential for designing and analyzing circuits. It is also a crucial factor in determining the overall size and shape of the coil.

3. Can the length of wire in a coil of known dimensions be measured directly?

No, the length of wire in a coil cannot be measured directly. It can only be calculated using the formula mentioned above. However, if the dimensions of the coil are not known, the length of wire can be measured by unwinding the coil and measuring the length of the wire.

4. How does the length of wire in a coil affect its inductance?

The length of wire in a coil has a direct impact on its inductance. A longer wire means more turns in the coil, which increases the inductance. Similarly, a shorter wire results in fewer turns and lower inductance. This is because the magnetic field generated by the coil is directly proportional to the number of turns.

5. Are there any factors that can affect the accuracy of the calculated length of wire in a coil?

Yes, there are some factors that can affect the accuracy of the calculated length of wire in a coil. These include the thickness and density of the wire, as well as any imperfections in the shape and dimensions of the coil. It is important to use precise measurements and take these factors into account when calculating the length of wire in a coil.

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