Geometric Mean Radius of Hollow Conductor

In summary, the Geometric Mean Radius of Hollow Conductor is a mathematical term used in electrical engineering to determine the effective size of a hollow conductor. It is calculated by taking the square root of the product of the inner and outer radii, and is significant in determining resistance, inductance, and capacitance in circuits. Unlike the arithmetic mean, it considers the logarithmic relationship between the radii and cannot be negative.
  • #1
sandy.bridge
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Homework Statement


[itex]GMR_{hollow cylinder}=Re^{-Kμ}[/itex] where [itex]K=\frac{AR^4-R^2r^2+Br^4+r^4ln(R/r)}{(R^2-r^2)^2}[/itex], where R is the outer radius and r is the inner radius, and mu is the relative permeability. We are to determine the numerical values of A and B.

I am stumped on how to begin attempting this question. Any hints or help would be greatly appreciated.
 
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  • #2
Figured it out thanks.
 
  • #3
Hey, we have the same question and were wondering how you did this?
Thanks
 

FAQ: Geometric Mean Radius of Hollow Conductor

1. What is the Geometric Mean Radius of Hollow Conductor?

The Geometric Mean Radius of Hollow Conductor is a mathematical term used to describe the average distance from the center of a hollow conductor to its inner and outer surfaces. It is a measurement used in electrical engineering to determine the effective size of a hollow conductor.

2. How is the Geometric Mean Radius of Hollow Conductor calculated?

The Geometric Mean Radius of Hollow Conductor can be calculated by taking the square root of the product of the inner radius and outer radius of the conductor. The formula is: sqrt(ri x ro) where ri is the inner radius and ro is the outer radius.

3. What is the significance of the Geometric Mean Radius of Hollow Conductor?

The Geometric Mean Radius of Hollow Conductor is an important measurement in electrical engineering as it helps determine the effective size of a hollow conductor. It is used in calculations for determining the resistance, inductance, and capacitance of a conductor, which are important factors in designing electrical circuits.

4. How does the Geometric Mean Radius of Hollow Conductor differ from the arithmetic mean?

The Geometric Mean Radius of Hollow Conductor is different from the arithmetic mean as it takes into account the logarithmic relationship between the inner and outer radii of a conductor. The arithmetic mean simply takes the average of the two radii, while the geometric mean considers their relative sizes.

5. Can the Geometric Mean Radius of Hollow Conductor be negative?

No, the Geometric Mean Radius of Hollow Conductor cannot be negative. It is a positive value that represents the average distance from the center of a conductor to its inner and outer surfaces. A negative value would not make physical sense in this context.

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