Help with electrical resistivity equation

In summary, the equation \rho = \frac{m}{ne^2} \frac{1}{\tau} represents the electrical resistivity and is part of a study of electrical resistivity lab. The variables m, n, e, and \tau represent the atomic mass, number density of free charge carriers, elementary charge, and relaxation time, respectively. The effective mass, m, is not the same as the electron mass and is connected to the band structure. For free electrons in silicon, the effective mass is about 0.35 times the electron mass.
  • #1
niqolas619
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Homework Statement



I'm just trying to understand what the variables in this equation represent. This is part of a study of electrical resistivity lab that I am doing. I don't have my Kittel book with me, and the lab manual for some reason doesn't define these variables.

Homework Equations



[tex] \rho = \frac{m}{ne^2} \frac{1}{\tau} [/tex]

The Attempt at a Solution



I could kind of guess at some of them - m = atomic mass, e = elementary charge, [tex]\tau[/tex] = relaxation time...but what about n? And I'm not sure about m, either.
Thanks.
 
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  • #2
n is the number density of the free charge carriers, electrons in the conduction band or holes in the valence band, and m is their effective mass, which is not the same as the electron mass, as it is connected to the band structure. For free electrons in silicon, the effective mass is about 0.35 times the electron mass.

ehild
 

What is the electrical resistivity equation?

The electrical resistivity equation is a mathematical expression that relates the resistance of a material to its dimensions and properties. It is represented as ρ = RA/L, where ρ is the electrical resistivity, R is the resistance, A is the cross-sectional area, and L is the length of the material.

What are the units of electrical resistivity?

The units of electrical resistivity are ohm-meters (Ω·m) in the SI system. In the cgs system, it is expressed as ohm-centimeters (Ω·cm).

How is the electrical resistivity of a material determined?

The electrical resistivity of a material can be determined by measuring its resistance and dimensions, and then using the resistivity equation ρ = RA/L. It can also be found in tables for commonly used materials.

What factors can affect the electrical resistivity of a material?

The electrical resistivity of a material can be affected by its temperature, composition, impurities, and microstructure. In general, materials with high resistivity have a low conductivity, while materials with low resistivity have a high conductivity.

How is the electrical resistivity of a material used in practical applications?

The electrical resistivity of a material is used in many practical applications, such as in the design of electrical circuits, conductors, and insulators. It is also used in the measurement and testing of materials, and in the development of new materials for specific purposes.

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