Resistivity equation help

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In summary, the author has found the resistivity of silver to be dependent on frequency. They have calculated it to be 10 times higher at a frequency of 10 hertz than it is at a frequency of 1 hertz. The author is unsure how to solve for the phase difference between current and voltage at this frequency.f
  • #1

Homework Statement

Considering silver as a plasma, I have taken the equation of motion for electrons in an electric field and found the resistivity to be

[tex]\sigma_{N}=\frac{Ne^{2}}{m_{e}(i\omega + \tau^{-1})}[/tex]

The first part of the questions asks me to calculate the scattering time [tex]\tau[/tex] at low frequencies. [tex]\sigma_{N}[/tex] and [tex]N[/tex] are provided. I did this by ignoring the imaginary part since the frequencies are small, and rearanging for [tex]\tau[/tex].

The next part, and the final part are what i am having trouble with.


It asks at what frequency would i expect the resistivity to increase by a factor of 10.

Now, surely this should still be considered a low frequency, and if so the imaginary term vanishes in the conductivity equation above. However if this is considerd to now be a significant frequency, how would i solve the equation to obtain [tex]\omega[/tex], i know i would put in [tex]10\sigma_{N}[/tex] but how do i deal with the imaginary part?


I am asked to comment on the phase difference between the current and the voltage along a silver wire at this frequency. Dont know where to start with this one...
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  • #2

First of well, are you sure what you've calculated is resistivity? Because [tex]\sigma[/tex] is the usual symbol for conductivity, whereas resistivity is [tex]\rho = 1/\sigma[/tex]...

Anyway, instead of neglecting the imaginary term in the denominator entirely, you could write the resistivity in polar form, then figure out what frequency makes the magnitude of the resistivity increase by a factor of 10. Writing it in polar form would help you with the last part too ;-)
  • #3

Given the following data on copper, how do i calculate the resistivity?

Relaxation time: 2.50e10-14s
Density: 8940Kgm-3
molar mass: 63.5g

is there an equation for it.

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