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## 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.

**NEXT PART**

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?

**FINAL 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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