What is Tau? Baby, don't hurt me, don't hurt me, no more.

[Plant_Boy]

I'm reading a number of papers, journals, reports and what not trying to grasp at what the actual definition of $\tau$.

$\tau = \frac {m_{e}}{\rho e^{2} n}$

Am I correct in thinking:
$m_{e}$ - mass of an electron
$\rho$ - resistivity
$e$ - charge of electron
$n$ - number of electrons per unit mass

In one I read it is Mean Free Time between Collisions of Electrons. Another states it is Relaxation Time. Are these two definitions dependent on whether you use a DC or AC energy source?

I understand from the equation as the mass in kilogram of an electron is divided by an ohm, kilogram meter squared per second${}^3$ per ampere${}^2$, times an ampere second times a number. The values cancel out to leave an ampere second${}^2$ per meter${}^2$.
Or,
$\tau = (A s^2 m^{-2})$

So, one amp takes s${}^2$ seconds to decay into an area?

 

[JorisL]

You did something wrong with the units.
The Ampère drops because the electric unit charge is squared.
Try to find the other mistakes. There are 2 more mistakes.

One note, if $n$ is the number of particles per unit mass, what is its unit?

Final hint, try to write it out in full detail using latex. That way it is easier to spot any mistakes you've made.
I had to read the words you wrote several times in a row be for getting it.

 

[ehild]

I'm reading a number of papers, journals, reports and what not trying to grasp at what the actual definition of $\tau$.

$\tau = \frac {m_{e}}{\rho e^{2} n}$

Am I correct in thinking:
$m_{e}$ - mass of an electron
$\rho$ - resistivity
$e$ - charge of electron
$n$ - number of electrons per unit mass

n is the number of electrons in unit volume. An the dimension of tau must be [time]